V.S.B. ENGINEERING COLLEGE, KARUR

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

ACADEMIC YEAR 2019-20 (EVEN SEMESTER)

2 MARK AND 16 MARK QUESTION BANK

CLASS II YEAR/ IV SEMESTER

S.NO SUBJECT CODE SUBJECT NAME PAGE NO

1 MA8491 Numerical Methods 1

2 EE8451 Linear Integrated Circuits 40

3 EE8403 Measurements and Instrumentation 56

4 IC8451 Control Systems 74

5 EE8401 Electrical Machines-II 102

6 EE8402 Transmission and Distribution 129

Subject name:Numerical Methods

Faculty name:Dr.M.Sathishkumar

V.S.B.ENGINEERING COLLEGE, KARUR

UNIT-I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS

PART-A

1. What do you mean by the order of convergence of an iterative method for finding the root of the equation f(x)=0? (AU –N/D 2013)

The convergence is linear of order 1 2. Define algebraic and transcendental equation.

The equation f(x) = 0 is called Algebraic equation of degree n. if f(x) is purely a polynomial in x If f(x) contains some other functions such as trigonometric, logarithmic, exponential etc, Then f(x)=0 is called a transcendental equation.

3. State the fixed point iteration theorem

Let f(x) = 0 be the given equation whose exact root is . The equation f(x)=0 be rewritten

as x = x. Let I be the interval containing the root x = . If ' x 1 for all x in I, then

the

sequence of approximations x1 , x2 , ........ xn will converge to , if the initial starting value

x0 is

chosen in I. 4. Write down the order of convergence and the condition for convergence of fixed

point iteration method. ( AU –A/M 2018,N/D 2018)

The order of convergence in fixed point iteration method is 1 and the condition is

g'x <1 for all x in I.

5. State the Newton Raphson formula and the criteria for convergence. (AU –

A/M2017) x x

f xn , n 0,1,2.... n1 n

f 'x n

Criteria for convergence is f (x) f '' (x) f ' (x) 2

6. What is the condition for convergence and the order of convergence of Newton Raphson Method? (AU –A/M2018)-3 The order of convergence in Newton’s Raphson method is 2.

Newton – Raphson method converges if f (x) f '' (x) f ' (x) 2

in the interval considered.

7. Find an iterative formula to find the reciprocal of a given non zero number N

(OR) Find an iterative formula to find the number 1

N . (AU –M/J 2013, N/D 2018)

Let x=1/N

f(x)= 1 N ; f’ f ' (x)

1

x x 2

Using these in Newton’s formula we have xn1 xn (2 Nxn )

N

8. Derive a formula to find the value of where N is a real number, by

15

Newton’s method. (AU – N/D2017)-4

The square root of a positive number N is the root of the equation.

x 2 N 0

i.e f x x 2 N

f ' x 2x

By Newton’s algorithm

x 2 N 2x

2 x

2 N

x x k k k

k 1 k 2x

2xk

xk

x 2 N

1 k

2x k

Taking x2 = N and using Newton Raphson formula x 1 x

2 N

n

n 1 2 x

9. Evaluate using Newton – Raphson formula. (AU –

M/J 2014) 1 x

2 N

Newton Raphson formula x n

n 1 2 x

1 x2 15

Put N=15 x n1 n

Taking x0 = 4 , We get x1 = 3.875, x2 = 3.873, x3 = 3.873.

3.873

2 xn

10. Name the two methods to solve a system of linear equations. (AU - M/J 2016)

1. Gauss Elimination method 2.Gauss-Jordan method 11. Write the procedure involved in Gauss-Jordan elimination method. (AU –

N/D 2015) The augmented matrix [A,B] of the system AX=B is reduced in to [D,K],(D is a diagonal

matrix) or (I,K) where I is the identity matrix, from which the solution is obtained directly.

12. Solvex+y=2, 2x+3y=5 by Gauss elimination method. (AU –A/M

2011) 1 1 2 1 1 2

(A,B) = 2 3 5 ~ 0 1 1 R2=2R2-2R1 ; x=1 ,y=1

13. Solve the following system of equations by Gauss – Jordan method. 5x + 4y = 15, 3x + 7 y = 12.

(AU – A/M2014)

5 4 x 153 7 y 12

The given system is equivalent to AX = B

15

n

K

n

23 15

2 3

R

5

[A, B] = 3

4 `15

7 12

Now , we will make the matrix A is a diagonal matrix.

5 4 `15

= 0 R 2 5R2 – 3R1

115 0 `285 0 23 15

R 23R – 3R

=

115x = 285

x 57

2.4783

23

23y 15

y 15

0.6522

23

1 1 2

14. Using Gauss Jordan method find the inverse of the matrix 1 2

(AU-

M/J-2012) 1 22 3

1 2 1 0

A, I 2

3 0 1

1 2 1 0

R 2R

0 1 2 1 0 3

2

1 2

R R

2 1

2R , R R

0 1 2 1 1 1 2 2 2

A1 3

2

1

15. What is meant by diagonally dominant matrix? The absolute value of the largest coefficient is greater than the sum of the absolute

values of the

remaining coefficients.

16. Compare Gauss Jacobi and Gauss Seidal method. (AU –

N/D2010)

S.No. Gauss-Jacobi Gauss-seidal

1. Convergence rate is slow The rate of convergence of Gauss-seidal method is roughly twice that of Gauss-jacobi

2. Indirect method Indirect method

A

2

3. Condition for convergence is the coefficient matrix is diagonally dominant

Condition for convergence is the coefficient matrix is diagonally dominant

17. State the condition under which Gauss-Seidel method is convergent. (AU- A/M2018)

The coefficient matrix of the system must be diagonally dominant. 18. Which of the iterative methods for solving linear system of equations

converge faster? Why? (AU- N/D2016)-2

Gauss seidal method of iteration converge faster since the recent values of the unknowns

used immediately for computing iteration values. 19 .What are the advantages of iterative methods over direct methods for

solving simultaneous equations. (AU – N/D 2012)

S.No. Direct method Iterative method 1. We get exact solution Approximate solution.

2. Simple, take less time Time consuming laborious.

3. This method determines all the roots at the same time.

This method determine only one root at a time.

20. Why Gauss-Seidel method is better than Gauss-Jordan method? (AU – A/M 2018)

Gauss-Seidel method is an iterative method and the convergence will be more rapid than

Gauss-Jordan method which is a direct method. 21. State the rate of convergence of Gauss Jacobi method and Gauss Seidel method.

(AU- N/D2017)

The co-efficient matrix should be diagonally dominant, The rate of convergence of Gauss-Seidel

method is roughly twice as fast as that of Gauss-Jacobi method.

22. Define eigen value of a matrix.

The roots of the characteristic equation , A I

matrix.

0 are called eigen value of the

23. What is the use of power method? (AU – M/J2013)

The use of power method is to find the largest eigen value in magnitude and the corresponding eigen vector of A.

1 24. Find the dominant eigen value of A =

3

2 by power method? (AU-

4

N/D-2009) AX

1 21

3

0.43

1 3 41 7

7 1 7 X 2

1

Let X 1 AX 20.43

2.43 5.29

0.46 5.29 X

1 1 2 3 4 1 5.29 1 3

1

AX

20.46 2.46 0.463 3 4 1

5.38 5.389 1 5.38X 4

1

The dominant eigenvalue = 5.38 and the corresponding eigenvector = 0.46

1 2 3

25. Find the dominant eigen value A= A

5

by power method upto 1 decimal 4

place 0 1

accuracy. Start with X (AU- 1

A/M-2017)

Let X 0 1

1

AX 2

31

5

0.6

9X ; AX

2 30.6

4.2

0.6

7 X

0 5 41 9 9 1 2 2 5 4 1 7

7 1 3

The dominant eigenvalue = 7 and the corresponding eigenvector = 0.6

PART – B 1. (a)Find the smallest positive root of x3-2x-5= 0 by the fixed point iteration method,

correct to

three decimal places. (AU –

A/M2018) (8)

(b) Find a root of x log10 x 12.34 0 using Newton Raphson method correct to three

decimal

places. (AU –

N/D2017) (8)

2. (a)Find by Newton’s method, the root of ex = 4x near x= 2 correct to four decimal

places.

(AU –

N/D2015) (8)

(b) Find the positive root of (i) x=cosx (ii) cosx=3x-1 using Newton’s method.

(AU-A/M2017,N/D

2018)-4 (8)

3. (a)Find the approximate root of x ex=3 by Newton’s method correct to three

decimal places. (AU –

M/J2016)(8)

(b) Using Newton-Raphson method, find the real root of f(x)=3x+sinx-ex=0 by

choosing the

initial approximation x0=0.5 (AU –A/M

2015)(8)

4. (a) Solve by Gauss Elimination method x+2y-5z=-9,3 x-y+2z=5, 2x+y-z=3 (AU-

A/M2017)(8)

(b) Solve by Gauss Elimination method 2x+y+z=10, 3x+2y+3z=18, x+4y+9z=16

(AU-

N/D2015(8)

5. (a) Solve by Gauss – Jordan method, the equations 2x + y + 4z = 12, 8x -3y +2z = 20,

4x +11y – z =33. (AU -

2010) (8)

4

3

(b) Solve by Gauss – Jordan method, 10x + y + z = 12, 2x +10y +z = 13, x +y +5z =7.

(AU –M/J

2016)(8)

6. (a)Using Gauss-Jordon method, solve 2x-y+3z=8; -x+2y+z=4; 3x+y-4z=0 (AU –

N/D2016)(8)

(b) Solve the system of equations by Gauss-Jordon method,

5x1-x2=9;-x1+5x2-x3=4; -x2+5x3=-6 (AU –

A/M2014)(8)

7. (a) Solve the following system of equations using Gauss – Jacobi method:

8x-3y+2z=20; 4x+11y-z=33; 6x+3y+12z=35 (AU –M/J

2012) (8)

(b) Solve the following system of equations by Gauss-Jacobi method:

27x+6y-z=85; x+y+54z=110; 6x+15y+2z=72 (AU –M/J

2013)- 4 (8)

8. (a) Solve the following system of equations using Gauss – Seidel method:

20x+y-2z=17,3x+20y-z=-18,2x-3y+20z=25 (AU –A/M

2018)(8)

(b) Solve the following system of equations, starting with the initial vector (0,0,0)T

using

Gauss-Seidal method. 6x1-2x2+x3=11; -2x1+7x2+2x3=5; x1+2x2-5x3=-1 (AU –

A/M2015)(8)

9. (a) Apply Gauss – Seidal to solve the equations 20x+y-2z=17;3 x+20y-z=-18; 2x-

3y+20z=25.

(AU –A/M

2018)-8 (8)

(b) Solve by Gauss – Seidel method x-2y+5z=12 ,5x+2y-z=6,2x+6y-3z=5 (AU –

A/M2017) (8)

10.(a) Using Gauss-Seidal method, solve the following system of linear equations:

28x+4y-z=32;x+3y+10z=24;2x+17y+4z=35. (AU –

N/D2017&18)(8)

(b) Using Gauss Seidal method, solve the following system of linear equations:

4x+2y+z=14;x+5y-z=10;x+y+8z=20 ( AU –

A/M2017)(8)

11.(a) Solve the system of equations 20x+y-2z=17; 3x+20y-z=-18; 2x-3y+20z=25

by Gauss – Seidel method. (AU –

A/M2018)-2 (8) 2

(b) Find the inverse of the matrix, using elimination process, A=

2

2 6

6 6

(AU

M/J2014)(8)

1 2 1

5 8

12. (a) Find the inverse of A=

4 1 0

by Gauss-Jordan method. (AU A/M-

2017)(8)

2 1

(b) Apply Gauss Jordan method , find the solution of the following system: 2x-y+3z=8 ,

0 3

4 3 1

0

6 3

-x+2y+z=4,3x+y-4z=0 (AU –M/J 2016) (8)

4 1 2 x

13. Consider the system of equations of the form AX=B,where A= 2 3 1 X= y1 2 2 z

and

7

B= 3 . Find by using Gauss- Jordan method, i) A-1 ii) the numerical solution of the

7

given

system. (AU –

A/M2018) (16)

14.(a) Find the largest eigen value and the corresponding eigen vector of the matrix 1 3 3 2 1 4

1

4 10

with initial vector(1 1 1)T (AU –A/M

2018) (8)

1 6 1

(b) Find the numerically largest eigen value of A = 1 2 0 and its corresponding

eigen

vectors by power method taking the initial eigen vector as (1 0 0)T. (AU–

N/D2017) (8)

15 4 3

15.(a) Using Power method, find all the eigen values of A= 10 12 20 4 6 2

(AU –

2016)-2(8)

16. (a)Using Jacobi method , find eigen values of A=

(8)

(b) Using Jacobi method , find eigen values of A=

(8)

3 4

2 3

6 2

17. (a) Find the inverse of A= 1 1 1

3 5 3

by Gauss-Jordan method (AU-N/D 2018)

(8)

(b) Solve by Gauss Elimination method 3x+4y+5z=18, 2x-y+8z=13,

M/J2016)(8)

5 0 1

(b)Using Power method, find all the eigen values of A= 0 2 0 (AU-N/D-

1 0 5

0 1

0 1 3 y

5x-2y+7z=20 (AU-N/D 2018) (8)

UNIT – II

INTERPOLATION AND APPROXIMATION PART-A

1. Using Lagrange’s interpolation, find the polynomial through (0,0), (1,1) and (2,20).

(AU –

A/M 2017) y (x x1)(x x2 ) y

(x x0 )(x x2 ) y (x x0 )(x x1) y

(x x )(x x ) 0 (x x )(x x )

1 (x x )(x x )

2

0 1 0 2 1 0 1 2 2 0 2 1

(x 1)(x 2)

0 (x 0)(x 2)

1 (x 0)(x 1)

20 x2 12x 10

(0 1)(0 2) (1 0)(1 2) (2 0)(2 1)

2. Find the second divided difference with arguments a, b, c if f(x)=

A/M 2018)

1 . (AU –

x

f (x) 1

, f (a) 1

, f (a, b)

f (b) f (a)

1

x

f (a, b, c)

a

f (b, c) f (a, b)

c a

1

abc

b a ab

f (a, b, c, d ) f (b, c, d ) f (a, b, c)

d a

1

abcd

3. Name any two methods for unequal intervals.

(AU -2012)

(i) Newton-divided difference formula

(ii) Lagrange’s interpolation formula 4. What is the Lagrange’s formula to find y if three sets of values x y , x , y and

0, 0 1 1

x

2015)-2

2, y

2 are given. (AU –N/D

y (x x1 )(x x2 ) y (x x0 )(x x2 ) y

(x x0 )(x x1 )

2

(x0 x1 )(x0 x2 ) (x1 x0 )(x1 x2 ) (x2 x0 )(x2 x1 )

5. Using Lagrange’s formula find y value when x=1 from the following data: (AU –N/D

(x x1)(x x2 )x x3 y (x x )( x x )( x x )

0

y

(x x0 )( x x2 )x x3 (x x )(x x )( x x )y

1(x x )( x x )x x

(x x )(x x )( x x ) 2

0 1 0 2 0 3 1 0 1 2 1 3 2 0 2 1 2 3

(x x0 )(x x1)x x2 (x x )( x x )( x x )y

3

3 0 3 1 3 2

(x 1)( x 3)

5 (x 0)( x 3)

6 (x 0)(x 1)

50 4.5

(0 1)(0 3) (1 0)(1 3) (3 0)(3 1)

6. Find the second degree polynomial through the points (0,2),(2,1), (1,0) using

Lagrange’s

y

X: 0 -1 2 3

Y: 2016)

-8 3 1 12

formula. (AU –

N/D2014)

y=f(x)= (x 2)(x 1)

(2) x(x 1)

(1) x 2 3x 2 x2

x 3x

2

7x

2

(2)(1) 3x

2

(2)(1) 7x

2 2 2 2

The polynomial f(x)= 2 2 2

7. Give the Newton’s divided difference interpolation formula? (AU

-2010)

f (x) f (x0 ) (x x0 ) f (x0 , x1 ) (x x0 )x x1 f (x0 , x1 , x2 ) .....

(x x0 )(x x1 ).....(x xn1 ) f (x0 , x1 , ... xn )

8. State any two properties of divided differences. (AU –

M/J2012)-2 (i) The divided differences are symmetrical in all their arguments. (ii) The divided differences of sum or difference of two functions is equal to the sum

or difference of the corresponding separate divided differences. 9. Find the divided differences of f(x) = x3+x+2 for thearguments 1,3,6,11. (AU – N/D2017)

The corresponding f(x) values are 4,32,224,1344. The divided differences are f(1,3) = 14. f(3,6) = 64, f(6,11) = 224, f(1,3,6) = 10, f(3,6,11) = 20 and f(1,3,6,11) = 1

10. Construct the divided difference table for (AU – N/D 2009)

x -1 0 2 3

y -8 3 1 12

The divided difference table for the given data is given as follows.

x y f (x)

2 f (x)

-1 -8 11

2 0 3

-1 -4

2 1 11

4

3 12

11. Construct the divided difference table for the following data: (AU –

M/J2016)-2

X: 0 1 2 5 F(x): 2 3 12 147

The divided difference table for the given data is given as follows.

X Y f (x) 2 f (x)

3 f (x)

0

1

2

5

1 3

12

147

2

9

45

3.5 9

1.1

12. Construct a table of divided difference for the given data:

X: 654 658 659 661

Y: 2.8156 2.8182 2.8189 2.8202 (AU- M/J-2016) The divided difference table for the given data is given as follows.

X Y f (x)

2 f (x)

654 2.8156 0.0007

658 2.8182 0.0007 0 659 2.8189 0.0007 0 661 2.8202

13. Constuct the divided difference table for the data (0,1),(1,4),(3,40)&(4,85)

(AU-N/D-

2015)

The divided difference table for the given data is given as follows.

X Y f (x) 2 f (x)

3 f (x)

0 1

1

1 4 3

18 5

3 40 45 9

4 85

14. What is meant by natural cubic spline? (AU

-2010) A cubic spline fixed to the given data such that the end cubics approach linearity at their extremities is called a natural cubic spline.

15. Define cubic spline. (AU –A/M-

2017)-3 A cubic polyminal which has contiuous slope and curvature is called a cubic spline

16. What are the advantages of cubic spline fitting? (AU – A/M-2015)

Cubic splines provide better approximations to the behavior of functions that have abrupt

local changes. Further splines perform better than higher order polynomial approximations.

17. For cubic splines, what are the 4n conditions required to evaluate the unknowns.

(AU – N/D-2015)

1. The function values must be equal at the interior nodes(2n-2) conditions. 2. The first and last functions must pass through the end points (2 conditions). 3. The first derivatives at the interior knots must be equal (n-1) conditions. 4. The second derivatives at the interior knots must be equal (n-1) conditions. 5. The second derivatives at the end knots are zero.(2 conditions).

The above five types of conditions provide the total of 4n equations required to solve for the 4n coefficients.

18. Given y0=3, y1=12, y2=81, y3=200, y4=100 find 4y0 (AU – A/M-2015)

4y0= (E-1)4y0

= E4y0-4E3y0+6E2y0-4E y0+ y0

= y4-4 y3+6 y2-4 y1+ y0

= 100-800+486-48+3= -259 19. Distinguish between interpolation and extrapolation. (AU – N/D-2017)

Interpolation Extrapolation

To find the values of a function

inside a given range is

interpolation

To find the values of a function

outside a given range is

interpolation

20. State Newton’s backward difference formula. (AU –N/D- 2014)-3

yx yn

v y

1! n

v(v 1)

2 y

2! n .....

where v x xn

h

21. Find the polynomial for the following data by Newton’s backward difference formula: (AU -

N/D-2009) X: 0 1 2 3 f(x) -3 2 9 18

X Y=f(x) y 2y 3y 0 -3

5

1 2 2

7 0 2 9 2

9

3 18

yx yn

v y

1! n

v(v 1)

2 y

2! n

..... ; v x xn

h

x 3

; y(x) = 2x2-x+3 1

22. State Newton’s forward interpolation formula for equal intervals. (AU –M/J-

2016)-3

P (x) P (x uh) Eu P (x ) E

u y

n n 0

(1 )u y

n 0 0

0

y u y

u(u 1)

2 y

u(u 1)(u 2)

3 y .....

0 1!

0 2!

0 3!

0

23. What is the nature of nth divided differences of a polynomial of nth degree? (AU – N/D-2017)

f x , x ,, x f x1, x2, xn f x0, x1, xn1 0 1 n

n x0

24. Find the value of Y at x =21 using Newton’s forward difference formula from the following table: (AU

-2010)

X: 20 23 26 29 Y: 0.3420 0.3907 0.4384 0.4848

yx y0

u y

1! 0

u(u 1)

2y

2! 0

u(u 1)(u 2)

3 y

3! 0

.....

x y y 2y 3y

20 0 .3420 0.487

23 0 .3907 -0.0046

0.441 26 0 .4348 0.0059

0.05

0.0105

29 0 .4848

where u = (x-x0)/h = 21 20

1 3 3

y(x) = 0.3420+0.0162+0.0005+0.00013 = 0.3583

25. When to use Newton’s forward interpolation and when to use Newton’s backward

interpolation formula? (AU –

A/M-2018)

For equal intervals , Newton’s forward and backward interpolation formula are used.

Newton’s forward interpolation is used to interpolate the values y near the start of a set

of tabular

values Newton’s backward interpolation is used to interpolate the values of y near the

end of a

set of tabular values.

26. Distinguish between Newton-divided difference interpolation & Lagrange’s

interpolation

x

(AU-

A/M-2015)

Newton-divided difference

Interpolation

Lagrange’s Interpolation

Divided difference are used for interpolation

Only the values the functions are used

There is relationship between consecutive polynomial. So, calculations become easier

Product of linear factors in each calculation, so the calculation become tedious

27. Write down the Newton’s backward interpolation formula. (AU-N/D-

2018)

Pn (x) Pn (xn vh) (1 )

v y

y v y

n

v(v 1)

2 y

v(v 1)(v 2)

3 y

.....

n 1!

n 2!

n 3!

n

28. When do you apply Newton’s divided difference interpolation formula for a given problem?

(AU – N/D2018)

If the intervals are unequal (for unequal intervals) then we apply Newton’s divided difference

interpolation formula.

PART – B

1. (a)Using Lagrange’s interpolation formula to fit a polynomial to the given data f(-1)=-8, f(0)=3,f(2)=1 and f(3)=2.Hence find the value of f(1). (AU –A/M-

2018) (8) (b)Using Lagrange’s interpolation formula ,find value of y when x=10, if the values of x

and y are as follows: (AU-M/J-

2012) (8) x 5 6 9 11 y 12 13 14 16

2. (a) Find the polynomial f(x) using Lagrange’s formula & hence find f(3) (AU-N/D- 2017)-4 (8)

X 0 1 2 5 f(x) 2 3 12 147

(b)Find the value of y at x=21 from the data given below: (AU-N/D-

2016)(8)

x 20 23 26 29

y 0.3420 0.3907 0.4384 0.4848

3. (a)Using Lagrange’s interpolation, calculate the profit in the year 2000 from the following data Year 1997 1999 2001 2002 Profit in Lakhs of Rs.: 43 65 159 248 (AU-N/D-

2015) (8) (b)Using Lagrange’s interpolation, find the interpolated value for x=3 of the table(AU-A/M-

2015) (8)

x: 3.2 2.7 1.0 4.8 f(x) 22.0 17.8 14.2 38.3

4. (a)Using Lagrange’s interpolation formula find y(2)given that y(0)=0,y(1)=1,y(3)=81,

Y(4)=256, y(5)=625 . (AU-M/J-

2014) (8)

(b)Given the table :

x 5 7 11 13 17 y=f(x) 150 392 1452 2366 5202

Evaluate f(9) using Newton’s divided difference formula. (AU-N/D-

2016) (8)

5. (a)Use Lagrange’s method to find log10323.5 given that, (AU-M/J-

2016)(8)

X 321.0 322.8 324.2 325.0

log10x

2.50651 2.50893 2.51081 2.51188

(b) Find f(1) by Newton’s divided difference formula for the following data :(AU-

A/M2017)-2(8)

X: -4 -1 0 2 5 Y: 1245 33 5 9 1335

6. (a)Using Newton’s divided difference formula find f(x) from the following data and hence and f(4): (AU-M/J-

2016) (8)

X: 0 1 2 5 f(x) 2 3 12 147

(b) Find f(8) by Newton’s divided difference formula for the following data: (AU-

A/M2017) (8)

x: -4 -1 0 2 5 Y: 1245 33 5 9 1335

7. (a) Using Newton’s divided difference formula find f(x) from the following (AU-A/M-

2013)(8)

(b)Given the values (AU-N/D- 2016)(8)

x: 5 7 11 13 17 f(x): 150 392 1452 2366 5202

Evaluate f(9) using Newton’s divided difference formula

8. (a) Find the cubic polynomial from the following table using Newtons divided difference

Formula and hence find f(4). x: 0 1 2 5

Y=f(x): 2 3 12 147 (AU-M/J- 2016)(8)

x: 0 1 2 4 5

x: 1 2 7 8 y 1 5 5 4

(b) Use Newton’s

divided difference formula to find f(3) from the following data:(AU-A/M-2015)(8)

9. (a) The following values of x and y are given:

X: 1 2 3 4 Y: 1 2 5 11

Find the cubic splines and evaluate y(1.5) and y’(3) (AU-N/D-

2015) (8)-2

(b) Fit the following four points by using the cubic spline (AU-A/M-

2018) (8)

x 0 2 4 6 y 1 9 41 41

Using the conditions M0=0 and M3=-12

10. Obtain the cubic spline for the following data to find y(0.5). (AU-N/D-

2017) (16)-2

X -1 0 1 2 Y -1 1 3 35

11. Fit the cubic spline for the following data (AU-A/M-

2018)(16)-2

x: 0 1 2 3 y: 1 2 33 244

12. (a) Obtain the cubic spline for the following data:

X 1 2 3 Y -8 -1 18

Hence evaluate y(1.5) and y’(1). (AU-N/D-

2016) (8)

(b) Using Newton’s forward interpolation formula, find the cubic polynomial which takes the

following values: (AU-N/D- 2015) (8)-3

X: 0 1 2 3 Y: 1 2 1 10

13.(a)Obtain the cubic spline for the following data:

X 1 2 3 Y -6 -1 16

Hence evaluate y(1.5) and y’(2). (AU-

M/J2016)(8)

(b) The table gives the distance in nautical miles of the visible horizon for the given

heights in

f(x): 1 14 15 5 6

feet above the earth’s surface. (AU-A/M

2015) (8)

x: height 100 150 200 250 300 350 400 Y:distance 10.63 13.03 15.04 16.81 18.42 19.90 21.27

Find the values of y when x=218 feet using Newton’s forward interpolation

formula.

14. (a) Employ a third order Newton polynomial to estimate f(2) with the four points given

in table

(AU-A/M

2015) (8)

X 1 4 6 5 f(x) 0 1.3863 1.7918 1.6094

(b) Find the interpolation polynomial f(x) by using Newton forward interpolation formula, from

the following data and hence find f(5).

(AU-N/D

2017)-4 (8)

15. (a) Find the value of tan 45015’ by using Newton’s forward differenceinterpolation

formula for

x 45 46 47 48 49 50

tan x 1.00000 1.03553 1.07237 1.11061 1.15037 1.19175

(AU-

A/M2018)(8)

(b)From the given table compute the value of sin380 (AU-

M/J2016)(8)

x 0 10 20 30 40

sinx 0 0.17365 0.34202 0.5 0.64279

16. (a) Using Newton’s divided difference formula, find the equation y = f(x) of least degree and

passing through the points (-1,21),(1,15),(2,12)(3,3).Find also y at x=0. (AU- N/D2018)(8)

(b) Using Lagrange’s interpolation formula ,find y(9.5) for the given data. (AU-N/D- 2018) (8)

x 7 8 9 10 y 3 1 1 9

17 Fit the following four points by cubic splines (AU-A/M-

2018)(16)

x: 0 1 2 3

X: 4 6 8 10

Y: 1 3 8 10

y y

y

x x0

y: 1 2 33 244 Use the end conditions " " 0 . Hence compute (i)y(1.5) and (ii) y’(2.0).

0 3

UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION

PART - A 1. Write down the forward difference formulae to compute the first two derivatives at

x=x0.

&N/D-7

dy

1 y

1

2 y

1

3 y

.....

(AU -2018)A/M

dx

x x0 h

0 2

0 3

0 d

2y 1 2 3 11 4

dx 2

h2

y0 y0 12

y0

x x 0

2. Find y’ (0) from the following table (AU2015)A/M

X 0 1 2 3 4 5 Y 4 8 15 7 6 2

Difference Table

dy

1 y

1

2 y

1

3 y

.....

=4-1.5-6-10-14.4=-27.9

dx

x x0

h 0 2

0 3

0

3. Find dy

at x=50 from the following table

dx (AU2017)-A/M

x: 50 51 52

Y: 3.6840 3.7084 3.7325

X Y

50 3.6840

y

0.0244

2 y

51 3.7084 -0.0003 0.0241

dy 52

13.73251

2 y

1

3 y

=

1 0.0244

1 0.0003

0.02455

dx

h 0

2 0

3 0 1

0 2

4. Write Newton’s backward difference formula to compute y’(x) at x=xn+ph. (AU - 2018) A/M-2

X Y y 2 y 3y 4y 5y

0 4

4

4 8 3

7 18

2 15 -15 40

-8 22 72 3 7 7 -32

-1 -10

4 6 -3

-4

5 2

0

a

6

dy 1 2v 1 2 3v 2 6v 2 4v

3 18v

2 22v 6 4

dx h yn

2 yn 24

yn

5. State Trapezoidal rule. (AU -2014

)-N/D-2

b h

ydx= 3 [( y0 +yn) + 4(y1+y3+..........+yn-1) + 2(y2 + y4+ ......+yn-2)]

a

6. Evaluate 1 dx using Trapezoidal rule. (AU -

1 x2

2012)N/D

x 0 0.5 1 Y 1 0.6666 0.5

1 h

ydx = 0

2 [(y0 + yn) + 2(y1+y2+ ..... +yn-1)]

= 0.5

[(1+0.5) + 2(0.6666)] 2

= 0.7083

7. Evaluate sin xdx by trapezoidal rule by dividing 10 equal parts (AU - 0

2013)M/J

x 0 π/10 2π/10 3π/10 4π/10 5π/10 6π/10 7π/10 8π/10 9π/10 π Y=sinx 0 0.309 0.5878 0.809 0.9511 1 0.9511 0.809 0.5878 0.309 0

xn h

By Trapezoidal rule I= f (x)dx.= x0

I = 1.9843

2 [(y0+ yn) + 2(y1+y2+ ....... +yn-1)]

8. How do you compute the error in numerical integration by Trapezoidal rule if the interval

is (a,b)? (AU - 2011)M/J

Trapezoidal rule: Error term E (b a)h

2 M

12

in theinterval (a,b) where h= b a

n

9. State Simpson’s one third rule. (AU -

2013)M/J

b h

ydx= 3 [( y0 +yn) + 4(y1+y3+..........+yn-1) + 2(y2 + y4+ ......+yn-2)]

10. Under what conditions, Simpson’s 1/3 rule can be applied and state the formula.

(AU -

2012)M/J

The number of subintervals should be taken as multiples of 2. xn

h

f (x)dx.= x0

3 [(y0+ yn) + 2(y2+ y4+ y6.......+yn-2)+4(y1+y3+ y5+….. yn-1 )]

2

11. Find x 4 dx. by Simpson’s rule taking h = 1. (AU -

2

2012)M/J x -2 -1 0 1 2 y 16 1 0 1 16

2

x 4 dx. =

2

1 [(16+16)+4(2)] = 13.3 sq units

3

12. What are the errors in simpson’s rules of numerical integration

(b a)h

4 M

(AU-2014)- N/D-3

Simpson’s rule: Error term E

180 State the local error term in simpson’s 1/3 rd rule

h5 M

Error term E=

of

; where M is the numerically greater value of the fourth derivatives 90

y=f(x) at x0,x2,,…,x2n-2 5.2

13. Find log e xdx by Simpson’s rule taking h = 0.2. 4

Divide the interval of integration into six equal parts each of width 0.2. The values of the function y= ln x are next calculated for each point of subdivision as given below.

x 4 4.2 4.4 4.6 4.8 5 5.2 ln x 1.3862h

1.4350

1.4816 1.5260 1.5686

1.6094 1.6486

5.2

log e xdx = 4

y0 y6 2( y2 y4 ) 4( y1 y3 y5 )

= 0.23.0349 2(3.0502) 4(4.5705) 3

=1.8278 14. Compare Trapezoidal rule and Simpson’s 1/3 rule for evaluating numerical integration.

S.No. Trapezoidal Rule Simpson’s 1/3 (AU- 2016)N/D-2

1. Number of intervals may be Number of intervals is even even or odd

2. Order of error = h2 Order of error = h4

3 . Principal part of the error Principal part of the error in the interval (x1,x2) = - y’’ in the interval (x1,x2) = - yiv

b

15. State Romberg’s method integration formula to find the value of I = f (x)dx. a

using h and h/2. (AU - 2014)M/J

I = I + I2 I1 ;

2 3

where I1 = value of I with interval size h, I2= value of I with interval size h

2

16. If I 1 = 0.775 , I 2 = 0.7828 find I using Romberg’s method.

3

2

1

1) dx = f

I = I + I2 I1 , I = 0.7828+

0.7828 0.775 = 0.7802

2 3 3

1

17. If I = e x2

dx. then I 1 = 0.731 , I 2 = 0.7430 with h = 0.5 and h = 0.25 Find I (AU - 0

2016) M/J using Romberg’s method.

I = I + I2 I1

3 0.743 0.731

I = 0.743+

= 0.747

3

18. Write down the general quadrature formula for equidistance ordinates. (AU - 2016) M/J

xn n2 1 n3

n2 1 n

4

f (x)dx hny

y 2 y

n3 n

2 3y

....

x0 2 2 3 2 0

6 4 dx

19. Apply two point Gaussian quadrature formula to evaluate

A/M -3

1

1 x2

(AU -2018)

1 1 1

f (x)dx f ( 1

f (x) 1

1 x2

) f ( ) 3 3

f ( 1

) 3 0.75

3 4

f ( 1

) 3 0.75

3 4 1

f (x)dx 1.5 1

2

20. Compute e x2

dx using Gaussian two point formula. (AU - 0

2016) M/J Given the range is not (-1,1) so by using the formula to make them as (0,2)

x = b a

z b a Here a = 0 , b =2

2 2

= 2 0

z 2 0

2 2 x = z+1 z=x-1; dx = dz;

2 1 1 1

e 2x dx = e

( Z

2

f = (0.8364+0.0831) = 0.9195

0 1

2

3 3

21. Change the limit sin xdx into(-1,1) 0

(AU2016)N/D

Given the range is not (0,2) so by using the formula to make them as (-1,1).

x = b a

z b a Here a = 0 , b =

2 2 2

0 0 0

4

9 5 9

4 4

0

0

= 2 z 2

x =

2 2

(1 t) ; dx =

dt

4 4 2

1

sin xdx sin 0 1

4 (1 t)dt

22. Write down three point Gaussian quadrature formula toevaluate

1

f (x)dx 1

A/M -4

Three points Gaussian quadrature formula is, 1

5 3 3 8

f (x)dx f f f (0)

1 5

(AU -2017)

This formula is exact for polynomials up to degree 5.

1 t

23. Using two point Gaussian quadrature formula, evaluate I= sin dt (AU - 1

2015)A/M 1

I f (t)dt 1

0.99847

f (0.5773) f (0.5773) sin( 0.10566 ) sin( 0.39434 ) 4

b

24. State Trapezoidal rule for evaluating a

d

f (x, y)dxdy. c

(AU -

2014)M/J

I = hk

[(Sum of values of f at the four corners ) + 2(Sum of values of f at the 4

remaining nodes on the boundary) + 4(Sum of the values of f at the interior nodes)]

b

25. State Simpson’s rule for evaluating a

d

f (x, y)dxdy. c

I = hk

[(Sum of the values of f at the four corners) + 2(Sum of the values of f at the 9

odd positions on the boundary except the corners) + 4(Sum of the values of f at the even positions on the boundary) +

4(Sum of the values of f at odd positions) + 8(Sum of the values of f at even positions) on the odd row of the matrix except boundary rows + 8(Sum of the values of f at the odd positions)+16(Sum of the values of f at the even positions) on the even rows of the matrix].

PART – B

1.(a) Find the first and second derivative of y with respect to x at x=10 from the followingdata x : 3 5 7 9 11 y : 31 43 57 41 27 (AU-2017)-N/D (8)-2

e 1

sin xdx

3

(b) Find dy

and dx

d 2 y

dx2 at x=1.5 from the following data:

x: 1.5 2 2.5 3 3.5 4 y: 3.375 7 13.625 24 38.875 59 (AU-2016)- M/J (8)

2.(a) Using backward difference, find y'(2.2) and y''(2.2) from the following table:

x: 1.4 1.6 1.8 2.0 2.2

y: 4.0552 4.9530 6.0496 7.3891 9.0250 (AU2017)A/M(8)

(b) Find f’(10) from the following data (AU-2016) M/J (8) X: 3 5 11 27 34 Y: -13 23 899 17315 35606

3.(a) From the following table of values of x and y, obtain y’(x) for x=16 (AU-2018)- A/M -(8) x : 15 17 19 21 23 25 y : 3.873 4.123 4.359 4.583 4.796 5

(b) A slider in a machine moves along a fixed straight rod. Its distance x cm along the rod is given below for various values of the time ‘t’ seconds. (AU-2015)-A/M(8)-3

Find the velocity of the slider when t=1.1 second t: 1.0 1.1 1.2 1.3 1.4 1.5 1.6 x: 7.989 8.403 8.781 9.129 9.451 9.750 10.031

4.(a)

(b)

The population of a certain town is shown in thefollowing table (AU-2016)N/D (8)-2 Year: 1931 1941 1951 1961 1971

Population(in thousands) 40.6 60.8 79.9 103. 6

132. 7

Find the rate of growth of the population in the year 1945.

The velocity v(km/min) of a moped which starts from rest, is given at fixed intervals of time t(min) as follows (AU-2015)A/M (8)

t 0 2 4 6 8 10 12 v 0 10 18 25 29 32 20

Estimate approximately the distance covered in 12 minutes by simpson’s 1/3 rule. Estimate the acceleration at t=2 seconds

5. (a) The following data give the corresponding values for pressure(p) and specific volume (v) ofa superheated steam. Find the rate of change of pressure with respect to volume when v=2.

(AU -2017)-N/D-(8)

(b) Calculate x

0.5

xdx taking 5 ordinates by trapezoidal rule and Simpson’s1/3 rule (8)

6. (a) 2

Find the value of log 21/3 from x dx using Simpson’s 1/3 rule with h=0.25.

0 1 x (AU-2016M/J)(8)

(b) Evaluate

/2

0

using Simpson’s 1

rule , by dividing the range into six equal subintervals. 3

(AU-2016)- M/J (8)-2 7. (a) Compute value of 1.4

(sin x log x e )dx taking h=0.2 and using Simpson’s rule (AU-2011)M/J (8) 0.2

(b) The velocity v of a particle at a distance ‘s’ from a point on its path is given by thetable: S(feet) 0 10 20 30 40 50 60 V(ft/sec) 47 58 64 65 61 52 38

Estimate the time taken to travel 60 feet by using simpson’s 1/3 rule.compare the result with

x

v: 2 4 6 8 10

p: 0.7

105 42.7 25.3 16.7 13.0

0

1

0

xy

1 1

x y 1

Simpson’s 3/8 rule (AU-2016)-N/D(8)-2 1.3

8. (a) Taking h = 0.05 evaluate

1

xdx using Trapezoidal rule and Simpson’s 1/3 rule.

(AU-2013) (8)

(b)

Using Simpson’s one-third rule, evaluate

0.6

ex2

dx correct to three decimal places by step-size=0.1 0

(AU -2017)- N/D -(8) 1 dx

9. Using Romberg’s method, evaluate 1 x

2 , correct to four decimal places. Also compute the

same integral using three point Gaussian quadrature formula. Comment on the obtained

values by comparing with the exact values of the integral which is equal to

4 (AU-2016)- M/J (16)-2

10.(a) Using Romberg’s method to get an improved estimate of the integral from x=1.8 to x=3.4 from the table with h=0.4 (AU-2015)A/M (8)

1 dx

(b) Using Romberg’s method, evaluate 1 x with step size 0.5,0.25 and 0.125 correct to three

decimal places and hence find the value of loge2. (AU-2018)- A/M -3 (10) 1

1

11.(a) The following table gives the values of y 1 x2 dx . Take h=0.5, 0.25, 0.125 and use Romberg’s

1

method to compute

1 2 dx . Hence deduce an approximate value of

(b)

1.5

2

01 x (AU-2017) A/M (8)

Evaluate e x

dxusing three point Gaussian quadrature formula (AU-2016) M/J -(8) 20.2

dx

12. (a) Evaluate 1 x3 using 3 point Gaussian formula (AU-2016)- M/J (8)-2

(b) Evaluate

1 x

2 2x 1

1 (1 x) 4

dx

5

by Gaussian three point formula. (8)

13.(a) Evaluate log10 (1 x)dx by three points Gauss quadrature formula. (AU-2017) A/M (8) 0

1.42.4 1

(b) Evaluate dxdy Using Trapezoidal rule by taking h=k=0.1 and verify with actual integration 1 2

(AU-2016)N/D (8) 2 2 1

14.(a) Using trapezoidal rule, evaluate x

2 y

2 dxdy numerically with h =0.2 along x-direction and

k = 0.25 along y-direction. (AU-2015)-N/D-3 (8) (b) Evaluate

1 1 dxdy

0 0

by using Trapezoidal rule taking h = 0.5 & k = 0.25. (AU-2016)- M/J (8)-2

0

0

x 1.6 1.8 2.0 2.2 2.4 2.6 f(x) 4.953 6.050 7.389 9.025 11.023 13.464 x 2.8 3.0 3.2 3.4 3.6 3.8 f(x) 16.445 20.056 24.533 29.964 36.598 44.701

xy

1 1

0

3

2 2

15.(a) Evaluate f (x, y)dxdy by Trapezoidal rule from the following data , correct to three decimal 0 0

places (AU -2017)-N/D-(8)

x y

0 0.5 1 1.5 2

0 2 3 4 5 5 1 3 4 6 9 11 2 4 6 8 11 14

1 1 dxdy

(b) Using simpson’s 1/3 rule, evaluate 1 xy with h=k=0.25 (AU-2017) A/M (8)

16. (a) Evaluate

/2

cos(x y) dxdy 0 / 2

using Simpson’s rule by taking h=k=π/4 (AU-2016)- M/J (8)-2

(b) Evaluate 2.64.4

1 by Simpson’s one-third rule with h=0.2 and k=0.3(AU-2018)A/M(8 ) dxdy

2 4

17. (a) From the following table find the value of y” at the point x = 0.96.

x : 0.96 0.98 1.00 1.02 1.04 (AU -2017)-

N/D-(8) f(x): 0.78225 0.7739 0.7651 0.7563 0.7473

dx

(b) Evaluate 1

using 3 point Gaussian formula (AU-2018)- N/D (8) 2 2

dxdy

18. (a) Using Trapezoidal rule, evaluate x y with h=k=0.5 (AU-2018) N/D (8)

1

x2

(b) Using Simpson’s 1/3 rule, evaluate 1 x

3dx with h=k=0.25 (AU-2018) N/D (8)

UNIT IV INTIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS

PART – A

1. Compute y(1.1) by Taylor’s series method, given

N/D-2

dy x y, y(1) 0.

dx

(AU -2014)-

Given y’ = x +y , x0 = 1, y0 = 0 We know that the Taylor’s series formula for y1 is

h h2 ''

h '''

y1 y0 1!

y '0 2!

y0 3!

y0 .......

0 0

x

y' x y y0 ' x0 y0 1 0 1

y'' 1 y' y0 '' 1 y0 ' 11 2

y''' y'' y0 ''' y0 '' 2

yiv y'''

iv

y0 y''' 2

y(1.1)=0.1+(0.1)2+

0.13

3

0.14

1.2

=0.1103

2. Find y(0.1) if

2012)M/J

dy x y, y(0) 1. using Taylor’s series method. (AU -

dx

y(0.1)=1+0.1+ (0.1)2+

0.13

3

0.14

1.2

=1.1103

y y h

y ' h2

y'' h3

y''' ....... 1 0

1! 0

2! 0

3! 0

3. Find by Taylor’s series method ,the value of y at x=0.1 from dy

y 2 x , y0 1

h

y1 y0 h2 ''

h3

dx ''' (AU -

.......

2015)A/M

1! y0 '

2! y0

3! y0

y' y2 x

2

y0 ' y0 x0 1 0 1

y'' 2 yy 1 y '' 2y y 1 2 1 3

0 0 0

y''' 2 yy''2 yy y ''' 2y y ''2y

y 6 2 8 0 0 0 0

y(0.1)=1+0.1+ 0.12

3

2! +

0.13 8

3! =1.1163

4. What is the major drawback of Taylor’s series method? (AU -

2012)M/J

In the differential equation

algebraical

dy = f(x, y), the function f(x, y) may have a complicated

dx

structure. Then the evaluation of higher of order derivatives may become tedious.This is

the

drawback of this method.

5. State the advantages and disadvantages of the Taylor’s series method. (AU -2014)-

M/J-2

The method gives a straight forward adaptation of classic calculus to develop the solution as an

infinite series. It is a powerful single-step method if we are able to find the successive derivatives

easily. If f(x,y) involves some complicated algebraic structures then the calculation of higher

derivatives becomes tedious and the method fails. This is the major drawback of this method.

However the method will be very useful for finding the starting values for powerful methods like R-K

+

+

y' x y y0 ' x0 y0 1 0 1

y'' 1 y' y0 '' 1 y0 ' 11 2

y''' y'' y0 ''' y0 '' 2

yiv y''' y

iv y''' 2

0

method, Milne’s method etc., 6. State Euler’s formula. (AU -

2014,2018)N/D yn+1= yn+hf(xn,yn) ,n=0,1,2,3,……………

7. Using Euler’s method, find y(0.1) given that dy

x y, y(0) 1 dx

(AU -

2016) M/J

Given x0=0, y0=1; Take h=0.1

By Euler’s algorithm yn+1= yn+hf(xn,yn) ,n=0,1,2,3,………… y1=y0+hf(x0,y0)=1+(0.1)f(x0+y0); y(0.1)=1.1

8. Using Euler’s method, find y(0.1) given that dy

1 y, y(0) 0

dx

(AU2017) A/M

Given x0=0, y0=0; Take h=0.1

By Euler’s algorithm yn+1= yn+hf(xn,yn) ,n=0,1,2,3,…………

y1=y0+hf(x0,y0)=0+(0.1)f(x0+y0)=0.1(1-y0)=0.1; y(0.1)=0.1

9. Using Euler’s method, find the solution of the initial value problem dy

log(x y), y(0) 2

dx

at x=0.2 by assuming h=0.2. (AU –

2012)M/J

By Euler’s algorithm yn+1= yn+hf(xn,yn) ,n=0,1,2,3,……………

y1=y0+hf(x0,y0)=2+(0.2)(log(x0+y0))

y(0.2)=2+0.2(log(0+2)=2+(0.2)(0.3010)=2.0602

y(0.2)=2.06

10. State modified Euler method to solve y ’ = f(x,y), y(x0)=y0 at x = x0 + h. (AU-2017)- N/D-2

y

n1

yn

hf xn

h

, y h

2 n

2 f (xn

,y

n )

h h

y1 y0 hf x , y f (x 0 0 , y

0 2 2 0 )

11. What is the error of Modified Euler’s method The error in one-step of the Modified Euler method is O(h3)

12. Write down the improved Euler’s formula first order differential equation.(AU - 2016) M/J

ym1 ym

h f (x

2 m , ym ) f [xm h, ym hf (xm, ym )]

13. Using Modified Euler’s method, find y(0,1) if

2014)N/D

dy x

2 y

2 , y(0) 1

dx

(AU -

Given f(x,y) = x2+y2,x0=0,y0=1,h=0.1,x1=0.1 By modified Euler method

yn1 yn

hf

xn

h

, y h

2 n

2 f (xn

,y

n ) ……… (1)

y y

h

, y h

f (x ……… (2)

1 0 hf x0 2

0 2 0 , y 0)

f(x0,y0) = x02+ y0

2 = 0 + 1 = 1

y1 = 1 + (0.1) f 0

0.1 ,1

0.1 (1)

2 2

= 1 + (0.1)f[0.05, 1.05] = 1 + (0.1)[(0.05)2+(1.05)2] = 1 + (0.1)[0.0025+1.1025] = 1+ 0.1105 = 1.1105

y(0.1) = 1.1105

14. Find the values of k1 and l1 to solve y’’+xy’+y=0, y(0)=1, y’(0)=0 by fourth order RK method. (AU -

2010)N/D

y'' xy' y, y0 1, y'0 0, h 0.1, y0 1

x0 0, y1 y0.1

The equation becomes y’’=z’=-xy-y dy

z

dx f1 x, y, z

dz xz y

dx f 2 (x, y, z)

By algorithm k1= hf1x0 , y0 , z0 =0

l1 hf 2 x0 , y0 , z0 0.1

15. State the fourth order Runge-Kutta algorithm. (AU -

2012)N/D

Let h denote the interval between equidistant values of x. If the initial values are (x0,y0), the first increment in y is computed from the formulas.

k1 = h f(x0,y0)

k2 = h f x0

h , y

2 0

k1

2 k = h f

h , y k 2

x

3 0 0

2 2 k4 = h f(x0+h,y0+k3) and ∆y= 1/6=(k1+2k2+2k3 + k4); then x1=x0 +h, y1 = y0 + ∆y

The increment in y in the second interval is computed in a similar manner using the same four formulas, using the values x1,y1 in the place of (x0,y0) respectively.

16. State the special advantages of Runge-Kutta method over Taylor’s method. (AU- 2015)-2

R-K methods do not require prior calculation of higher derivatives of y(x) as the Taylor method

does. Since the differential equations are using in applications often complicated, the calculation

of derivatives may be difficult. Also the R.K. formulas involve the computations of f(x,y) at various

positions,Instead of derivatives and this function occurs in the given equation 17. Use the Runge-Kutta fourth order method to find the value of y when x=1 given that

dy

dx

2015)-2

y x

y x ,y(0)=1. (AU-A/M

f (x, y) y x

, x

y x 0

0, y0 1, h 1

f 1,

k = hf(x ,y )=1 , k = h

h

, y k1 = 1 3 1

f x1 0 0 2

f

,

h k 0

2 0 2 2 2 2

k = h f x , y 2

f 1

, 5

3

3 0 0

2

2 2 4 7 k = h(x +h,y +k3)= 10 3

4 0 0

7 17

∆y= 1/6(k1+2k2+2k3 + k4) y1 = y0 + ∆1y y(1)= 1 2

1

3

3 1.4342

6

1

2 7

17

18. State Milne’s predictor corrector formulae tosolve dy f (x, y), y(x ) y numerically.

dx 0 0

(Or) Write down the Milne’s predictor and corrector algorithm (AU-

2016)-N/D-5 Milne’s predictor formula is

yn1

yn3

4h 2 y'

3 n2

y'

n1 2 y'n

Milne’s corrector formula is

yn1 yn1

h y'

3 n1 4 y'n y'

n1

19. What is the error term in Milne’scorrector formula? (AU – 2011)M/J

h The error term is -

90 0 20. What is the error term in Milne’s predictor formula?

The error term is 14h

4

y '

45 0

21. What do you mean by multi-step method? (AU -

2015)N/D-2

In a set of tabulated values of x and y, we obtain y by iterative process. The methods of Euler, Runge –Kutta, Millne, Adam-Bashforth, etc.,belong to this type. Here the values of y are computed by short steps for equal intervals h of the independent variable.These values are iterated we get the desired accuracy.Hence these methods are called multi step methods.

22. Compare single step and multistep methods. (AU- 2018) A/M -3

Single step method Multistep method

By this method , we cannot desired accuracy value

By this method,we get desired accuracy value

Eg.: Taylor’s series Eg.:Euler, Runge –Kutta, Millne, Adam-Bashforth are this type

23. State Adam’s Predictor Corrector Formulae. (AU -2018)- A/M -4

Adam’s predictor corrector formulas are

yk 1, p yk

h 55 y'

24 k

59 y'

k 1 37 y'

k 2 9 y'

k 3

4

'

y

yk 1,c yk

h 9 y'

24 19 y'k 5 y'

k 1 y'

k 2

24. What is the Error of Adam Bashforth method? (AU - 2012)M/J

predictor 251

h5 f (iv) ( ) 720

Corrector 251

h5 f (iv) ( ) 720

25. How many values are needed to use Milne’s predictor-corrector formula prior to the

required value? (AU -2017)- N/D-2

Four values are needed to use Milne’s predictor-corrector formula.

26. In solving dy f (x, y), y( x ), write down the Taylor’s series formula for y(x ) .(AU -

dx 0 1

2018)-N/D

y( x ) y h

y'

h 2

y"

.... 1 0 1! 0 2! 0

PART – B

1. (a) Using Taylor series method, compute the value of y(0.2) correct to 3 decimalplaces from

dy 1 2xy given that y(0)=0 (AU-2016)

dx M/J (8)

(b) Using Taylor’s series method, find y at x = 1.1by solving the equation dy x

2 y

2 , y(1) 2.

dx

Carry out the computations upto fourth order derivative. (AU-2014)- M/J (8)

2. (a) Using Taylor’s series method to find y(0.1) if

2013)N/D (8)

(b) Using Taylor’s series method, find y at x = 0 if

N/D(8)-2

y x2 y

2 , y(0) = 1 (AU-

dy x

2 y 1, y (0) = 1. (AU-2016)-

dx

3. (a) Using Taylor’s series method to find y at x=0.1, give

three

y x2 y , y(0) = 1, correct to

decimal places. (AU- 2018)A/M-3-(8)

(b) Find the value of y(0.1), y(0.2) with h=0.1, given dy

x 2 y 1 , y (0) = 1 by

dx

Taylor’s series method upto four terms. (AU-2017) A/M (8)

4.(a) Using modified Euler’s method to find y(0.1) and y(0.2) for the given equation

y x2 y

2 , given that y(0) = 1 (AU-2016)

M/J (8)

(b) Solve (1 x) dy

y 2 , y(0) 1 by Modified Euler’s methods by choosing h=0.1, dx

find y(0.1) and y(0.2) (AU-2017) A/M (8)

5. (a) Given dy

y x 2 1 , y(0)=0.5. Find y(0.2) by Modified Euler’s method. (AU- dx

2017)A/M- (8)

k 1

(b) Find the value of y at x=0.1 given that

method (AU-2010) (8)

y x2 y , y(0) = 1, by Modified Euler’s

6. (a)Find y(0.2), given

2010) (8)

dy log(x y), y(0) 1. using R.K. method of 4th order, taking h =0.1. (AU-

dx

(b)Employ the classical fourth order Runge-kutta method to integrate y 4e0.8t 0.5y

from t=0 to t=1 using a step size of 1 with y(0)=2 (AU- 2015)A/M (8)

7. (a)Using R-K method of fourth order solve dy

y 2 x

2

with y(0)=1 x=0.2 (AU- dx y

2 x

2

2016)-N/D (8)

(b)Using Runge-kutta method of order four, solve 2017)A/M (8)-2

y xy

2 y

2 , y (0)=1 , y’(0)=0, h=0.2.(AU-

8. (a)Find the value of y(1.1) using Runge-Kutta method of 4th order for the given equation

dy y

2 xy ;y(1)=1. (AU-2016,18) M/J&N/D

dx (8)(16) (b)Using Runge kutta method of fourth order, find the value of y at x=0.2, 0.4, 0.6 given

dy x

3 y , y(0)=2. Also find the value of y at x=0.8 using Milne’s predictor and

dx

corrector method (AU- 2014)M/J-(8)

9.(a)Determine the value of y(0.4) using Milne’s method given dy

xy y 2 y(0)=1. Use

dx

Taylor’s series method to get the values of y(0.1)y(0.2) and y(0.3) (AU-2016)- M/J (8)-2

(b) Given 5xy y 2 2, y(4)=1, y(4.1) = 1.0049, y(4.2) = 1.0097, y(4.3)=1.0143. Compute

y (4.4) using milne’s method. (AU- 2014)A/M (8)

10. (a)Derive the Milne’s predictor-corrector formula for solving first orderdifferential equation

y’=f(x,y), y0=y(x0). (AU-

2017)A/M (8)

11. (a) Using Adam’s method find y(4.4) given that 5xy’+y2 =2, y(4)= 1, y(4.1) = 1.0049, y(4.2)= 1.0097 and y(4.3)=1.0143. (AU-2015)-

N/D(8)-2

(b) By Adam’s method find y(0.6) given

y(0.2)=1.2427, and y(0.4)=1.5834

dy x y, y(0) 1

dx using h=0.2 if y(-0.2)=0.8373,

(8)

12. Find y(0.1),y(0.2) and y(0.3) from y’=x+y2, y(0)=1 by using Runge-Kutta method of Fourth

order and then find y(0.4) by Adam’s method. (AU-2016) M/J (16)

13. Consider the initial value problem

2012)M/J(16) a. using Taylor series, find y(0.2)

dy y x 2 1, y(0) 0.5.

dx (AU-

b. Using 4th order Runge-Kutta method, find y(0.4) and y(0.6)

c. Using Adam-Bashforth Predictor.

14. (a) Solve the initial value problem dy

x y 2 , y(0) 1 to find y(0.4) by Adam’s Bashforth

dx predictor corrector method and for starting solutions,use the information below. y(0.1)=0.9117,y(0.2)=0.8494.Compute y(0.3) using Runge Kutta method of fourth

order. (AU-2016)-N/D (8)

(b) Using Adam’s method find y(0.4) if

y(0.2)=1.022,y(0.3)=1.023. (AU-2017)-N/D-2- (8)

y xy / 2 ,y(0)=1,y(0.1)=1.01,

15. Given

A/M- (16)

dy xy y

2 y(0)=1, y(0.1)=1.1169 and y(0.2)=1.2774, find (AU-2018)-

dx

(i) Find y(0.3) by R.K Method of fourth order (ii) y(0.4) by Milne’s method.

16.Given that dy

1

(1 x2 ) y

2 ; y(0) 1, y(0.1) 1.06; y(0.2) 1.12 and y(0.3)=1.21.Evaluate

dx 2

y(0.4) by Milne’s predictor – Corrector method. (AU-2018)- N/D- (16)

UNIT V

BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFFERENTIAL EQUATIONS

PART - A 1. Define a difference quotient. (AU-

2011)M/J

A simple two-point estimation is to compute the slope of a nearby secant line through the points

(x,f(x)) and (x+h,f(x+h)). Choosing a small number h, h represents a small change in x, and it can be

i 1 i i 1

i1 i i1 i

i1 i i1 i i

i1 i i1 i i

i1 i

i

either positive or negative. The slope of this lineis

This expression is Newton’s difference quotient.

f (x h) f (x) .

h

2. Write the first forward and backward difference points with respect to x.

u ui1, j ui, j

x h ; Forward difference

u ui, j ui1, j

; Backward difference

x h

3. Write the finite difference approximations of y’(x) and y’’(x). (AU -

2016)- M/J -4

y’= yi1 yi

h

y" y

i 1 2 y

i y

i 1

h2

4. Write the finite difference scheme for the differential equation y”+y=0. (AU

-2009) yi 1 2 yi yi 1 y 0 h2

y 2 y y

h2 y 0

5. Obtain the finite difference scheme for the differential equation 2y”+y=5. (AU -

2014)M/J-2 2

yi 1 2 yi yi 1 y 5

2 y h2

2 y y

h2 y 5h2

2 y 2 y y h2 5 y

6. Obtain the finite difference scheme for differential equation y”+x+y=0,y(0)=y(1)=0.

yi1 2 yi yi1 x y 0 (AU -

h2

i i

2017) A/M y 2 y y h

2 x h

2 y 0

y 2 y y h2 (x y )

y y (2 h2 ) y h

2 x

7. Write the difference quotients of uxx and uyy. (AU- 2011)N/D

uXX

u

u

i 1, j 2u

i, j u

i 1, j ,

h2

u

i, j 1 2u

i, j u

i, j 1

YY h2

8. Classify the PDE uxx = ut (AU- 2012)M/J

2u u

Here A=1, B=0, C=0.

x2 t 0

B2-4AC = 0

The equation is parabolic.

i 1

i1 i1

u u

1

i, j 1 i, j

2u

2u

9. Classify the following equation : 4 2

u u 2 u

(AU -

2016)-N/D-2

Here A=1,B=4,C=4

B2-4AC=16-16=0

The equation is parabolic

x2 4

xy

y

2 x

y

10. Classify the following equation: 2u 2

2u

2u (AU -

2016) M/J

Here A=1,B=-2,C=1

B2-4AC=4-4=0

The equation is parabolic

x2 xy y2

0

11. Classify the following equation : xfxx yf yy 0,

2018)N/D

Here A=x, C=y

B2 4 AC 4x 0 when x>0,y>0.

The equation is Elliptic

x 0, y 0 (AU-

12. Write down diagonal five point formula to solve the equation uxx+uyy=0. (AU- 2017)N/D-2

ui, j

1

4 i1, j1 u

i1, j 1 u

i1, j 1

i1, j 1

13. Write down the standard five point formula to solve uxx+uyy=0. (AU -2016)- N/D-4

2u

2u

x2

y 2

0

ui, j

4 u

i1, j

ui 1, j

ui, j 1

ui, j 1

ui, j 1

14. Write Leibmann’s Iteration process. (AU -

2013)N/D

un 1

1 u(n 1) un u

n

u(n 1) i, j

4 i 1, j i 1, j i, j1 i , j 1

15. Express a2uxx = utt in terms of difference quotients. (or)

Write down the explicit formula to solve one dimensional wave equation.

(AU -2016,18)-

M/J, N/D-4

u 2(1 2 a

2 )u 2

a2

(u

i1, j u

i1, j ) u

i, j1

16. Express the Poisson equation 2u f (x, y)

2010)

in terms of finite differences. (AU -

ui1, j ui1, j ui, j1 ui, j1 4u i, j h2 f (ih, jh)

17. Write the difference scheme for solving the Poisson equation 2u f (x,y) . (AU -

2012)M/J

ui 1, j ui 1, j ui, j 1 4ui, j h2 f (ih, jh)

18. Write down Bender Schmidt’ s difference scheme in general form and using

suitable

0

u

i, j 1 i, j

value of λ, write the scheme in simplified form. (AU -2017)

A/M -2

(Or) Write down explicit finite difference scheme for ut=uxx

u 1 u u

u u (1 2)u u i , j 1 i 1, j i 1, j i, j 1 i 1, j i, j i 1,j ; 2

19. State Schmidt’s explicit formula for solving heat equation (AU

-2009)

ui, j 1

ui 1, j

(1 2)ui, j u

i 1, j

20. What is the Bender Schmidt recurrence equation when 2

ui, j1

1

2 i1, j ui1, j

21. State Crank Nicholson’s scheme to solve uxx=aut whenk=ah2 . (AU - 2010)

u 1 u

u u u

i , j 1 4

i 1, j 1 i 1, j 1 i 1, j i 1, j

22. State Crank Nicholson’s difference scheme. (AU -2018)-

A/M -2 1 u

2 i1, j1

1 u

2 i1, j1 ( 1)u

i, j1 1

u 2

i1, j

1 u

2 i1, j ( 1)uij

23. State whether the Crank – Nicholson scheme is an explicit or implicitscheme.

Justify.

(AU-

2014)M/J

The solution value at any point (i,j+1) on the (j+1)th level is dependent on the solution

values at

the neighboring points on the same level and on three values on the jth level. Hence it is

an

implicit method.

24. State implicit scheme to solve one dimensional heatequation numerically. (AU-

2011)N/D u

i 1, j 1 (2 2)u

i, j 1 u

i 1, j 1 u

i 1, j (2 2)u

i, j u

i 1, j

25. Write down the finite difference scheme for the solution of one dimensional wave

equation. (AU-

2011)M/J

u 2(1 2 a

2 )u 2

a2 (ui1, j ui1, j ) ui, j1

PART – B

1.(a)Solve y”-y=0 with the boundary conditions y(0)=0 and y(1) = 1. (AU- 2015)N/D -2(8)

(b) Solve y”=x+y with the boundary conditions y(0)=y(1) = 0 using finite differences by dividing the interval into four equal parts. (AU-2016)- M/J (8)-3

2.(a) Solve the boundary value problem xy'' y 0 with the boundary conditions y(1)=1 and

y(2)=2 taking h=1/4 by finite difference method. (AU-2017- N/D-(8)

(b) Solve the boundary value problem y’’=xy subject to the conditions y(0)+y’(0)=1, y(1)=1,

taking h=1/3, by finite difference method. (AU-2018)- A/M- (8)

3. Given the values of u(x,y) on the boundary of the square given in the following figure evaluate the

function u(x,y) satisfying Laplace equation 2u 0 at the pivotal points

1000 1000 1000 1000 (AU- 2015)A/M(16)

2000

2000

500

0

1000 500 0 0

4. By Iteration method solve the elliptic equation uxx+uyy=0 over the square region of side 4, satisfying

the boundary conditions u(0,y)=0, 0 y 4 , u(4,y)=12+y, 0 y 4 , u(x,0)=3x, 0 x 4 ,

u(x,4)=x2, 0 x 4 . By dividing the square into 16 square meshes of side 1 and always correcting

the computed values to two places to decimals. Obtain the values of u at 9 interior pivotal points.

(AU-2018)-2- A/M (16)

5. Solve uxx u yy 0 for the following square mesh with boundary condition as shownbelow.

Iterate until the maximum difference between successive values at any grid point is less than 0.001 (AU-

2015)N/D (16)

A 1 2 B

1 2

2 1

C 2 1 D

u1

u2

u3

u4

u1

u2

u3

u4

6. Solve the elliptic equation uxx+uyy=0 for the following squaremesh with boundary values as shown: (AU-2012)M/J (16)

0 500 1000 500 0

1000 1000

2000 2000

1000 1000

0 500 1000 500 0

7. Solve the Laplace’s equation uxx+uyy=0 at the interior points of the square region given as below: (AU- 2016) M/J (16)

0 11.1 17.0 19.7 18.6

0

41

42

43

21.9

0

44

45

46 21.0

0 47 48 49 17.0

0 8.7 12.1 12.8 9.0

8. Solve uxx+uyy=0 over the square mesh of side 4 units; satisfying the boundary conditions: (a) u(0,y) =0 for 0<y<4 (b) u(4,y) =12+y for 0<y<4 (c) u(x,0)=3x for 0<x<4 (d)u(x,4)=x2 for 0<x<4 (AU-2018)-A/M

&N/D-4(16)

9. Solve the Poisson equation 2u 10(x

2 y

2 10) over the square mesh with sides

x=0,y=0,x=3,y=3 with u=0 on the boundary and mesh length 1 unit. (AU-

2017)N/D-3(16)

10.(a) Solve the Poisson equation uxx u yy 81xy, 0<x<1;0<y<1 u(0,y)=0,

u(1,y)=100,u(x,0)=0,

u(x,1)=100 and h 1

. (AU-2017)

3

A/M (8)

(b)Solve: 2u 4(x y) in the region given 0 x 4,0 y 4 with all boundaries kept at

00

and choosing x y 1. Start with zero vector and do 4 Gauss seidal iterations

(8)

u1

u 2

u 3

u 4

u 5

u 6

u 7

u 8

u 9

ij

11. Solve the Poisson’s equation 2u 8x

2 y

2 for the square mesh of fig. with u(x,y)=0

on the boundary and mesh length=1. (AU-2015)- A/M-2 (16)

Y

X

12.(a) Solve the uxx = ut subject to the conditions u(x,0)=sinπx, u(0,t) =u(1,t) =0,using Bender

Schemidt method (AU-2016) M/J (8)

(b) Solve 2u u subject to u(0,t) =u(1,t)=0 and u(x,0) = sinπx , 0<x<1 using Bender

x2 t , Schmidt method. (AU-

2016)N/D-(8)-2

13. (a)Given

and

2

f

x2

f

t , f (0,t) 0 f (5,t), f x,0 x

2 25 x2

find f in the range taking h=1

upto 5 seconds. (AU- 2015)N/D (8)

2u u

subject to u(0,t) =u(1,t)=0 and

(b) Using Bender-schmidt’s method Solve x2 t , u(x,0) = sinπx , 0<x<1 and h=0.2. Find the value of u upto t=0.1. (AU-2016)-

M/J - (8)-2

14.(a) Given

by

u

t

2u

x 2

,u(0,t)=0,u(4,t)=0 and u(x,0)

x (16 x

3

). Find u : i=1,2,3,4 and j=1,2 3

using Crank-Nicholson method. (AU- 2016)M/J (8)

(b) Solve ut = uxx in 0<x<4, t>0, given that u(0,t)=0, u(4,t)=0, u(x,0)=x(4-x).Compute u upto t=4

with x t 1 N/D (8)

15. (a) Solve by Crank-Nicolson’s method

and

2u u

x2

t

(AU-2017)

for 0<x<1 ,t>0 given that u(0,t)=0,u(1,t)=0

u(x,0)=100x(1-x).Compute u for one time step with h= 1

4 and k

1 . (AU-

64 2014)N/D- (8)

u1

u2

u1

u2

u3

u2

u1

u2

u1

(b) Using Crank-Nicholson scheme, solve uxx 16ut , 0<x<1, t>0 given u(x,0)=0, u(0,t)=0

and

u(1,t)=100t. Take x 1

and t 1. Compute u for one time step at the interior mesh 4

poin (AU-2017) A/M (8)

16. (a)Evaluate the pivotal values of the equation utt 16uxx taking x 1 upto t=1.25.

The boundary conditions are u(0,t)=u(5,t)=u(x,0)=0 and u(x,0)=x2(5-x). (AU- 2016)A/M-(8)-2

(b) Solve 4utt uxx u(0,t)=0,u(4,t)=0,u(x,o)=x(4-x), ut x,0 0 h=1 upto t=4. (AU-

2014,18)N/D (8)

17. (a) Solve

2u

t 2

2u

x2 , 0<x<1, t>0 given u(x,0)=0,

u (x,0) 0 , u(0,t)=0 and

t

u(1,t)=100 sin t . Compute u(x,t) for four times steps with h=0.25. (AU-

2018)-A/M-(8)

the

2u

(b) Solve numerically, 4 x

2

2u

t 2 with the boundary conditions u(0,t)=0, u(4,t)=0 and

initial condition ut(x,0)=0 and u(x,0)=x(4-x) taking h=1 (for 4 times steps) (AU- 2017)A/M(8)

Subject Name:LIC

Faculty

Name:Mr.K.KARTHI

Book:Roy chowdry

UNIT I

IC FABRICATION

PART-A

1. Define an Integrated circuit. .(Nov/Dec 2014)

An integrated circuit(IC) is a miniature, low cost electronic circuit consisting of active and

passive components fabricated together on a single crystal of silicon. The active components are

transistors and diodes and passive components are resistors and capacitors.

2. Give the difference between monolithic and hubrid Ics.(Nov/Dec 2010)

Monolithic Integrated Circuits Hybrid Integrated Circuits

1. In Monolithic circuits, all circuit components

both active and passive elements and their

interconnections are manufactured into or on

top of a single chip of silicon.

2. It is used for more applications in Linear and digital IC 3. Cost wise is less.

1. 1.Hybrid Integrated circuits separated

component parts are attached to a ceramic

substrate and interconnected by means of either

metallization pattern or wire boards.

2.It is used for adopt less applications

3. Cost wise is slightly higher compared to

3. What are the basic processes involved in fabricating ICs using planar

technology?(Nov/Dec 2011)

1. Silicon wafer (substrate) preparation

2. Epitaxial growth

3. Oxidation

4. Photolithography

5. Diffusion

6. Ion implantation

7. Isolation technique

8. Metallization

9. Assembly processing & packaging

4. List out the steps used in the preparation of Si – wafers.

1. Crystal growth &doping

2. Ingot trimming & grinding

3. Ingot slicing

4. Wafer policing & etching

5. Wafer cleaning

5. Write the basic chemical reaction in the epitaxial growth process of pure silicon.

The basic chemical reaction in the epitaxial growth process of pure silicon is the

Hydrogen reduction of silicon tetrachloride.

SiCl4 + 2H2 = Si + 4 HCl

6. What the advantages of IC over Discrete Components (Apr/May 2015) (Nov/Dec 2014)

Mass production.

Economical due to (1) above.

Easy maintenance- being modular, ICs are use and throw.

Less power consumption being small in size.

Smaller space. Decreased circuit board size.

Even complex circuit enclosed in a small chip making it deceptively easy to use

7. What are the two important properties of SiO2?

1. SiO2 is an extremely hard protective coating & is unaffected by almost all reagents except

by hydrochloric acid. Thus it stands against any contamination.

2. By selective etching of SiO2, diffusion of impurities through carefullydefined

Windows in the SiO2 can be accomplished to fabricate various components.

8. What is meant by oxidation?(Apr/May 2010)

The silicon wafers are stacked up in a quartz boat & then inserted into quartz furnace tube.

The Si wafers are raised to a high temperature in the range of 950 to 1150Oc & at the same

time, exposed to a gas containing O2 or H2O or both. The

chemical action is

Si + 2H2O = SiO2+ 2H2

9. What are the advantages of Molecular Beam Epitaxy ( MBE )?

( i ) It is a low temperature process, useful for VLSI. This minimizes out diffusion & auto

doping. ( ii ) It allows precise control of doping & permits complicated profiles to be generated. ( iii ) Linear doping profile desirable for varactor diode in FM , can be obtained with MBE.

( iv ) Wider choice of dopants can be used.

10. What are the process involved in crystal growth and wafer preparation?

(i) Silicon crystal ingots growing

(ii) Ingot trimming and grinding

(iii) Ingot slicing

(iv) Wafer etching

(v) Wafer polishing

(vi) Wafer cleaning

11. Name the material used for fabrication of IC.

Silicon, germanium and gallium arsenide

12. What is lithography? (Nov/Dec 2010)(Apr/May 2017)

Lithography is a process by which the pattern appearing on the mask is transferred to the

wafer. It involves two steps: the first step requires applying a few drops of photoresist to the

surface of the wafer & the second step is spinning the surface to get an even coating of the

photoresist across the surface of the wafer.

13. What are the two processes involved in photolithography?

a) Making a photographic mask

b) Photo etching

14. What is the significance of using buried layer?(May/June 2012)

In general bipolar integrated circuits use epitaxial layer process in which high resistivity epitaxial

is formed over a low resistivity substrate. To provide isolation between the epitaxial growth and

the substrate, the doping used in both layers is of opposite type. Due to this a heavily doped buried

layer is formed. The buried layer is also called diffusion layer.

15. Distinguish between dry etching & wet etching.

Dry etching

1. Gaseous mixture is used as the chemical reagent.

2. Smaller line openings ( 1μm) are possible with dry etching.

3. It produces straight walled etching process.

Wet etching

1. Chemical reagents used are in the liquid form.

2. Line opening is larger. (> 1μm)

3. It produces patterns with undercutting.

16. Why inductors are difficult to fabricate in integrated circuits. (Nov/Dec 2012)(May/June

2013)

No satisfactory integrated inductors exist. If high Q inductors with inductance of values larger

than 5μH are required, they are usually supplied by a wound inductor which is connected

externally to the chip. Therefore, the use of inductors is normally avoided when integrated circuits

are used.

17. What are isotropic & anisotropic etchings processes?

Isotropic etching is a wet etching process which involves undercutting. A isotropic

etching is a dry etching process which provides straight walled patterns.

18. Define diffusion.

The process of introducing impurities into selected regions of a silicon wafer is called

diffusion. The rate at which various impurities diffuse into the silicon will be of the order of

1μm/hr at the temperature range of 900oC to 1100oC .The impurity atoms have the tendency to

move from regions of higher concentrations to lower concentrations.

19. What is meant by ion implantation?(Nov/Dec 2011) (Nov/Dec 2012) (Apr/May 2015)

The conductivity of the semiconductor increases when small impurity is added to it. The process of

adding impurity is called doping while the impurity to de added is called dopant.so ion

implantation is a process of adding dopant to the silicon substrate. The ion implantation process is

controllable, reproducible and also there are no unwanted side effects.

20. State the Limitations of IC Technology (Nov/Dec 2016)

1. Coils or indicators cannot be fabricated.

2. It can be handle only limited amount of power.

3. High grade P-N-P assembly is not possible.

4. It is difficult to be achieved low temperature coefficient.

5. The power dissipation is limited to 10 watts.

6. Low noise and high voltage operation are not easily obtained.

7. Inductors and transformers are needed connecting to exterior to the semiconductor chip as

it is not possible to fabricate inductor and transformers on the semiconductor chip surface.

8. Inductors cannot be fabricated directly.

9. Low noise and high voltage operation are not easily obtained.

.

PART-B

1. Explain briefly the classification of Integrated Circuits.

2. Explain the principle of epitaxial growth and also the types of epitaxial processes.

3. Describe the various steps involved in the fabrication of a typical monolithic IC with neat

diagrams.

4. Explain the fabrication processes of diodes and capacitors.

5. With a neat sketch explain the following photolithography processes

6. Describe the various fabrication processes of FETs and resistors.

7. Explain the processes of oxidation and metallization.

8. Discuss the basic planar processes in IC fabrication.

9. Describe the process of crystal growth and wafer preparation

10. Describe the principle of the following process

(i) Diffusion

(ii) Photo mask generation

UNIT II

CHARACTERISTICS OF OP-AMP

PART-A

1. What is OPAMP?

An operational amplifier is a direct coupled high gain amplifier consisting of one or more

differential amplifiers, followed by a level translator and an output stage. It is a versatile device

that can be used to amplify ac as well as dc input signals & designed for computing

mathematical functions such as addition, subtraction , multiplication, integration &

differentiation

3. What are the features of differential amplifier? APRIL/MAY 2018

The various features of a differential amplifier are:

(i) High differential voltage gain

(ii) Low common mode gain

(iii) High CMRR

(iv) High input impedance

(v) Low offset voltages and current

4. List out the ideal characteristics of OPAMP?

( i )Open loop gain infinite

(ii)Input impedance infinite

(iii)Output impedance low

(iv)Bandwidth infinite

(v)Zero offset,ie,Vo=0 when V1=V2=0

5. What are the different kinds of packages of IC741?

a) Metal can (TO) package

b) Dual-in-line package

c) Flat package or flat pack

6. What are the assumptions made from ideal op-amp characteristics? NOV/DEC 2016

i) The current drawn by either of the input terminals (non-inverting/inverting) is negligible.

ii) The potential difference between the inverting & non-inverting input terminals is zero.

7. Mention some of the linear applications of op – amps:

Adder, subtractor, voltage –to- current converter, current –to- voltage converters,

instrumentation amplifier, analog computation, power amplifier, etc are some of the linear op-

amp circuits.

8. Mention some of the non – linear applications of op-amps.

Rectifier, peak detector, clipper, clamper, sample and hold circuit, log amplifier, anti –log amplifier, multiplier are some of the non – linear op-amp circuits.

9. What happens when the common terminal of V+ and V- sources is not grounded? If the common point of the two supplies is not grounded, twice the supply voltage will get

applied and it may damage the op-amp.

10. Define input offset voltage.

A small voltage applied to the input terminals to make the output voltage as zero when the two input terminals are grounded is called input offset voltage.

11. Define input offset current.

The difference between the bias currents at the input terminals of the op-amp is called as

input offset current.

12. State the reasons for the offset currents at the input of the op-amp.

The input terminals conduct a small value of dc current to bias the input transistors. Since

the input transistors cannot be made identical, there exists a difference in bias currents.

13. Define CMRR of an op-amp.

The relative sensitivity of an op-amp to a difference signal as compared to a common –

mode signal is called the common –mode rejection ratio. It is expressed in decibels.

CMRR= Ad/Ac

14. In practical op-amps, what is the effect of high frequency on its performance?

The open-loop gain of op-amp decreases at higher frequencies due to the presence of

parasitic capacitance. The closed-loop gain increases at higher frequencies and leads to

instability.

15. Define input bias current. For ideal op-amp, no current flows into the input terminals. The practical op-amps do have

some input currents which are very small, of the order of 10-6 A to 10-14 A. It is called as input bias current.

16. Mention the frequency compensation methods.

1. Dominant-pole compensation

2. Pole-zero compensation.

17. What are the merits and demerits of Dominant-pole compensation?

1. Noise immunity of the system is improved.

2. Open-loop bandwidth is reduced.

18. Define slew rate.NOV/DEC 2017

The slew rate is defined as the maximum rate of change of output voltage caused by a step

input voltage. An ideal slew rate is infinite which means that op-amp’s output voltage should

change instantaneously in response to input step voltage.

19. Drawbacks of IC 741? NOV /DEC 2017

IC741 has a low slew rate because of the predominance of capacitance present in the circuit

at higher frequencies. As frequency increases the output gets distorted due to limited slew rate.

20. What causes slew rate?

There is a capacitor with-in or outside of an op-amp to prevent oscillation. It is this

capacitor which prevents the output voltage from responding immediately to a fast changing

input.

21. Define thermal drift. The bias current, offset current & offset voltage change with temperature. A circuit

carefully nulled at 25oC may not remain so when the temperature raises to 35oC.This is called

thermal drift. Often, offset current drift is expressed in nA/ oC and offset voltage drift in mV/ oC.

22. Define supply voltage rejection ratio (SVRR)

The change in OPAMP’s input offset voltage due to variations in supply voltage is called

the supply voltage rejection ratio. It is also called Power Supply Rejection Ratio (PSRR) or

Power Supply Sensitivity (PSS).

23. What is output offset voltage?

The output voltage present when both the input terminals of the op-amp are grounded is called output offset voltage.

24. Write the applications of practical integrator.

(i) In the analog computers.

(ii) In solving the differential equations.

(iii) In analog to digital converters.

(iv) Various signal wave shaping circuits.

(vi) In ramp generators.

25. Write the applications of practical differentiator.

(i) In the wave shaping circuits to detect the high frequency components in the signal.

(ii) As a rate-of-change detector in the FM demodulators.

PART-B

1. Discuss the DC characteristics of an Op-amp.

Current is taken from the source into the op-amp inputs respond differently to current and

2. Explain the AC characteristics of an Op-amp.

3. Describe the operation of Op-amp as Inverting amplifier and also derive the output equation.

4. Explain the operation of Op-amp as (i) Summer

5. Discuss the operation of Integrator and differentiator as also write output equation.

6. With circuit diagram derive the expression of differential amplifier.

7.. Describe the operation of Op-amp as Non-inverting amplifier and also derive the output

equation.

8. Describe the working of (i) V to I converter (ii) I to V converter.

PART-A

UNIT III

APPLICATIONS OF OP AMP

1. What is the need for an instrumentation amplifier?

In a number of industrial and consumer applications, the measurement of physical quantities

is usually done with the help of transducers. The output of transducer has to be amplified So

that it can drive the indicator or display system. This function is performed by an

instrumentation amplifier.

2. List the features of instrumentation amplifier:

¯ High gain accuracy

¯ High CMRR

¯ High gain stability with low temperature co-efficient

¯ Low dc offset

¯ Low output impedance

3. What is a comparator?

A comparator is a circuit which compares a signal voltage applied at one input of an op-amp

with a known reference voltage at the other input. It is an open loop op - amp with output +

Vsat.

4. What are the applications of comparator?

1. Zero crossing detectors

2. Window detector

3. Time marker generator

4. Phase detector

5. What is a Schmitt trigger? Schmitt trigger is a regenerative comparator. It converts sinusoidal input into a square wave

output. The output of Schmitt trigger swings between upper and lower threshold voltages,

which are the reference voltages of the input waveform.

6. What is a multivibrator?

Multivibrators are a group of regenerative circuits that are used extensively in timing

applications. It is a wave shaping circuit which gives symmetric or asymmetric square output.

It has two states either stable or quasi- stable depending on the type of multivibrator.

7. What do you mean by monostable multivibrator?

Monostable multivibrator is one which generates a single pulse of specified duration in

response to each external trigger signal. It has only one stable state.

8. What is an astable multivibrator?

Astable multivibrator is a free running oscillator having two quasi-stable states. Thus, there

is an oscillation between these two states and no external signals are required to produce the

change in state.

9. What is a bistable multivibrator? Bistable multivibrator is one that maintains a given output voltage level unless an external

trigger is applied. Application of an external trigger signal causes a change of state, and this

output level is maintained indefinitely until an second trigger is applied. Thus, it requires two

external triggers before it returns to its initial state

10. What are the different types of filters?

Based on functions: Low pass filter, High pass filter, Band pass filter, Band reject filter

Based on order of transfer function: first, second, third higher order filters.

Based on configuration: Bessel, Chebychev, Butterworth filters.

11. List the broad classification of ADCs.

1. Direct type ADC.

2. Integrating type ADC.

12. List out the direct type ADCs.

1. Flash (comparator) type converter

2. Counter type converter

3. Tracking or servo converter

4. Successive approximation type converter

13. List out some integrating type converters.

1. Charge balancing ADC

2. Dual slope ADC

14. What is integrating type converter? An ADC converter that perform conversion in an indirect manner by first changing the

analog I/P signal to a linear function of time or frequency and then to a digital code is known

as integrating type A/D converter.

15. What is principle of successive approximation ADC?

The circuit of successive approximation ADC consists of a successive approximation

register (SAR), to find the required value of each bit by trial & error. With the arrival of

START command, SAR sets the MSB bit to 1. The O/P is converted into an analog signal & it

is compared with I/P signal. This O/P is low or High. This process continues until all bits are

checked.

16. What are the main advantages of integrating type ADCs?

i. The integrating type of ADC’s do not need a sample/Hold circuit at the input.

ii. It is possible to transmit frequency even in noisy environment or in an isolated form.

17. Define the term conversion time.

It is defined as the total time required to convert an analog signal into its digital output. It depends on the conversion technique used & the propagation delay of circuit components.

The conversion time of a successive approximation type ADC is given by

T(n+1)

where T---clock period, Tc---conversion time, n ---no. of bits

18. Define resolution of a data converter.

The resolution of a converter is the smallest change in voltage which may be produced at

the output or input of the converter.

Resolution (in volts)= VFS/2n-1=1 LSB increment. The resolution of an ADC is defined as the smallest change in analog input for a one-bit

change at the output.

19. Explain in brief stability of a converter:

The performance of converter changes with temperature age & power supply variation. So

all the relevant parameters such as offset, gain, linearity error & monotonicity must be

specified over the full temperature & power supply ranges to have better stability

performances.

20. What is a sample and hold circuit? Where it is used? NOV/DEC 2017

A sample and hold circuit is one which samples an input signal and holds on to its last

sampled value until the input is sampled again. This circuit is mainly used in digital

interfacing, analog to digital systems, and pulse code modulation systems.

21. Define sample period and hold period. The time during which the voltage across the capacitor in sample and hold circuit is equal

to the input voltage is called sample period. The time period during which the voltage across

the capacitor is held constant is called hold period.

PART-B

1. Explain the working of instrumentation amplifier with neat circuit and also derive the

expressions.

2. Explain the operation of Log and Antilog amplifier.

3. Draw the circuit of integrator and differentiator and explain. Also derive the expressions

using Op-amp.

4. Explain the circuit of monostable multivibrator and also derive the expressions.

5. Describe in detail about A/D conversion by dual slope & successive approximation

methods.

6. Draw and explain the working of different types of clipper and clamper circuits with neat

sketches.

7. Briefly explain the following D/A converter.

a. R-2R ladder type

b. Binary weighted register type

8.Explain the following OP-Amp Application

1.Adder 2.Comparator 3.S/H Circuits 4.peak Detector

9.Explain the multivibrator and wavefor Generator

PART-A

UNIT IV

SPECIAL ICs

1. What are the applications of 555 Timer? (May/June 2012) · Astable multivibrator

· monostable multivibrator

· Missing pulse detector

· Linear ramp generator

· Frequency divider

· Pulse width modulation

· FSK generator

· Pulse position modulator

· Schmitt trigger

2. List the applications of 555 timers in monostable mode of operation.

*missing pulse detector

*Linear ramp generator

*Frequency divider

*Pulse width modulation.

3. List the applications of 555 timers in Astable mode of operation:

*FSK generator

*Pulse-position modulator

4. Define 555 IC?

The 555 timer is an integrated circuit specifically designed to perform signal generation and

timing functions.

5. List the basic blocks of IC 555 timer.

· A relaxation oscillator

· RS flip flop

· Two comparator

· Discharge transistor.

6. List the features of 555 Timer?

· It has two basic operating modes: monostable and astble

· It is available in three packages. 8 pin metal can , 8 pin dip, 14 pin dip.

· It has very high temperature stability.

7. Define duty cycle?

The ratio of high output and low output period is given by a mathematical parameter called

duty cycle. It is defined as the ratio of ON Time to total time.

8. Define VCO.

A voltage controlled oscillator is an oscillator circuit in which the frequency of oscillat ions can be controlled by an externally applied voltage.

9. List the features of 566 VCO.

· Wide supply voltage range (10-24V)

· Very linear modulation characteristics

· High temperature stability

10. What is meant by PLL? A PLL is a basically a closed loop system designed to lock output frequency and phase to

the frequency and phase of an input signal.

11. Define lock range.

When PLL is in lock, it can trap frequency changes in the incoming signal. The range of

frequencies over which the PLL can maintain lock with the incoming signal is called as lock

range.

12. Define capture range. (Nov/Dec2011) The range of frequencies over which the PLL can acquire lock with the input signal is

called as capture range.

13. Define pull-in time.

The total time taken by the PLL to establish lock is called pull-in time.

14. List the applications of 565 PLL.

· Frequency multiplier

· Frequency synthesizer

· FM detector

15. What is IC AD 633?

The versatility of the AD633 is not compromised by its simplicity. The Z input provides access to

the output buffer amplifier, enabling the user to sum the outputs of two or more multipliers,

increase the multiplier gain, convert the output voltage to a current, and configure a variety of

applications.

16. Why VCO is called voltage to frequency converter (Nov/Dec 2012)

A voltage-controlled oscillator (VCO) is one in which the frequency of oscillations varies as a

function of voltage. The same circuit is also called a voltage-to-frequency converter (VFC)

because a given voltage gives rise to a specific frequency.

17. What are th e basic blocks in a PLL IC?

It is basically a flip flop consisting of a phase detector, a low pass filter (LPF),and a Voltage

Controlled Oscillator (VCO).

18. Applications of analog multiplier

• rectification,

• modulation,

• demodulation,

• frequency translation,

• multiplication, and

• division.

19. Draw the IC 555 timer Pin Diagram

20. a.Define pull-in time

The total time taken by the PLL to establish lock is called pull-in time.

b.What is the use of LPF used in PLL?

The LPF removes the high frequency components and noise , and also controls the dynamic

characteristics of the PLL. These characteristics include capture and lock range bandwidth and

transient response.

PART-B

1. Explain the function of monostable multivibrator using IC 555 timer with neat diagrams and

also derive the frequency of oscillation.

2. Explain with a neat sketch how IC 555 can be used as Astable multivibrator.

3. With block diagram explain the functions and working of IC 566 voltage controlled oscillator.

4. With relevant diagrams explain about IC 565 phase locked loop in detail.

5. Discuss the applications of IC 555 timer.

6. Discuss the various application circuits of phase locked loop IC 565 in detail.

7. Explain the functions of analog multiplier IC AD633 and also discuss any one application.

8. Explain with a neat sketch how IC 555 can be used Monostable multivibrator.

9. Explain with a neat sketch how IC 555 can be used as BIstable multivibrator.

PART-A

UNIT V

APPLICATION ICs

1. What is a voltage regulator?

A voltage regulator is an electronic circuit that provides a stable dc voltage independent of

the load current, temperature, and ac line voltage variations.

2. Give the classification of voltage regulators:

*Series / Linear regulators

*Switching regulators.

3. What is a linear voltage regulator?

Series or linear regulator uses a power transistor connected in series between the

unregulated dc input and the load and it conducts in the linear region .The output voltage is

controlled by the continuous voltage drop taking place across the series pass transistor.

4. What is a switching regulator?

Switching regulators are those which operate the power transistor as a high frequency

on/off switch, so that the power transistor does not conduct current continuously. This gives

improved efficiency over series regulators.

5. What are the advantages of IC voltage regulators?

*low cost

*high reliability

*reduction in size

*excellent performance

6. Give some examples of monolithic IC voltage regulators:

78XX series fixed output, positive voltage regulators 79XX series fixed output, negative voltage regulators

723 general purpose regulators.

7. What is the purpose of having input and output capacitors in three terminal IC

regulators?

A capacitor connected between the input terminal and ground cancels the inductive effects due to long distribution leads. The output capacitor improves the transient response.

8. Define line regulation.

Line regulation is defined as the percentage change in the output voltage for a change in

the input voltage. It is expressed in mill volts or as a percentage of the output voltage.

9. Define load regulation.

Load regulation is defined as the change in output voltage for a change in load current. It is

expressed in mill volts or as a percentage of the output voltage.

10. What is meant by current limiting? Current limiting refers to the ability of a regulator to prevent the load current from

increasing above a preset value.

11. Give the drawbacks of linear regulators.

*The input step down transformer is bulky and expensive because of low line frequency.

*Because of low line frequency, large values of filter capacitors are required to decrease the

ripple.

*Efficiency is reduced due to the continuous power dissipation by the transistor as it operates

in the linear region.

12. What are the advantages of switching regulators?

*Greater efficiency is achieved as the power transistor is made to operate as low impedance

switch. Power transmitted across the transistor is in discrete pulses rather than as a steady

current flow.

*By using suitable switching loss reduction technique, the switching frequency can be

increased so as to reduce the size and weight of the inductors and capacitors.

13. Define ripple rejection with respect to voltage regulators.

Power supply ripple rejection ratio (PSRR) is a measure of how well a circuit rejects ripple

coming from the input power supply at various frequencies and is very critical in many RF and

wireless applications.

14. Why do switching regulators have better efficiency then series regulators?

(May/June 2012)

In switching regulators, the transistor is operated in cut off region or saturation region. In cut off

region, there is no current and hence power dissipation is almost zero. In the saturation region

there is negligible voltage drop across it hence the power dissipation is almost zero.

15. Name the various protection circuits used for voltage regulators. (Nov/Dec 2012)

1. Constant current limiting

2. Fold back current limiting

3. Over voltage prodection

4. Thermal prodection

16. What is the principle of switch mode power supplies. (May/June 2013)

A switched-mode power supply (switching-mode power supply, SMPS, or switcher) is an electronic

power supply that incorporates a switching regulator to convert electrical power efficiently. Like other

power supplies, an SMPS transfer’s power from a source, like mains power, the pass transistor of a

switching-mode supply continually switches between low-dissipation, full-on and full-off states, and

spends very little time in the high dissipation transitions, which minimizes wasted energy. Ideally, a

switched-mode power supply dissipates no power.

17. List the important parts of regulated power supply. (April/May2010) 1. Reference voltage circuit

2. Error amplifier

3. Series pass transistor

4. Feedback network

18. What are the disadvantages of linear voltage regulators? (Nov/Dec2011)

The input step down transformer is bulky and expensive because of low line frequency. Because of

low line frequency, large values of filter capacitors are required to decrease the ripple. Efficiency is

reduced due to the continuous power dissipation by the transistor as it operates in the linearregion.

19. what is the use of Function generators or Signal wave generators

i) To test an electrical or electronic circuit.

ii) To generate periodic signals.

iii) For computers and control system it woks as a timer.

20. what is function voltage regulator (May/June 2013)

regulator circuit is a circuit used after the filter, which not only makes the dc voltage smooth and

almost ripple free but also keeps the dc output voltage constant though input dc voltage varies under

certain condition. Thus input to a regulator is an unregulated dc voltage while the output of a

regulator is a regulated dc voltage, to which the load is connected.

PART-B

1. Describe the working of IC 723 voltage regulator with neat diagram and also writethe

features.

2. Draw the basic switching regulator block diagram and explain the function of each block.

3. Draw and explain the functional block diagram of the LM 317 three terminal adjustable

regulators.

4. Describe the operation of simplified circuit for ICL 8038 function generator

5. Explain the AD623 Instrumentation Amplifier and its application for weight measurement

6. Explain about SMPS with block diagram

Subject Name: Measurements and Instrumentation

Faculty Name: Dr.P.ELAMURUGAN Book: Gnanavadivel

TWO MARK & 16 MARK QUESTIONS & ANSWERS

UNIT-I INTRODUCTION 1. Give the methods of obtaining experimental data.

1. Direct method 2. Indirect method

2. List out the dynamic characteristics of any measurement system.

1. Step change 2. Linear change 3. Sinusoidal change

4. Speed of response

5. Lag 6. Fidelity

7. Dynamic error.

3. What are the types of errors in measurement?

Instrumental errors, Limiting errors, Environmental errors.

4. What are the static characteristics of an instrument? The static characteristics of an instrument are considered for instruments which are used to measure

an unvarying process condition. All the static performance characteristics are obtained by one form or

another o a process called calibration.

5. What is a standard? A standard is a physical representation of a unit of measurement. A known accurate measure of

physical quantity is termed as standard.

Types:

International standards

Primary standards

Secondary standards

Working standards.

6. What is primary sensing element?

The primary sensing element is called as transducer that senses and converts the desired input to a more convenient and practicable form to be handled by the measurement system.

7. What is calibration?

Calibration is the process of checking the accuracy of instrument by comparing the instrument reading with a standard or against a similar meter of known accuracy. It is also defined as a marking the

scale of an instrument.

8. Define arithmetic mean. The average value, or arithmetic mean value, is the most probable value obtained from a series of

reading of a given quantity. As a general rule, the more readings, the more closely the computer average represents the most probable value. The average value X is calculated by taking the sum of all the reading

and dividing by the number of readings, so that

X=∑xi x1+x2+x3+…+xn

n n

Where X=the average value or arithmetic mean. Xi = the value of the ith reading.

N = the number of readings.

9. Define variance.

The variance is the mean square deviation, which is the same as standard deviation, except that

square root is not extracted.

V= (SD)2

=d2+d22+d2

3+…d2

N

=∑d2

n 10. Define standard deviation.

The standard deviation or root mean square deviation of a sample is both mathematically more

convenient and statistically more meaningful for analyzing grouped data than is the average deviation. By

definition, the standard deviation of a sample is given by

S ∑(X-xi)2

√ n √ n

11. Define average deviation. The mean or average is a measure of how much the data is dispersed, or varies from the average

value. The mean D is calculated by adding all the absolute values of deviations of a set of measured values

and dividing this sum by the number of observation ‘n’, so that

D = d + d2 + … dn

n

n

12. Define the terms précising and sensitivity.

Precision:

It is a measure of the consistency or repeatability of a series (successive) of measurements. Although accuracy implies precision, precision does not necessarily accuracy. A precise instrument can be very inaccurate. The precision of a given measurement can be given by

Precision =1- xi -X

xi

Where xi = the value of the ith measurement X=the average value of a measurements.

Sensitivity: It is a measure of the change in reading of an instrument for a given change in the measured

quantity.

13. Define static error. The static error of a measuring instrument is the numerical difference between the value of a

quantity and its value as obtained by measurement, i.e., repeated measurement of the same quantity gives

different indications.

14. Distinguish re-predictability and repeatability.

Reproducibility:

It is defined as the degrees of closeness with which a given value may be repeatedly measured. It is specified in terms of unit for a given period of time. Perfect reproducibility means that the instrument has

no drift.

=∑ di

∑d 2 1

n

Repeatability:

It is defined as variation of scale reading and is random in nature.

15. Define dynamic response of an instrument.

The behaviour of the instrument when inputs very with time (i.e., inputs are dynamic in nature) and

so does the output, is called dynamic response of an instrument or system.

16. What are the different calibration methodologies?

1. Primary calibration 2. Secondary calibration

(a) Direct calibration

(b) Indirect calibration

17. Define limiting errors.

Instruments having analog meters are usually guaranteed to be accurate within certain percentage

limits, called limiting errors or guarantee errors.

18. Define median.

The middle value of a set of an odd number of readings, if variables are arranged in numerical order, is called median.

19. Mention any four static characteristics of measurement instruments. 1. Accuracy.

2. Precision

3. Sensitivity

4. Resolution 5. Error

20 What is the significance of calibration? All measuring instruments are to prove themselves their ability to measure reliably and accurately.

For this, the results of measurement are to be compared with higher standards which are traceable to

national or international standards. The calibration of a measuring instrument means introducing an accurately known sample of the

variable that is to be measured and then observing the system’s response.

21. Why do instruments to be calibrated? Instruments must be calibrated since it gives the opportunity to check the instrument against a

known standard and subsequently to find errors and accuracy.

22. Define the term, accuracy.

It is a measure of the closeness with which an instrument measures the true value of a quantity.

23. List the main functional elements used in most of the measurement systems.

1. Primary sensing element. 2. Variable conversion element.

3. Variable manipulation element. 4. Data transmission element. 5. Data presentation element.

24. Distinguish between accuracy and precision.

Accuracy Precision

Accuracy refers to degree of Closeness of the

measured value to the true value.

Precision refers to degree of agreement among

group of Readings.

Accuracy gives the maximum error that is

maximum departure of the final result from its true

value.

Precision of a measuring system gives its capability

to reproduce a certain reading with a given

Accuracy

UNIT-II ELECTRICAL AND ELECTRONIC INSTRUMENTS

1. What is the working principle of wattmeter employed in measuring equipment?

A wattmeter consists of two coils namely, current coil and pressure coil. The current coil is

connected in series with the load and it will measures the current flowing through the load whereas

the voltage coil is connected across the load and it will measures voltage across the load. The

deflecting torque of the moving coil (pressure coil) is directly proportional to the current flowing

through the load, voltage across the load and the power factor of the load

Single phase power, P=VI cos Φ

Where, V Voltage across the load.

I Current flowing through the load

cosO Power factor of the load.

2. How are the analog instruments classified on the basis of method used for comparing the known

quantity?

(i) Electrostatic type instruments.

(ii) Electromagnetic type instruments.

(iii) Instruments using magnetic effect.

(iv) Instruments using heating effect.

(v) Instruments using Hall Effect.

3. Give the advantages of moving iron meters.

Various advantages of moving iron instruments are,

The same instrument can be universally used for both A,C and D,C measurement.

Torque/weight ratio is very high and hence errors due to friction are very small.

As the single moving system can be used for wide range of measurement, this

instrument, are cheaper than other types of instruments.

These instruments are robust and simple in construction as there are no current

carrying moving parts.

These instruments are highly accurate.

They are available with 240˚circular scales.

4. What are the different methods of measurement of frequency in the power frequency range?

Mechanical resonance type/vibrating reed type frequency meter.

Electrical resonance type/ferrodynamic type frequency meter.

Weston type frequency meter.

5. Why it is necessary to make the potential coil circuit purely resistive in wattmeters?

The inductance of the potential coil can cause error in wattmeter measurement. Hence the

inductance of the potential coil is compensated by a capacitance thus making the potential coil

circuit purely resistive in nature.

6. What are the advantages of digital instruments over analog instruments?

Highly accurate reading can be taken

Better resolution

High input impedance

Digital display eliminates observational errors, interpolation errors and parallax

errors committed by operators.

Reading speed is very high.

Digital output can be directly recorded.

Portable.

They can be used for the measurement of quantities like current, impedance,

capacitance, temperature, pressure etc.

7. How are resistors checked using digital multimeters?

For the measurement of various ranges of resistances, ohms convertor is used which is

nothing but a low current source. A known current from the low current source is passed through

the unknown resistance and the voltage drop across the resistance is measured. This voltage drop

gives the direct indication of the unknown resistance.

8. What is auto ranging?

Auto ranging is the process of changing the range of the digital voltmeter for getting a

reading with the optimum resolution under all the circumstances.

9. Define resolution of DVM?

Resolution of DVM is given by,

R=1/10n

Where, R=resolution of DVM. N=number of full digits in a digital display For a 4.5 digit display, n=4 and hence

R=1/104=0.0001 or 0.001%

10. What is volt ampere hour and watt-hour?

Volt ampere hour is the reactive power consumed by the load whereas watt-hour is the real

power consumed by the load.

11. What is the need to evaluate phase-angle error is instrument transformers?

The main condition to be satisfied by the instrument transformer is, that the phase angle of

the secondary (V or I) must be displaced exactly by 180˚ from that of primary

Parameter (V or I). If this condition is not satisfied, heavy phase angel error will occur in the

measurement using instrument transformer, Hence this phase angle error should be reduced to

minimum and its value should be evaluated and included in the measuring quantity to get highly

accurate measurement.

12. What is the purpose of instrument transformers?

The transformers used in conjunction with the measuring instruments for measuring very

large values of current or voltage which cannot be directly measured are called instrument

transformers. Two types of instrument transformers are

o Current transformer and

o Voltage transformer/potential transformer.

13. What are the various types of Digital Voltmeters?

DVM

Non integrating type integrating type

V4 converter

type

Linear type

Staircase

Type

Potentiometric

type

Dual slope

Integrating type

14. Give the importance of iron loss measurement.

Iron loss is the loss of power due to hysteresis and eddy currents. Knowledge of iron loss in

ferromagnetic materials is important to design an apparatus made up of ferromagnetic material.

15. What is the reason for using MI instruments on both A.C and D.C? MI instruments can be used for both A.C and D.C measurement because, whatever may be the

direction of the current through the coil in the instrument, the iron vanes get magnetized and there

will be a force of attraction in the attraction type instrument will be a force of repulsion in the

repulsion type instrument.

16. What is the precaution to be followed while using current transformer?

A transfer instrument is one that may be calibrated with a d.c source and then used to measure A.C without any modification. Example for transfer instrument is electrodynameter type instruments.

17. Why the PMMC instruments are not used for a.c measurements?

When the PMMC instruments are connected to a.c, the torque reverses as the current reverses and the pointer cannot follow the rapid reversals. Hence the deflection corresponding to mean

torque is zero thus making the PMMC instruments not suitable for a.c. measurements.

18. State the principle of digital phase meter. When two signals of same frequency, whose phase difference is to be measured are applied

to the phase meter, the signal are converted to a square waveform without changing the phase

relationship using two separate preamplifier and attenuator block. The converted square pulses are

fed to the flip flop. The function of two flip flops is that, one flip flip enables the AND gate while

the other disables it. The number of pulses allowed to pass during enabling and disabling the gate

are counted which is proportional to the phase difference between the two signals.

19. Which torque is absent in energy meter? why?

In energy meter, there is no controlling torque, as the driving torque alone is enough to

cause continuous revolution of the disc.

20. What are the sources of errors in D.C voltage measurement? Sources of errors in D.C voltage measurements are (i)Change in resistance with time and

(ii) Change in resistance with temperature.

Servo potentiometric type

Successive potentiometric type

Null balance type

21. Define ratio Kn rated primary current

Rated Secondary current

Kn rated primary voltage

Rated Secondary voltage

For C.T and

For P.T and

UNIT – III COMPARISION METHOD OF INSTRUMENTS

1. What are the characteristics of a DC amplifier?

It may need balanced differential inputs giving a high common mode rejection ratio (CMRR)

It should have an extremely good thermal and long term stability.

2. List the merits and demerits of a DC amplifier. It is easy to calibrate at low frequencies.

It is able to recover from an overload condition unlike it’s AC counterpart.

3. Give the purpose of bridge circuits. What is the different type?

The bridge circuits are used in instrumentation systems for the measurement of resistance ,

inductance and capacitance.

Types: DC type and

AC type.

4. What are the 2 types of Wheatstone bridge?

Null type bridge

Deflection Type Bridge.

5. What are the different types of AC bridges?

AC bridge using push-pull transducers

AC bridge with push-pull inductive transducers

Inductive transducer Blumlein bridge

Capacitive transducer Blumlein bridge

6. Define slew rate

Slew rate is defined as the maximum output voltage change per unit time.

7. List the requirements of an instrumentation amplifier

Low drift

High i/p impedance

High linearity

High CMRR

High noise rejection capability

8. Give few applications of instrumentation amplifier.

The instrumentation amplifier finds increasing application in the amplification of the output

signals obtained from thermocouples, strain gauge bridge and biological electrode.

9. What is a filter?

A filter is often a frequency selective circuit that passes a specified band of frequencies and blocks

or attenuated signal of frequencies outside this band.

10. List the different types of filters.

Analog or digital filters

Passive or active filters

Audio (AF) or radio (RF) filters.

11. Specify the advantages of an active filter

Gain and frequency adjustment flexibility

No loading problem

Low cost

12. What is frequency scaling? The procedure of converting a cutoff frequency to a new cutoff frequency is called

frequency scaling.

13. What is quality factor?

The ratio of resonant frequency to bandwidth is known as the quality factor Q.

14. What is acquisition time of S/H circuit?

Acquisition time is the time required for the capacitor to charge up to the value of the input voltage

after the switch is first started.

15. Define transformer Ratio Bridge. Transformer Ratio Bridge uses a ratio transformer which is highly accurate and versatile.

Instead of conventional bridges it can replaced and it act as a ideal transformer which is having

following properties

No flux linkage

No core loss.

No resistance of winding.

16. What is mean by Electromagnetic interference?.

The interference caused by the electromagnetic waves is called Electromagnetic

interference.

17. What is mean by common mode and series mode voltages?.

The common mode voltages are those voltages which appear on both sides of a signal into

a common reference point which is generally ground.

The voltage is considered to be in series with transducer voltage is called series voltage.

18. Define input guarding.

The complete measuring or input circuit unit of a differential amplifier is placed inside a

metallic guard.

19. What are all basic requirement of A.C potentiometers?

While comparing two voltages in A.C potentiometer it is necessary to measure the potentiometer voltage accurately as A.C reference is not available in the circuit.

At all the instants of time both the voltages being compared must be equal to magnitude and phase

both.

20. Define sensitivity of Wheatstone bridge.

Sensitivity S=Deflection D/Current I

UNIT-IV STORAGE AND DISPLAY DEVICES

1. What are the different types of amplifiers used for CRO’s?

1. Vertical amplifier 2. Horizontal amplifier

2. Give the principle of LCD type display device.

LCDs are passive type display devices used for display of numeric and alphanumeric character in dot-matrix and segmental display.

When the cell is not activated, the transmittive type cell simply transmits the light through

the cell in the straight lines. In this condition, the cell will not appear bright.

When the cell is activated, the incident light is scattered forward, as the cell appears quite

bright even under high intensity light conditions.

3. Write two advantages of LED on electronic displays.

1. Low power consumption.

2. Very fast action.

3. Very small size and weight.

4. Extremely long life.

4. State the features of ink-jet printers.

1. They can print from two or four pages per minute.

2. Resolution is about 360 dots per inch; therefore better printing quality is achieved.

3. The operating cost is quite low; the only needs replacement is the ink cartridge.

4. Colour ink jet printers have flour ink nozzles with colour cyan, magneter, and yellow.

5. What are the various methods or recording data?

1. Direct recording.

2. Frequency modulated (FM recording).

3. Pulse duration modulation recording.

6. Differentiate between LED and LCD.

LED LCD

Consumes more power (in.mW) Consumes less power (in mW).

Capable of generating its own light. Requires an external of internal light source.

High cost. Low cost.

More life time. Less life time.

Colour depends on the materials Monochrome in nature.

7. In what ways line printer are advantageous over dot matrix printer?

1. Prints one line at a time.

2. Printing speed is better.

3. Printing quality is better.

8. What are the different types of magnetic recording?

1. Direct recording.

2. Frequency Modulated (FM) recording.

3. Pulse duration modulation recording.

9. What are the different materials used in LED? Also name the colours emitted.

Materials:

Gallium Arsenide phosphate

Gallium Arsenide (GaAs)

Gallium Phosphide (GaP)

Colours emitted:

Infrared, red, yellow, green.

10. What are data loggers?

The data loggers are used to automatically make a record of the readings of instruments

located at different parts of the plant.

11. What are the functions of a data logger?

The data logger is used to automatically make a record of the readings of instruments

located at different parts of the plant.

The main function is to measure electrical output from virtually any type of transducer and

log the value automatically.

12. List out the advantages and disadvantages of LCD.

Advantages:

1. Low cost.

2. Low power consumption.

3. It requires very low voltage.

Disadvantages:

1. Life time is very less compared with LED.

2. Response time is more compared with LED.

3. The occupy large area.

4. Reliability is quite low.

13. What are the advantages of LCD over LED?

1. Low cost

2. Low power consumption.

3. It requires very low voltage.

14. What is the sweeper in oscilloscope?

1. Triggered sweep.

2. Delayed sweep.

15. What is the basic operating of digital tape recording?

Digital data can be recorded and stored in magnetic tapes using a variety of techniques.

The basic principle used is to modulate the digital data in some form and then record this

modulated data in the tape.

16. Discuss the advantages and disadvantages of PDM recording.

Advantages:

1. Capable to record information simultaneously from a large number of channels.

2. Has high s/w ratio

3. Has high accuracy due the fact that it can be SD/f calibreated.

Disadvantages:

1. Limited frequency response.

2. Highly complicated electronic circuitry and therefore the reliability of system is low.

17. Define the deflection sensitivity of CRT.

The deflection sensitivity of a CRT is defined as the deflection of the screen per unit deflection voltage.

18. List out the main parts of cathode ray tube.

1. Electron gun assembly.

2. Deflection plates assemble.

3. Fluorescent screen.

4. Glass envelope.

19. What is recorder? How they are classified?

A recorder is a device that records electrical and non-electrical quantities as a function of

time classifications.

-Analog recorders

Graphic recorders

Magnetic tape recorder

Oscilloscope recorder

-Digital recorder

20. What is magnetic recorder? Magnetic recorder is a recorder which records analog data in such a manner that they can

be retrieved or reproduced in electrical form again.

21. What are the basic components of a tape recorder?

1. Recording head. 2. Magnetic tape.

3. Reproducing head. 4. Tape transport mechanism.

5. Conditioning devices.

UNIT-V TRANSDUCERS AND DATA ACQUISITION SYSTEMS

1. What is transducer? A transducer is defined as a device that receives energy from one system and transmits it to

another, often in a different form. A transducer, in general form, may be defined as a device which

energy from one form to another.

2. Mention some advantages of electrical transducers.

1. Electrical amplification and attenuation can be easily done.

2. The effects of friction are minimized.

3. Mass-intertia effects are minimized.

4. Very small power is required for controlling the electrical or electronic system.

5. The electrical output can be amplified to any desired level.

3. How the transducers are classified?

The transducer can be classified.

1. on the basis of transduction form used.

2. As primary and secondary transducers.

3. As active and passive transducers.

4. As analog and digital transducers.

5. as transducers and inverse transducers.

4. What is an active transducer?

An active transducer generates an electrical signal directly in response to the physical

parameter and does not require an external power source for its operation. Such transducers draw

energy from the system under measurement. Active transducers are also called self generating

type transducers.

5. Mention some example for active transducer.

Typical examples of active transducers are tacho-generators used for measurement of

angularvelocity, thermocouples used for measurement of temperature, piezoelectric crystal used

for measurement of force.

6. What is a passive transducer? Transducers, in which electrical parameters i.e. resistance, inductance or capacitance

changes with the change in input signal, are called the passive transducers. These transducers

require external power source for energy conversion. These transducers may draw some energy

from the system under measurement. Typical examples are strain gauges, thermistors etc.

7. What is an analog transducer?

Analog transducer converts input signal into output signal, which is a continuous function

of time such as thermistors, strain gauge, LVDT, thermocouple.

8. What is a digital transducer?

Digital transducer converts input signal into the output signal. Which is in the form of

pulses i.e.it gives discrete output.

9. What is an inverse transducer?

It is defined as a device which converts an electrical quantity into a non-electrical quantity.

10. Give the factors to be considered in selecting a transducer.

1. Operating range

2. Sensitivity.

3. Electrical output characteristics

4. Environmental conditions.

5. Errors

6. Accuracy

11. Define strain gauges.

The strain guage is an example of a passive transducer that uses the variation in electrical

resistance in wires to sense the strain produced by a force on the wires.

12. Define gauge factor.

The gauge factor is defined as the ratio of per unit change in resistance to per unit change

in length.

Gauge factor Gf=R/R

L/L

13. Mention the different types of strain gauges.

The strain gauges are mainly of four types namely

1. Wire strain gauges

2. Foil strain gauges

3. Thin film strain gauges

4. Semiconductor strain gauges

14. What are thermistors?

Thermistors (thermally sensitive res IS TOR) are non-metallic resistors (semiconductor

material) made by sintering mixtures of metallic oxides such as manganese, nickel, cobalt, copper

and uranium. Thermistors have a Negative temperature coefficient (NTC) i.e.,resistance decreases

as temperature rises.

15. Mention some applications of thermistors.

Applications of Thermistors:

1. Measurement of temperature.

2. Control of temperature.

3. Temperature compensation.

4. Measurement of power at high frequencies.

5. Measurement of thermal conductivity, level, flow, pressure of liquids, vacuum,

composition of gases.

16. What is an inductive transducer? An inductive transducer is a device that converts physical motion into a change in

inductance. Transducers on the variable inductance type work upon one of the following

principles.

1. Number of turns

2. Geometric configuration

3. Permeability of the magnetic material or magnetic circuits.

17. Mention some advantages of LVDT.

1. The output of LVDT is practically linear for displacements up to 5 mm. The LVDTs

have a very high range of measurement of displacement.

2. LVDT has infinite resolution as it gives step less output and it has got no mechanical

element to change output in discrete steps. Now –a-days transducers are available with the

resolution up to 1 micron.

3. LVDT has high sensitivity. It usually varies from 10 mv/mm to 40 v/mm.

4. The LVDT gives a high output and many a times there is no need for amplification.

18. Mention the applications of LVDT. LVDTs are used to measure

1. Displacement

2. Force

3. Weight

4. Pressure

5. Position

19. What is piezoelectric effect?

A piezoelectric material is one in which an electric potential appears across certain surfaces

of a crystal if the dimensions of the crystal are changes by the application of a mechanical force.

This potential is produced by the displacement of charges. The effect is reversible also i.e. if a

varying potential is applied to the proper axis of the crystal, it will change the dimensions of the

crystal thereby deforming it. This phenomenon is known as piezoelectric effect.

20. What are the materials used for piezoelectric transducers?

Common piezoelectric materials include Rochelle salt, ammonium dihydrogen phosphate

(ADP), quartz and ceramics made with barium titanate, dipotassium tartrate, potassium dihydrogen

phosphate and lithium sulfate are used in real applications.

21. List out the applications of DAS.

1. Aerospace application.

2. Biomedical field.

3. Telemetry industries.

4. Industries.

22. Mention any four types of analog to digital converter.

1. Direct type

2. Indirect type

Direct types are classified as:

1. Flash (comparator) type converter.

2. Staircase type converter.

3. Tracking or servo converter.

4. Successive approximation type converter.

Indirect types are classified as:

1. Charge balancing analog to digital converter.

2. Dual slope analog to digital converter.

23. What are the types of digital to analog converters?

1. Binary weighted resistors DAC 2. R-2Rladder 3. Inverted R-2R ladder

24. What is smart sensor?

Smart sensors are sensors with integrated electronics that can perform one or more of the

following functions.

Logic functions, Two-way communication, Make decisions.

25. Mention some applications of smart sensor.

Smart sensor also enhances the following applications:

Self calibration

Computation

Communication

Multisensing

16 MARK QUESTIONS

UNIT I

1. Explain the block diagram and functional elements of measurement system with neat diagram.

2. Classify and explain the different types of standards and errors of measurements.

3. With suitable illustrations, elaborate the significance of calibration.

4. Write a technical note on static and dynamic characteristics of instrumentation systems.

5. (i) Define accuracy and reproducibility of an instrument and explain.

(ii) Describe the primary and secondary standards in instruments.

6. A circuit was tuned for resonance by eight different students and the values ofresonant

frequency in kHZ were recorded as 532,548,543,535,531,543,and 536.Calculate (i)

Arithmetic mean (ii) Deviation (iii) Average deviation (iv) Standard deviation.

7. Describe the various modes of statistical evaluation of measurement data.

8. What are the three categories of systematic errors in the instrument and explain in detail.

9. Explain the normal or Gaussian curve of errors in the study of randomeffects.

10. Describe the functional elements of an instrument with its block diagram. Also illustrate

them with pressure gauge, pressure thermometer and D’Arsonval galvanometer.

UNIT II

1. With circuit and phasor diagram, explain the working of single phase ac energy meter.

2. (i) Obtain B-H curve of a ring specimen.

(ii) Describe how to obtain iron loss of a ring specimen using wattmeter.

3. With a neat sketch explain the working principle of PMMC instrument. Also derive the

expression for deflection.

4. Explain the construction and its working principle of electrodynamometer type wattmeter.

5. Discuss in detail, about the working principle and characteristics of CT with itsphasor

diagram.

6. Write short notes on (i) Current transformer (ii) Weston frequency meter.

7. Explain the functions three phase wattmeter.

8. Draw and explain the circuit diagram of digital frequency meter.

9. Explain with a neat diagram the working of successive approximation type digital voltmeter.

10. Describe the construction functioning of mechanical type (vibrating reed type) frequency

meter.

UNIT III

1. With a circuit diagram, explain the principle of operation of Duo-range DC Potentiometer.

2. Draw a neat diagram of Kelvin double bridge and explain how to measure low resistance.

3. Obtain an expression for measurement of inductance using Maxwell’s Inductance bridge with

a neat circuit diagram.

4. Explain the theory and working principle of Wheatstone’s bridge . Derive the relation for

finding unknown resistance.

5. Describe any one method for the measurement of high resistance.

6. Explain how the inductance is measured in terms of known capacitance using Maxwell’s

bridge. Derive the condition for balance.

7. Explain the following (i) Grounding techniques (ii) Causes of electromagnetic interferences in

measurements.

8. Explain how wein bridge used for frequency measurement wit neat circuit diagram. Also

derive the suitable expression.

9. Discuss the effects of electrostatic and electromagnetic interference in instruments.

10. Explain the construction of Anderson’s bridge. Derive the unknown quantities at balance

conditions. Also write it’s advantages and disadvantages.

UNIT IV

1. Describe the construction and working of magnetic tape recorder.

2. With a block diagram, explain the working of digital CRO.

3. Draw a neat block diagram of X-Y recorder and describe its working.

4. Explain the principle and working of CRT display with a neat diagram.

5. Compare and contrast the construction, working principle and applications of LED and LCDs.

6. Write a detailed note on Data loggers. Explain how they differ from Data Acquisition systems.

7. Write a detailed technical note on dot matrix display.

8. Explain in detail, how the data is stored in a magnetic disk and tape?

9. Describe the pulse duration modulation as used in magnetic tape recording and explain its

merits and demerits.

10. Describe the mesh storage technique used in storage oscilloscope.

UNIT V

1. Describe the construction and working of potentiometer type resistance transducer for

measuring linear displacement.

2. Explain the working of D/A converter with a neat diagram.

3. What is called Piezo electric transducer? Explain its working with a diagram.

4. Explain how to measure pressure using capacitive type transducer.

5. Describe in detail, the working principle of capacitive microphones.

6. Write a detailed note on smart sensors. Explain also the various built in features of them

compared to conventional sensors.

7. Detail the construction and working principle of linear variable differential transformer

(LVDT).

8. Discuss the successive approximation type ADC with its characteristics.

9. Explain the principle of the following transducers (i) Thermistors (ii) LVDT

10. How is differential output taken from an inductive transducer? Discuss in detail.

Subject Name:Control Systems

Faculty Name:Mr.R.ARUNKUMAR

TWO MARKS WITH ANSWER

UNIT I

1. Define System.

A system is a combination or an arrangement of different physical components which act together as an entire unit to achieve certain objective.

2. Define Control system.

To control means to regulate, to direct or to command. Hence a control system is an arrangement of different physical elements connected in such a manner so as to regulate, direct or command itself or some other system.

3. Define Plant.

The portion of a system which is to be controlled or regulated is called the plant or the

process.

4. Define Controller.

The element of the system itself or external to the system which controls the plant or the

process is called controller.

5. Define Input.

It is an applied signal or an excitation signal applied to a control system from an external energy

source in order to produce a specified output.

6. Define Output.

It is the particular signal of interest or the actual response obtained from a control system when

input is applied to it.

7. Define disturbance.

Disturbance is a signal which tends to adversely affect the value of the output of a system.

8. Define internal disturbance.

If such a disturbance is generated within the system itself, it is an internal disturbance.

9. Define external disturbance.

The disturbance generated outside the system acting as an input to the system in addition to its normal input, affecting the output adversely is an external disturbance.

10. Write any four major classification of control system.

1. Open loop and closed loop control system.

2. Time varying and time-invariant system.

3. Linear and nonlinear system.

4. Lumped parameter and distributed parameter control system.

11. What is mean by Principle of superposition?

Principle of superposition means the response to several inputs can be obtained by

considering one input at a system and the algebraically adding the individual results.

12. What is mean by Deterministic control system?

A control system is said to be deterministic when its response to input as well as behaviour to

external disturbance is predictable and repeatable.

13. Write short notes about SISO and MIMO.

A system having only one input and one output is called single input and single output

system. Some systems may have multiple input and multiple outputs, these are called

multiple input and multiple output systems.

14. Define Open loop system.

A system in which output is dependent on input but controlling action is totally

independent of the output or changes in input of the system, is called an open loop system.

15. Define closed loop system.

A system in which controlling action or input is somehow dependent on the output or

changes in output is called closed loop system.

16. Write any four advantages of open loop system.

1. Such systems are simple in construction.

2. Very much convenient when output is difficult to measure.

3. Such systems are easy when maintenance point is view.

4. Such systems are economical.

17. Write any four disadvantages of open loop system.

1. Such systems are inaccurate and unreliable because accuracy of such system is totally

dependent on the accurate precalibration of the controller.

2. Such systems give inaccurate results if there are variations in the external environment.

3. Similarly they cannot sense internal disturbances in the system, after the controller stage.

4. To maintain the quality and accuracy, recalibration of the controller is necessary, time to

time.

18. Give any four real time application of open loop system.

1. Sprinkler used to water a lawn.

2. Stepper motor positioning system.

3. Automatic toaster system.

4. Traffic light controller.

19. Give any four real time application of closed loop system.

1. Human being.

2. Home heating system.

3. Ship stabilization system.

4. Voltage stabilizer.

20. Define feedback.

Feedback is a property of the system by which it permits the output to be compared with the

reference input to generate the error signal based on which appropriate controlling action can be

decided.

21. What are called feedback systems?

Systems in which the effect of the disturbance must show up in the error before the

controller can take proper corrective action are called feedback systems.

22. Define Laplace Transform.

The Laplace transform is defined as below,

Let f (t) be a real function of a real variable t defined for t>0, then α

F(s) =L [f (t)] = f (t).e−st dt 0

Where F (s) is called Laplace transform of f (t). And the variable ‘s’ which appears in F(s) is

frequency dependent complex variable. It is given by,

s = σ + jω Where σ =real part of complex variable ‘s’.

ω = Imaginary part of complex variable ‘s’.

22. Define Linearity of Laplace transform.

The transform of a finite sum of time functions is the sum of the Laplace transforms of the

individual functions.

So if F1(s), F2(s), ……, Fn(s) are the laplace transforms of the time functions f1 (t), f2(t),……, fn(t) respectively then, Lf1(t)+f2(t)+…..+fn(t)=F1(s)+F2(s)+……Fn(s).

24. Define scaling Theorem.

If K is a constant then the Laplace transform of k(t) is given as K times the Laplace transform of f(t).

L [K f (t)] =K F(s) where K is constant.

25. Define Real translation or shifting theorem.

This theorem is useful to obtain the Laplace transform of the shifted or delayed function of

time.

If F(s) is the Laplace transform of f (t) then the Laplace transform of the function delayed by

time T is

L f (t-T) =e-Ts

F(s).

25. Define Initial value theorem.

The Laplace transform is very useful to find the initial value of the time function f (t). Thus if F(s)

is the Laplace transform of f (t) then,

f (0+ ) = Lim f (t) = Lim sF(s) . t→0

+ s→α

The only restriction is that f (t) must be continuous or at the most, a step discontinuity at

t=0.

27. Define Final value theorem.

The Laplace transform is very useful to find the final value of the time function f (t). Thus if F(s)

is the Laplace transform of f (t) then,

Lim f (t) = Lim sF(s) . t→α s→0

The only restriction is that the roots of the denominator polynomial of F(s) i.e. poles of F(s) have

negative or zero real parts.

28. What is called Transfer function?

The effect of system parameters, role of system parameters in the performance of system can be expressed as ratio of output to input. Mathematically such a function explaining the effect of such parameters on input to produce output is called transfer function.

29. Define Transfer function.

Mathematically it is defined as th ratio of laplace transform of output (response) of the system to the laplace transform of input (excitation or driving function), under the assumption that all initial conditions are zero.

30. Define impulse function.

The impulse function is defined as,

F (t) = A for t=0

= 0 for t=0

30. Define poles of a transfer function.

The values of ‘s’, which make the T.F. infinite after substitution in the denominator of a T.F. are called ‘Poles’ of that T.F.

32. Define characteristic equation of a transfer function.

The equation obtained by equating denominator of a transfer function to zero, whose roots are the poles of that transfer function is called characteristic equation of that system.

F(s) = b0sn+b1s

n-1+b2s

n-2+…… + bn = 0 is called the characteristic equation.

33. Define Zero of a transfer function.

The value of ‘s’ which make the T.F. zero after substituting in the numerator are called

‘zeros’ of the T.F.

34. Define order of a transfer function.

The highest power of ‘s’ present in the characteristic equation i.e. in the denominator polynomial of a closed loop transfer function of a system is called ‘order’ of a system.

35. What is the basic concept of block diagram representation?

If a given system is complicated, it is very difficult to analyse it as a whole. With the help of

transfer function approach, we can find transfer function of each and every element of the

complicated system. And by showing connection between the elements, complete system can be

splitted into different blocks and can be analyzed conveniently. This is the basic concept of

block diagram representation.

36. Define Pole Zero plot. Plot obtained by locating all poles and zeros of a T.F. in s-plane is called pole-zero plot of a system.

37. What is called functional block?

To draw the block diagram of a practical system, each element of practical system is

represented by a block. The block is called functional block.

38. What is called branches?

The connection between the blocks is shown by lines called branches of the block diagram. An

arrow is associated with each and every branch which indicates the direction of flow of signal

along the branch.

39. What are the basic elements of block diagram?

1. Blocks, 2. Transfer functions of elements shown inside the blocks, 3. Summing points,

4. Take off points, 5. Arrows.

40. What are the advantages of block diagram?

1. Very simple to construct the block diagram for complicated systems.

2. The function of individual element can be visualized from block diagram.

41. What are the disadvantages of Block diagram?

1. Block diagram does not include any information about the physical construction ofthe

system.

2. Source of energy is generally not shown in the block diagram. So number of different block diagrams can be drawn depending upon the point of view of analysis. So block diagram for given system is not unique.

42. What is simple or canonical form of closed loop system?

A block diagram in which, forward path contains only one block, one summing point and one take off point represents simple or canonical form of a closed loop system.

43. What is called signal flow graph representation?

The graphical representation of the variables of a set of linear algebraic equations

representing the system is called signal flow graph representation.

44. Write about branches?

All the dependent and independent variables are represented by the nodes. The relationships between various nodes are represented by joining the nodes as per the equations. The lines joining

the nodes are called branches.

45. What are called nodes of a graph?

As variables are important elements of the set of equations for the system, these are represented

first in signal flow graph by small circles called nodes of signal flow graph. Each node represents a separate variable of the system.

46. Define forward path.

A path from the input to output node is defined as forward path.

47. Define Source node source node and chain node.

The node having only outgoing branches is known as source or input node. The node having an only incoming branch is known as sink node or output node.A node having incoming and

outgoing branches is known as chain node.

48. Define feedback loop.

A path which originates from a particular node and terminating at the same node, traveling through at least one other node, with out tracing any node twice is called feedback loop.

49. Define self loop.

A feedback loop consisting of only one node is called self loop. A self loop cannot appear while

defining a forward path or feedback loop as node containing it gets traced twice which is not

allowed.

50. Define path gain and loop gain.

The product of branch gains while going through a forward path is known as path gain. This can be also called as forward path gain. The product of all the gains of the branches forming a loop is called loop gain.

51. Define dummy node.

If there exists incoming and outgoing branches both at first and last node representing input and

output variables then as per definition these cannot be called as source node or sink node. In such a

case a separate input and output nodes can be created by adding branches with gain 1. Such nodes

are called dummy nodes.

52. Define non-touching loops.

If there is no node common in between the two or more loops, such loops are said to be non-

touching loops. 53. State mason’s formula. The formula can be stated as

OverallT.F = TK ∆K .

∆

Where k= no. of forward paths

54. What are the two methods of obtaining electrical analogous network?

1. Force-voltage analogy (Direct)

2. Force-current analogy (indirect)

55. Write short notes about servomotors.

The servo system is one in which the output is some mechanical variable like position, velocity

or acceleration. Such systems are generally automatic control systems which work on the error

signals. The error signals are amplified to drive motors used in such systems. These motors used

in servo systems are called servomotors.

56. What is stepper motor?

Stepper motor is a device which transforms electrical pulses into equal increments of rotary

shaft motion called steps.

57. What is servomotor?

The motors used in automatic control systems or in servomechanism are called

servomotors. They are used to convert electrical signal into angular motion.

58. What is servomechanism? The servomechanism is a feedback control system in which the output is mechanical position (or time derivatives of position velocity and acceleration,)

UNIT II

1. Define Zero.

The zero of a function, F(s) is the value at which the function, F(s) becomes zero, Where F(s) is a function of complex variable s.

2. What is the order of a system?

The order of the system is given by the order of the differential equation governing the

system. It is also given by the maximum power of s in the denominator polynomial of transfer

function. The maximum power of s is also gives the number of poles of the system and so the

order of the system is also given by number of poles of the transfer function.

3. What is called time constant form?

Those elements are constant of system ‘K’ and poles of G(s)H(s) at origin of G(s)H(s) is

expressed in a particular form called time constant form.

4. Write any four disadvantages of static error co-efficient method.

1. Method cannot give error if inputs are other than the three standard test inputs.

2. Most of the times, method gives mathematical answer of the error as ‘0’ or infinite and hence does not provide precise value of the error.

3. Method does not provide variation of error with respect to time, which will be

otherwise very useful from design point of view.

4. The method is applicable only for stable systems

5. Define time response.

The response given by the system which is function of the time, to the applied excitation is called

time response of a control system.

6. Define transient response.

The output variation during the time, it takes to achieve its final value is called as transient response. The time required to achieve the final value is called transient period.

7. Define steady state response.

It is that part of the time response which remains after complete transient response vanishes from

the system output.

8. What is called steady state error?

The difference between the desired output and the actual output of the system is called steady

state error which is denoted as ess. This error indicates the accuracy and plays an important role

in designing the system.

9. Define step input. It is the sudden application of the signal as shown.

Mathematically it can be described as,

r(t) = A for t>=0

= 0 for t<0

10. Define ramp input.

It consist of rate of change in input i.e. gradual application of input as shown.

Magnitude of ramp input is nothing but the slope.

Mathematically,

r (t) = At for t>=0

= 0 for t<0

10. Define parabolic input.

This is the input which is one degree faster than a ramp type of input as shown.

Mathematically,

r(t) = (A/2)t2

= 0

for t >=0

for t < 0

12. Define Impulse input.

It is the input applied instantaneously (for short duration of time) of very high amplitude as

shown.

It is the pulse whose magnitude is infinite while its width tends to zero i.e. t 0, applied

momentarily.

Mathematically,

r(t) = A, for t=0

= 0, for t=0

12. Define damping ratio.

The damping ratio is defined as the ratio of actual damping to critical damping.

14. Give the expression for damping ratio of mechanical and electricalsystem.

The damping ratio of second order mechanical translational system, =B/2 MK.

The damping ratio of second order mechanical rotational system, =B/2 JK.

The damping ratio of second order electrical system, =R/2 L/C.

15. How the system is classified depending on the value of damping?

Depending on the value of damping, the system can be classified into the following four

cases

Case 1: Undamped system, =0

Case 2: Underdamped system, 0< <1

Case 3: Critically damped system, =1

Case 4: Over damped system, >1.

16. What is the importance of test signals?

The test signals can be easily generated in test laboratories and the characteristics of test

signals resembles, the characteristics of actual input signals. The test signals are used to

predetermine the performance of the system.

17. Name the test signals used in control system.

The commonly used test input signals in control system are impulse, step, ramp,

acceleration and sinusoidal signals.

18. What is weighting function?

The impulse response of system is called weighting function. It gives inverse laplace transform of system transfer function.

19. Define Pole.

The pole of a function, F(s) is the value at which the function, F(s) becomes infinite, Where F(s) is

a function of complex variable S.

20. How the system is classified depending on the value of damping.

Depending on the value of damping, the system cen be classified into the following four

cases

Case 1: Undamped system

Case 2: Under damped system

Case 3: critically damped system

Case 4: over damped system

21. What will be the nature of response of a second order system with different types of

damping? For Undamped system the response is oscillatory.

For Under damped system the response is damped oscillatory. For

Critically damped system the response is exponentially rising.

For over damped system the response is exponentially rising but the rise time will be very large.

23. What is damped frequency of oscillation?

In under damped system the response is damped oscillatory. The frequency of damped

Oscillation is given by

24. List the time domain specifications.

The time domain specifications are

1. Delay time

2. Rise time

3. Peak time

4. Maximum peak overshoot

5. Settling time.

25. Define delay time.

It is the time taken for response to reach 50% of the final value, for the very first time.

26. Define rise time.

It is the time taken for response to raise from 0 to 100% for the very first time. For under

damped system, the rise time is calculated from 0 to 100%. But for over damped system, it is the

time taken by the response to raise from 10% to 90%. For critically damped system, it is the time

taken for response to raise from 5% to 95%.

27. Define Peak time.

It is the time taken for the response to reach the peak value for the very first time (or) It is the

time taken for the response to reach peak overshoot, Mp.

28. Define Peak overshoot.

It is defined as the ratio of the maximum peak value measured from final value to final value.

Let final value= c( ), Maximum value=c(tp)

Peak over shoot, Mp=

29. Define Settling time. It is defined as the time taken by the response to reach and stay with in a specified error and the error is usually specified as % of final value. The usual tolerable error is 2% or 5% of the final value.

30. What is type number of a system? What is its significance?

The type number is given by number of poles of loop transfer function at the origin. The type number of the system decides the steady state error.

31. Distinguish between type and order of a system.

1. Type number is specified for loop transfer function but order can be specified for any transfer function. (open loop or closed loop transfer function).

2. The type number is given by number of poles of loop transfer function lying at origin of

s-plane but the order is given by the number of poles of transfer function.

32. For the system with following transfer function, determine type and order of the system.

1. Type-1, Order-4

2. Type-2, Order-4

3. Type-0, Order-2

4. Type-3, Order-5

33. What are static error constants?

The Kp,Kv and Ka are called static error constants. These constants are associated with steady

state error in a particular type of system and for a standard input.

34. Define positional error constant.

The positional error constant Kp = Lt G(s)H(s). The steady state error in type-0 system when

the input is unit step is given by 1/(1+Kp).

35. Define Velocity error constant. The Velocity error constant Kv=Lt sG(s) H(s). The steady state error in type-1 system for unit ramp input is given by 1/Kv.

36. Define acceleration error constant.

The acceleration error constant Ka=Lt s2G(s) H(s). The steady state error in type-2 system for

unit parabolic input is given by 1/Ka.

37. What are generalized error coefficients?

They are the coefficients of generalized error series. The generalized error series is given by.The

Coefficients C0,C1,C2 are called generalized error coefficient or dynamic error coefficients. The

nth coefficient, Cn=Lt dnF(s)/ds

n, Where F(s)=1/(1+G(s)H(s)).

38. Give the relation ship between generalized and static error coefficients.

The following expressions shows the relation between generalized and static error

coefficient

C0=1/(1+Kp), C1=1/Kv,C2=1/Ka.

39. Mention two advantages of generalized error constants over static error constants.

1. Generalized error series gives error signal as a function of time.

2. Using generalized error constants the steady state error can be determined for any type of the input but static error constants are used to determine steady state error when the input is anyone of the standard input.

40. What is the effect on system performance, when a proportional controller is

introduced in a system?

The proportional controller improves the steady state tracking accuracy, disturbance signal rejection and relative stability of the system. It also increases the loop gain of the system which results in reducing the sensitivity of the system to parameter variations.

41. What is the disadvantage in proportional controller?

The disadvantage in proportional controller is that it produces a constant steady state error.

42. What is the effect of PI controller on the system performance?

The PI controller increases the order of the system by one, which results in reducing, the steady

state error. But the system becomes less stable than the original system.

43. What is the effect of PD controller on the system performance?

The effect of PD controller is to increase the damping ratio of the system and so the peak

overshoot is reduced.

44. Why derivative controller is not used in control systems?

The derivative controller produces a control action based on rate of change of error signal and it

does not produce corrective measures for any constant error. Hence derivative controller is not

used in control systems.

UNIT III

1. What is frequency response?

The frequency response is steady-state output of the system, when the input is a sinusoidal

signal.

2. What are the advantages of frequency response analysis?

1. The absolute and relative stability of the closed loop system can be estimated fromthe knowledge of the open loop frequency response.

2. The practical testing of system can be easily carried with available sinusoidal

signal generators and precise measurement equipments.

3. What are the frequency domain specifications?

1. Resonant peak 2. Resonant frequency

3. Band width 4. Cut-off rate

5. Gain margin 6. Phase Margin

4. Define resonant peak?

The maximum value of the magnitude of closed loop transfer function is called resonant peak.

5. What is resonant frequency?

The frequency at which resonant peak occurs is called resonant frequency. The resonant peak is the maximum value of the magnitude of closed loop transfer function.

6. Define bandwidth?

The bandwidth is the range of frequencies for which the system gain is more than -3db.

7. What is cut-off rate?

The slope of the log-magnitude curve near the cut-off frequency is called cut-off rate.

8. Define Gain Margin?

The gain margin, kg is defined as the reciprocal of the magnitude of open loop transfer function, at phase cross over frequency,

Gain Margin, Kg=1/ |G(jw)| and when expressed in decibels it is 20 log kg.

9. Define phase Margin?

The phase margin, is that amount of additional phase lag at the gain cross-over frequency,

required to bring the system to the verge of instability. It is given by, 180+ , where is the phase

of g(jw) at the gain cross over frequency.

Phase Margin, = 180+

10. What is phase and gain cross over frequency?

The gain cross over frequency is the frequency at which the magnitude of the open loop

transfer function is unity.

The phase cross over frequency is the frequency at which the phase of the open loop transfer function is 180.

12. Write short note on the correlation between the time and frequency response? There exists a correlation between time and frequency response of first or second order

systems. The frequency domain specification can be expressed in terms of the timedomain

parameter

and .For a peak overshoot in time domain specification there is a corresponding resonant peak in frequency domain. For higher order systems there is no explicit correlation between time and frequency response.

13. What is bode plot?

The bode plot is a frequency response plot of the transfer function of a system. It consists of two plots-magnitude plot and phase plot.

The magnitude plot is a graph between magnitude of a system transfer function in db and the

frequency . The phase plot is a graph between the phase or arguments of a system transfer

function in degrees and the frequency . Usually, both the plots are plotted on a common x-axis in

which the frequencies are expressed in logarithmic scale.

14. What is approximate bode plot? In approximate bode plot, the magnitude plot of first and second order factors are approximated by

two straight lines, Which are asymptotes to exact plot. One straight line is at odb,

for the frequency range 0 to and other straight line is drawn with a slope of +20n db/dec for the

frequency range . Here is the corner frequency.

15. Define corner frequency?

The magnitude plot can be approximated by asymptotic straight lines. The frequencies

corresponding to the meeting point of asymptotes are called corner frequency. The slope of

the magnitude plot changes at every corner frequencies.

16. What are the advantages of bode plot?

1. The magnitudes are expressed in db and so a simple procedure is available to add magnitude of each term one by one.

2. The frequency domain specification can be easily determined.

17. What is the value of error the approximate magnitude plot of a first order factor at the

corner frequency?

The error in the approximate magnitude plot of a first order factor at the corner frequency is

+3mdb, where m is multiplicity factor. Positive error for numerator factor and negative error for denominator factor.

18. What is the value of error in the approximate magnitude plot of a quadratic

factor with at the corner frequency?

The error is +6db, for the quadratic factor with =1. Positive error for numerator factor and negative

error for denominator factor.

19. What is polar plot?

The polar plot of a sinusoidal transfer function g(j ) is a polar plot of the magnitude of G(j ) versus the phase angle/argument of G(j ) on polar or rectangular co-ordinates as is varied from zero to infinity.

20. What is minimum phase system? The minimum phase systems are systems with minimum phase transfer functions. In minimum phase transfer functions, all poles and zeros will lie on the left half of s-plane.

21. What are All-Pass systems?

The all pass systems are systems with all pass transfer functions. In all pass transfer functions, the magnitude is unity at all frequencies and the transfer function will have anti-

symmetric pole zero-pattern.

22. What is non-minimum phase transfer function?

A transfer function which has one or more zeros in the right half s-plane is known as non-

minimum phase transfer function.

23. What is Nichols plot?

The Nichols plot is a frequency response plot of the open loop transfer function of a system. It is a graph between magnitude of G(j ) in db and the phase of g(j ) in degree, plotted on a ordinary graph sheet.

24. What are M and N circles?

The magnitude, m of closed loop transfer function with unity feedback will be in the form of

circle on complex plane for each constant value of M. The family of these circles is called M circles.

Let N=tan where is the phase of closed loop transfer with unity feedback. For each constant

value of N, a circle can be drawn in the complex plane. The family of these circles are called

N circles.

25. How closed loop frequency response is determined from open loop frequency using M

and n circles?

The G(j ) locus or the polar plot of open loop system is sketched on the standard M and n circles chart. The meeting point of M circle with G(j ) locus gives the magnitude of closed loop system. The locus with N-circle gives the value of phase of closed loop system.

26. What is Nicholas Chart?

The Nicholas chart consists of m and n contours superimposed on ordinary graph. Along each M

contour the magnitude of closed loop system, M will be constant. Along each N contour, the phase

of closed loop system will be constant. The ordinary graph consists of magnitude in db, marked on

the y-axis and the phase in degrees marked on x axis. The Nicholas chart is used to find the closed

loop frequency response from the open loop frequency response.

27. How the closed loop frequency response is determined from the open loop frequency

response using Nicholas chart?

The G(jw) locus or the Nicholas plot is sketched on the standard Nicholas chart. The meeting

point of M-contour with G (jw) locus gives the magnitude of closed loop system and the meeting point with N circle gives the argument/phase of the closed loop system.

28. What are the advantages of Nicholas chart?

1. The gain of the system can be adjusted to satisfy the given specification.

2. The frequency domain specification can be easily determined.

UNIT-IV

1. Define BIBO stability.

A linear relaxed system is said to have BIBO stability if every bounded (finite) input results in a

bounded (finite) output.

2. What is impulse response?

The impulse response of a system is the inverse Laplace transform of the system transfer

function.

3. What is the requirement for BIBO stability?

The requirement for BIBO stability is that, where m(τ )

is the impulse response of the α

m(τ )dτ < α

system. 0

3. What is characteristic equation?

The denominator polynomial of C(s)/R(s) is the characteristic equation of the system,

5. How the roots of characteristic equation are related to stability? If the roots of characteristic equation has positive real part then the impulse response of the

system is not bounded (the impulse response will be infinite as t → α

). Hence the system will be unstable. If the roots have negative real parts then the impulse response is bounded (the impulse

response becomes 0 as t → α

). Hence the systemwill be stable.

6. What is the necessary condition for stability?

The necessary condition for stability is that all the coefficients of the characteristic

polynomial be positive.

7. What is the relation between stability and coefficient of characteristic polynomial?

If the coefficients of characteristic polynomial are negative or zero, then some of roots lies on

right half of s-plane. Hence the system is unstable. If the coefficients of characteristic polynomial

are positive and if no coefficient is zero then there is a possibility of the system to be stable

provided all the roots are lying on left half of s-plane.

8. What will be the nature of impulse response when the roots of characteristic equation

are lying on imaginary axis?

If the roots of characteristic equation lie on imaginary axis the nature of impulse response is

oscillatory.

9. What will be the nature of impulse response if the roots of characteristic equation are

lying on left half of s-plane?

When the roots are lying on the real axis on the right half of s-plane. The response is exponentially increasing. When the roots are complex conjugate and lying on the right half of

s-plane, the response is oscillatory with exponentially increasing amplitude.

10. What is principle of argument?

The principle of argument states that let F(s) be an analytic function and if an arbitrary closed

contour in the clockwise direction is chosen in the s-plane so that F(s) is analytic at every point

of the contour. Then the corresponding F(s)-plane contour mapped in the F(s) plane will encircle.

11. What is the necessary and sufficient condition for stability.

The necessary and sufficient condition for stability is that all of the elements in the first coloumn

of the routh array should be positive.

12. What is routh stability criterion?

Routh Criterion states that the necessary and sufficient condition for stability is that all of the

elements in the first coloumn of the routh array be positive .If this condition is not met,the system

is unstable and the number of sign changes in the elements of the first column of routh array

corresponds to the number of roots of characteristics equation in the right half of the S plane.

13. What is auxillary Polynomial?

In the construction of routh array a row of all zero indicates the existence of an even polynomial

as a factor of the given characteristic equation. In an even polynomial the exponents of s are even

integers or zero only.This even polynomial factor is called auxiliary Polynomial. The coefficients

of auxillary polynomial are given by the elements of the row just above the row of all zeros.

14. What is Quadrantal Symmetry?

The symmetry of roots with respect to both real and imaginary axis is called Quadrantal

Symmetry.

15. In routh array what conclusion you can make when there is a row of all zeros?

All zero row in array indicates the existence of an even polynomial as a factor of the given

characteristic equation. The even polynomial may have roots on imaginary axis.

16. What is limitedly stable system?

For a bounded input signal, if the output has constant amplitude oscillations then the system may be stable or unstable under some limited constraints .such system is called limitedly stable system.

17. What is Nyquist stability Criterion?

If G(s) H(s) contour in theG(s) H(s) plane corresponding to Nyquist contour in s-plane encircles the point -1+j0 in the clockwise direction as many times as the number of right half s-plane poles of G(s) H(s).Then the closed loop system is stable.

18. What is root locus?

The path taken by a root of characteristic equation when open loop gain K is varied from 0 to ∞ is called root locus.

19. What are asymptotes? How will you find the angle of asymptotes?

Asymptotes are straight lines which are parallel to root locus going to infinity and meet the root

locus at infinity.

Angles of asymptotes= +_180(2q+1)/(n-m);q=0,1,2,…..,(n-m)

20. What is centroid? How the centroid is calculated?

The meeting point of asymptotes with real axis is called centroid. The centroid is given by,

Centroid=(sum of poles-sum of zeros)/(n-m)

21. What is breakaway and breakin point? How to determine them?

At breakaway point the root locus breaks from the real axis to enter into the complex plane. At breakin point the root locus enters the real axis from the complex plane.

To find the breakaway or breakin points, form an equation for k from the characteristic equation

and differentiate the equation of k with respect to s. Then find the roots of equation dk/ds=0.The

roots of dk/ds=0 are breakaway or breakin points provided for this value of root the gain k should

be positive and real.

22. How to find the crossing point of root locus in imaginary

axis? Method (i): By Routh Hurwitz criterion.

Method (ii): By letting s=jw in the characteristic equation and separate the real and imaginary part. These two equations are equated to zero. solve the two equations for w and k. The value of w gives the point where the root locus crosses imaginary axis and the value of k is the gain corresponding to the crossing point.

23. What are root loci?

The path taken by the roots of the open loop transfer function when the loop gain is varied from 0 to _ are called root loci.

24. What are the main significances of root locus?

The main root locus technique is used for stability analysis.

Using root locus technique the range of values of K, for as table system can be determined

25. What are the main advantages of Bode plot?

The main advantages are:

i) Multiplication of magnitude can be in to addition.

ii) A simple method for sketching an approximate log curve is available.

iii) It is based on asymptotic approximation. Such approximation is sufficient

if rough information on the frequency response characteristic is needed.

iv) The phase angle curves can be easily drawn if a template for the phase angle curve of 1+ jw is available.

26. Define Corner frequency?

The frequency at which the two asymptotic meet in a magnitude plot is called corner frequency.

27. How is the Resonant Peak(Mr), resonant frequency(Wr ) , and band width

determined from Nichols chart? i) The resonant peak is given by the value of µ.contour which is tangent to G(jw ) locus.

ii) The resonant frequency is given by the frequency of G(jw ) at the tangency point.

iii) The bandwidth is given by frequency corresponding to the intersection point of G(jw ) and

– 3dB M-contour.

28. What are the advantages of Nichols

chart? The advantages are:

i) It is used to find the closed loop frequency response from open loop frequency response.

ii) Frequency domain specifications can be determined from Nichols chart.

iii) The gain of the system can be adjusted to satisfy the given specification.

29. What are root loci?

The path taken by the roots of the open loop transfer function when the loop gain is varied from 0 to _ are called root loci.

30. What is a dominant pole?

The dominant pole is a air of complex conjugate pair which decides the transient response of the

system.

31. What are the main significances of root locus?

i. The main root locus technique is used for stability analysis.

ii. Using root locus technique the range of values of K, for as table system can be determined

33. Why is negative feedback invariably preferred in closed loop system?

The negative feedback results in better stability in steady state and rejects any disturbance signals

34. What are the effects of adding a zero to a system.

Adding a zero to a system results in pronounced early peak to system response thereby the peak overshoot increases appreciably.

35. State-Magnitude criterion.

he magnitude criterion states that s=sa will be a point on root locus if for that value of s , | D(s) |

= |G(s)H(s) | =1

36. State – Angle criterion.

The Angle criterion states that s=sa will be a point on root locus for that value of s, , _D(s) =

_G(s)H(s) =odd multiple of 180°

UNIT V

1. What is frequency response?

A frequency response is the steady state response of a system when the input to the system is a sinusoidal signal.

2. Define –resonant Peak (Zr)?

The maximum value of the magnitude of closed loop transfer function is called

resonant peak.

3. Define –Resonant frequency(Zf)?

The frequency at which resonant peak occurs is called resonant frequency.

4. What is bandwidth?

The bandwidth is the range of frequencies for which the system gain Is more than 3 dbB.The bandwidth is a measure of the ability of a feedback system to reproduce the input signal ,noise rejection characteristics and rise time.

5. Define Cut-off rate?

The slope of the log-magnitude curve near the cut-off is called cut-off rate. The cut-off

rate indicates the ability to distinguish the signal from noise.

6. Define –Gain Margin?

The gain margin,kg is defined as the reciprocal of the magnitude of the open loop

transfer function at phase cross over frequency. Gain margin kg = 1 / Z G(j pc)

7. Define Phase cross over?

The frequency at which, the phase of open loop transfer functions is called phase cross

over frequency Z pc.

8. What is phase margin?

The phase margin ,Z is the amount of phase lag athet gain cross over frequency

required to bring system to the verge of instability.

9. Define Gain cross over?

The gain cross over frequency Z gc is the frequencyat which the magnitude of the

open loop transfer function is unity.

10. Define Corner frequency?

The frequency at which the two asymptotic meet in a magnitude plot is called corner frequency.

11. Define Phase lag and phase lead?

A negative phase angle is called phase lag.

A positive phase angle is called phase lead.

12. What are M circles?

The magnitude of closed loop transfer function with unit feed back can be shown to be

in the for every value if M.These circles are called M circles.

13. What is Nichols chart? The chart consisting if M & N loci in the log magnitude versus phase diagram is called Nichols chart.

14. What are two contours of Nichols chart?

Nichols chart of M and N contours, superimposed on ordinary graph. The M contours

are the magnitude of closed loop system in decibels and the N contours are the phase

angle locus of closed loop system.

15. How is the Resonant Peak(Mr), resonant frequency(Wr ) , and band

width determined from Nichols chart?

i) The resonant peak is given by the value of Z.contour which is tangent to

G(jZ ) locus.

ii) The resonant frequency is given by the frequency of G(jZ ) at the tangency point.

iii) The bandwidth is given by frequency corresponding to the intersection point of G(jZ ) and –3dB M-contour.

16. What are the advantages of Nichols chart?

The advantages are: i) It is used to find the closed loop frequency response from open

loop frequency response.

ii) Frequency domain specifications can be determined from Nichols chart.

iii) The gain of the system can be adjusted to satisfy the given specification.

17. What are the two types of compensation?

i. Cascade or series compensation

ii. Feedback compensation or parallel compensation

18. What are the three types of compensators?

i. Lag compensator

ii. Lead compensator

iii. Lag-Lead compensator

19. What are the uses of lead compensator?

1. speeds up the transient response

2. increases the margin of stability of a system

3. increases the system error constant to a limited extent.

20. What is the use of lag compensator?

Improve the steady state behavior of a system, while nearly preserving its transient response.

21. When is lag lead compensator is required?

The lag lead compensator is required when both the transient and steady state response of a system has to be improved

22. What is a compensator?

A device inserted into the system for the purpose of satisfying the specifications is called as a compensator.

23. What is nyquist contour?

The contour that encloses entire right half of S plane is called nyquist contour.

24. State Nyquist stability criterion.

If the Nyquist plot of the open loop transfer function G(s) corresponding to the

nyquist control in the S-plane encircles the critical point –1+j0 in the counter

clockwise direction as many times as the number of right half S-plane poles of

G(s),the closed loop system is stable.

25. Define Relative stability

Relative stability is the degree of closeness of the system,it an indication of strength or degree of stability.

26. What are the two segments of Nyquist contour?

i. An finite line segment C1 along the imaginary axis.

ii. An arc C2 of infinite radius.

27. What are root loci?

The path taken by the roots of the open loop transfer function when the loop gain is

varied from 0 to _ are called root loci.

28. What is a dominant pole?

The dominant pole is a air of complex conjugate pair which decides the transient

response of the system.

29. What are the main significances of root locus?

i. The main root locus technique is used for stability analysis.

ii. Using root locus technique the range of values of K, for as table system can be determined

30. What are the effect of adding a zero to a system?

Adding a zero to a system increases peak overshoot appreciably.

31. What are N circles?

If the phase of closed loop transfer function with unity feedback is _, then tan _ will

be in the form of circles for every value of _. These circles are called N circles.

32. What is servomechanism?

The servomechanism is a feedback control system in which th output is mechanical

position (or time derivatives of position velocity and acceleration,)

33. Why is negative feedback invariably preferred in closed loop system?

The negative feedback results in better stability in steady state and rejects any

disturbance signals.

34. What is the need for a controller?

The controller is provided to modify the error signal for better control action

35. State-Magnitude criterion. The magnitude criterion states that s=sa will be a point on root locus if for that value of s , | D(s) | = |G(s)H(s) | =1

36. State – Angle criterion.

The Angle criterion states that s=sa will be a point on root locus for that value of s, , _D(s) = _G(s)H(s) =odd multiple of 180°

37. What is quadrantal symmetry?

The symmetry of roots with respect to both real and imaginary axis called

quadrantal symmetry.

38. What is limitedly stable system?

For a bounded input signal if the output has constant amplitude oscillations .Then the

system may be stable or unstable under some limited constraints such a system is called limitedly stable system.

IC8451 - CONTROL SYSTEMS

PART B-16 Mark Questions

UNIT - I

1. Draw the signal flow graph and find C/R for the figure shown.

2. Write the differential equations and obtain X3(S)/F(S) for the mechanical system shown. Also draw the force voltage and force current analogies.

3. a) (i)Reduce the block diagram given below to find the closed loop Transfer function by reduction

method when the I/P R is at station-II

(ii) Reduce the block diagram given above to find the closed loop Transfer function by signal flow

graph when the I/P R is at station-I

4. Obtain Transfer function of the system.

5. Obtain analogous electrical network.

6. Using mason’s gain formula find C/R.

7. Write the differential equations governing the mechanical system. Draw the force-voltageand

force current electrical analogous circuits and verify by writing mesh and node equations.

8. Using Mason’s gain formula, find C/R of the signal flow graph shown in figure.

9. Derive the transfer function for Armature controlled DC servo motor.

10. Derive the transfer function for Field controlled DC servo motor.

UNIT - II

1. (a) Derive the expressions and draw the response of first order system for unit step input.

(b) Draw the response of second order system for critically damped case and when input is

unit step.

2. Derive the expressions for Rise time, Peak time, Peak overshoot.

3. Derive the response of undamped second order system for unit step input.

4. The unity feedback system is characterized by an open loop transfer function is k

. s(s 10)

Determine the gain k so that system will have damping ratio of 0.5.For this value of k,

determine peak overshoot and peak time for a unit step input.

5. A positional control system with velocity feedback is shown in fig. What is the response c(t) to the

unit step input. Given that ς =0.5.and also calculate rise time, peak time, Maximum overshoot and

settling time.

6. A unity feedback control system has an open loop transfer function G(S) = 10/S(S+2).Find the

rise time, percentage over shoot, peak time and settling time.

7. Consider a second order model Y(s)/R(s)= ωn2/ (S2+2ξωnS+ωn2) ; 0 < ξ < 1. Find the response

y(t) to a input of unit step function..

8. For a unity feedback control system the open loop transfer function G(S)

= 10(S+2)/ S2 (S+1).Find (a) position, velocity and acceleration error constants. (b) The steady

state error when the input is R(S) where R(S) =3/S –2/S2 +1/3S3

9. The open loop transfer function of a servo system with unity feedback system is

G(S) = 10/ S(0.1S+1).Evaluate the static error constants of the system. Obtain the steady state

error of the system when subjected to an input given by the polynomial r(t) = a0 +a1t +a2 /2 t2 .

10. The open loop transfer function of a system with unity feedback gain is given as G(S) =

20/S2+5S+6. Determine the damping ratio, maximum overshoot, rise time and peak time. Derive

the used formulae.

11. Evaluate te static error constants for a unity feedback system having a forward path transfer

function G(S)=50/S(S+10). Estimate the steady state errors of the system for the input r(t) given

by r(t)=1+2t+t2.

12. The closed loop transfer function of a second order system is given by

T(s) = 100

s

2 10s 100

Determine the damping ratio, natural frequency of oscillations, rise time, settling time and

peak overshoot.

13. With necessary diagrams explain the P,PI,PD controller and explain its output equations. 14. Sketch the root locus of the system having G(S)H(S)=K(S+2)/(S+1)(S+3+j2)(S+3-j2) for

positive value of K.

15. Sketch the root locus for unity feedback system whose open loop transfer function is

G(s) = K (s 2 6s 25)

s(s 1)(s 2)

16. Sketch the root locus plot of a unity feedback system with an open loop transfer function

G(s) = K / s (s+2) (s+4). Determine the value of K so that the dominant pair of complex poles of

the system has a damping ratio of 0.5.

17. Sketch the root locus of unity feedback system whose open loop transfer function is

G(s)H(s)=K/s(s+4)(s2+4s+13). Find the marginal value of K which causes sustained oscillations

and find the frequency of these oscillations.

18. Sketch the root locus of the system having G(s) = k(s 3)

s(s 1)(s 2)(s 4) .

UNIT - III

1. Sketch the Bode plot for the system G(s) = K(e-0.2s)/s(s+2) (s+8). Find the value of K so that the

system is stable with gain margin = 6 db and phase margin= 45 degree.

2. The open loop transfer function of a unity feedback system is G(S) = 1/ S(1+S) (1+2S). Sketch the

Polar plot and determine the Gain margin and Phase margin.

3. Sketch the Bode plot and hence find Gain cross over frequency, Phase cross over frequency, Gain

margin and Phase margin. G(S) = 0.75(1+0.2S)/ S(1+0.5S) (1+0.1S)

4. Sketch the Bode plot and hence find Gain cross over frequency, Phase cross over frequency, Gain

margin and Phase margin.G(S) = 10(S+3)/ S(S+2) (S2+4S+100)

5. Sketch the polar plot for the following transfer function .and find Gain cross over frequency,

Phase cross over frequency, Gain margin and Phase margin. G(S) = 10(S+2)(S+4)/ S (S2 -3S+10)

6. Construct the polar plot for the function GH(S) =2(S+1)/ S2. Find Gain cross over frequency,

Phase cross over frequency, Gain margin and Phase margin.

7. Plot the Bode diagram for the following transfer function and obtain the gain and phase cross over

frequencies. G(S) =KS2 / (1+0.2S) (1+0.02S). Determine the value of K for a gain cross over

frequency of 20 rad/sec.

8. Sketch the polar plot for the following transfer function and find Gain cross over frequency, Phase

cross over frequency, Gain margin and Phase margin. G(S) = 400/ S (S+2)(S+10).

9. Derive the expression for Lag - Lead compensator and also find its frequency response.

10. Sketch the Bode plot and hence find Gain cross over frequency, Phase cross over frequency,

Gain margin and Phase margin. G(S) = 10(1+0.1S)/ S(1+0.01S) (1+S).

11. Explain the closed loop frequency response with the help of M and N circles.

12. Explain in detail the design procedure of lead compensator using Bode plot.

UNIT - IV

1. Obtain Routh array for the system whose characteristic polynomial equation is given by

s6+2s5+8s4+12s3+20s2 +16s+16=0. Comment on location of roots and check the stability.

2. F(S)=S6 +S5-2S4-3S3-7S2-4S1-4 =0.Find the number of roots falling in the RHS plane and LHS

plane.

3. Draw the Nyquist plot for the system whose open loop transfer function is

G(S)H(S) =K/S (S+2) (S+10).Determine the range of K for which closed loop system is stable.

4. Construct Nyquist plot for a feedback control system whose open loop transfer function is given

by G(S)H(S) =5/ S(1-S).comment on the stability of open loop and closed looptransfer function.

5. Sketch the Nyquist plot for a system with the open loop transfer function G(S)H(S) =K(1+0.5S)

(1+S) / (1+10S) (S-1).determine the range of values of K for which the system is stable.

6. The open loop transfer function of a unity feedback system is given by

G(S) = K/(S+2)(S+4)(S2+6S+25) by applying the Routh criterion, discuss the stability of the

closed loop system as a function of K. Determine the value of K which will cause sustained

oscillations in the closed loop system. What are the corresponding oscillation frequencies?

UNIT - V

1. The transfer function of a control system is given by

controllability.

Y (s) = U (s)

(s 2)

s3 9s 2 26s 24

. Check for

2. Find the state variable equation for a mechanical system shown below.

.Identify the first state

3. A system is characterized by the transfer function

Y (s) =

U (s)

3

s3 5s

2 11s 6

as the output. Determine whether or not the system is completely controllable and observable.

4. Explain the analysis of sampler and zero-order hold circuits.

5. Obtain the state transition matrix for the state model whose system matrix A is given by

1 10 1

6. Determine the transfer matrix from the data given below.

7. The state space representation of a system is given below. Obtain the transfer function.

8. A system is characterized by the transfer function Y (s)

U (s)

3

s3 5s

2 11s 6

. Identify the first

state as the output. Determine whether or not the system is completely controllable and

observable.

9. Write the state equation for the system shown below in which x1,x2 and x3 constitute the state

vector. Determine whether the system is completely controllable and observable.

10. Obtain the state model of the system described by the following transfer function.

Y (s)

U (s)

5

s3 5s

2 6s 7

11. Determine the state model of armature and field controlled dc motor.

A=

12. (i) Explain the analysis of sampler and zero order hold circuits.

(ii) Find the inverse Z- transform of F(Z) = (3Z2+2Z+1)/(Z2-3Z+2).

Subject Name:Electrical Machines-II

Faculty Name:Mr.C.Maheshkhumar

UNIT-I

1. Why a 3-phase synchronous motor will always run at synchronous speed?

Because of the magnetic coupling between the stator poles and rotor poles the motor runs exactly at synchronous speed.

2. What are the two classification synchronous machines?

The classification synchronous machines are:

i. Cylindrical rotor type

ii. Salient pole rotor type

3. What are the essential features of synchronous machine?

i. The rotor speed is synchronous with stator rotating field.

ii. Varying its field current can easily vary the speed.

iii. It is used for constant speed operation.

4. What are the principal advantages of rotating field system type of construction of synchronous machines?

Form Stationary connection between external circuit and system ofconditions (armature) enable the machine to handle large amount of volt-ampere as high as 500 MVA.

The relatively small amount of power required for field system can be easily supplied to the rotating field system via slip rings and brushes.

More space is available in the stator part of the machine for providing more insulation to the system of conductors.

Insulation to stationary system of conductors is not subjected to mechanical stresses due to centrifugal action.

Stationary system ofconductors can easily be braced to prevent deformation.

It is easy to provide cooling arrangement.

5. Write down the equation for frequency of emf induced in an alternator.

f = pN / 120 Hertz

Where p = No. of poles

N = Speed in rpm.

6. What are the advantages of salient pole type of construction used for synchronous

machines?

They allow better ventilation.

The pole faces are so shaped radial air gap length increases from the pole center to the

pole tips so that flux distribution in the air gap is sinusoidal in shape which will help to generate sinusoidal emf.

Due the variable reluctance, the machine develops additional reluctance power, which is independent of excitation.

7. Why do cylindrical rotor alternators operate with steam turbines?

Steam turbines are found to operate at fairly good efficiency only at high speeds. The high-speed operation of rotor tends to increase mechanical losses, so the rotors should have smooth external surface. Hence smooth cylindrical type rotors with less diameter and large axial length are used for synchronous generators driven by steam turbines with either 2 or 4 poles.

8. Which type of synchronous generators are used in Hydroelectric plants and why?

As the speed of operation is low, for hydro turbines used in hydroelectric plants, salient pole type synchronous generators are used. These allow better ventilation and also have other advantages over smooth cylindrical type rotor.

9. What is the relation between electrical degree and mechanical degree?

Electrical degree θe and mechanical degree are related to one another by the number of poles p, the electrical machine has, as given by the following equation.

θe = (p/2) θm

10. What is the meaning of electrical degree?

Electrical degree is used to account the angle between two points in rotating electrical machines.

Since all electrical machines operate with the help of magnetic fields, the electrical degree is accounted with reference to the polarity of magnetic fields. 180 electrical degrees is accountedas the angle between adjacent North and South poles

11. Why short-pitch winding is preferred over full pitch winding?

Advantages: -

Waveform of the emf can be approximately made to a sine wave and distorting harmonics can be reduced or totally eliminated.

Conductor material, copper is saved in the back and front-end connections due to less coil span.

Fractional slot winding with fractional number of slots/phase can be used which in turn reduces the tooth ripples.

Mechanical strength of the coil is increased.

11. Write down the formula for distribution factor.

Kd = sin (mβ/2) or Kdn = sin (mnβ/2)

msin(β/2) msin(nβ/2)

Where

m - number of slots/pole/phase

β - angle between adjacent slots in electrical degree n -

order of harmonics.

13. Define winding factor.

The winding factor Kw is defined as the ratio of phasor addition of emf induced in all the coils belonging to each phase winding of their arithmetic addition.

14. Why are alternators rated in kVA and not in kW?

The continuous power rating of any machine is generally defined as the power the machine or apparatus can deliver for a continuous period so that the losses incurred in the machine gives rise to a steady temperature rise not exceeding the limit prescribed by the insulation class.

Apart from the constant loss the variable loss incurred in alternators is the copper loss, occurring in the 3-phase winding, which depends on I2R, the square of the current delivered by the generator. It is directly related to apparent power delivered by the generator, Thus the alternators have only their apparent power in VA/kVA/MVA as their power rating.

15. What are the causes of changes in voltage of alternators when loaded?

Voltage variation due to the resistance of the winding R.

Voltage variation due to the leakage reactance of the winding X1.

Voltage variation due to the armature reaction.

16. What is meant by armature reaction in alternators?

The interaction between flux set up by the current carrying armature conductors and the main field flux is defined as the armature reaction.

17. What do you mean by synchronous reactance?

It is the sum of the leakage reactance X1 and armature reactance Xa

Xs = X1 + Xa

18. What is effective resistant [Reff]?

The apparent increase in resistance of the conductor when an alternating current is flowing through it is known as effective resistance.

19. What is synchronous impedance?

The complex addition of resistance R and synchronous reactance jXs is synchronous impedance Zs.

Zs = (R+jXs) = Zs∟θ

Where θ = tan–1(Xs/R)

|Zs| = √(R2+jXs2)

20. What is meant by load angle of an alternator?

The phase angle introduced between the induced emf phasor E and terminal voltage phasor V during the load condition of an alternator is called load angle. The load angle increases with increase in load. It is positive during generator operation and negative during motor operation.

21. Define the term voltage regulation of alternator.

It is defined as the change in terminal voltage from no load-to-load condition expressed as a function or terminal voltage at load condition, the speed and excitation conditions remaining same.

% Regulation = (E-V)/V x 100

21. What is the necessity for predetermination of voltage regulation?

Most of the alternators are manufactured with large power rating and large voltage ratings

Conduction load test is not possible for such alternators. Hence other indirect methods of testing are used and the performance can be predetermined at any desired load currents and power factors.

23. Why is the synchronous impedance method of estimating voltage regulation is considered as pessimistic method?

Compared to other methods, the value of voltage regulation obtained by this method is always higher than the actual value and therefore is called pessimistic method.

24. Why is the MMF method of estimating the voltage regulation is considered as the optimization method?

Compared to EMF method, MMF method involves more number of complex calculation steps. Further the OCC is referred twice and SCC is referred once while predetermining the voltage

regulation for each load condition. Reference of OCC takes core saturation effect. As this method requires more effort, the final result is very close to the actual value. Hence this method is called the optimistic method.

25. What is direct axis?

The mmf wave is height when it is aligned with the field pole axis called the direct axis or ‘d’ axis.

26. What is quadrature axis?

The permeance offered to a mmf wave is lower when it is oriented 90o

To the field pole axis called the quadrature axis or q axis.

27. What are the three methods of determining voltage regulation?

i. Synchronous impedance method or EMF method.

ii. The ampere-turn or MMF method.

iii. Zero power factor or portier method.

28. What are the two curves required for POTIER method?

i. No load curve.

ii. Full load zero power factor curve called wattless load characteristic.

28. What is the main advantage of POTIER method?

The voltage regulation calculated by potier’s method is quite accurate.

29. What is a synchroscope?

Synchroscope is an instrument, which shows the phase relationship of emf of the incoming

alternator. It also indicates whether the incoming alternator is running slow or fast.

30. What is synchronizing?

The operation of connecting an alternator in parallel with another alternator or with common bus bars is known as synchronizing.

31. Define SCR.

Short circuit ratio (SCR) is defined as the ratio of field current required to produce rated voltage on open-circuit to field current required to produce rated armature current with the terminals shorted, while the machine runs at synchronous speed.

UNIT-II

1. What does hunting of synchronous motor mean?

When the load applied to the synchronous motor is suddenly increased or decreased, the rotor

oscillates about its synchronous position with respect to the stator field. This action is called hunting.

2. State the causes for hunting.

Sudden change in load.

Sudden change in field current.

A load containing harmonic torque.

Fault in supply system.

3. What are the effects of hunting?

It may lead to loss of synchronism.

Produces mechanical stresses in the rotor shaft.

Increases machine losses and cause temperature rise.

Cause greater surges in current and power flow.

It increases possibility of resonance.

3. Mention the methods used to avoid hunting

Use of Damper Winding : It consists of low electrical resistance copper / aluminum brush embedded in slots of pole faces in salient pole machine.

Damper winding damps out hunting by producing torque opposite to slip of rotor.

The magnitude of damping torque is proportional to the slip speed.

2. What could be the reasons if a 3-phase synchronous motor fails to start?

It is usually due to the following reasons

a. Voltage may be too low.

b. Too much starting load.

c. Open circuit in one phase or short circuit.

d. Field excitation may be excessive

3. Mention the methods of starting of 3-phase synchronous motor.

a. A D.C motor coupled to the synchronous motor shaft.

b. A small induction motor coupled to its shaft.(pony method)

c. Using damper windings

d. Started as a squirrel cage induction motor.

4. What is synchronous condenser?

An over-excited synchronous motor under no load ,used for the improvement of power factor is called as synchronous condenser because, like a capacitor it takes a leading current.

5. Write the applications of synchronous motor.

a. Used for power factor improvement in sub-stations and in industries.

b. Used in industries for power applications.

c. Used for constant speed drives such as motor-generator set, pumps and compressors.

6. What is an inverted 'V' curve?

For a constant load, if the power factor is plotted against various values of field exciting current, the curve formed is inverted V Shape and called as inverted 'V' curve.

7. A synchronous motor starts as usual but fails to develop its full torque. What could it be due to?

a. Exciter voltage may be too low.

b. Field spool may be reversed.

c. There may be either open-circuit or short-circuit in the field.

8. Write the two extra features of slip ring induction motors. a. Rotor is having 3-phase winding.

Extra resistance can be added in the rotor circuit by connecting through the help of three slip rings for improving the power factor, increasing Starting Torque, limiting the starting current.

9. Can we add extra resistance in series with squirrel cage rotor? State the reason?

We cannot add extra resistance in series with the rotor because all the copper bars of the rotor are short circuited in both the sides by copper end rings to have a closed circuit.

10. Why an induction motor is called rotating transformer?

The rotor receives electrical power in exactly the same way as the secondary of a two winding transformer receiving its power from primary. That is why an induction motor can be called as a rotating transformer i.e., in which primary winding is stationary but the secondary is free to rotate.

11. Why an induction motor will never run at its synchronous speed?

If it runs at synchronous speed then there would be no related speed between the two, hence no rotor emf, no rotor current so no rotor torques to maintain rotation. That is why the rotor runs at its synchronous speed.

12. Why is open circuit characteristics called magnetic characteristic?

The OCC is called magnetic characteristic because it gives the variation of space component of flux in air gap and mmf / pole of magnetic circuit.

13. What are the losses determined from SCC?

i. Copper loss

ii. Mechanical loss

14. What are stray load losses?

Stray load loss is the sum of load core loss and loss due to the additional conductor resistance offered to the ac.

15. When does a synchronous motor get over excited?

If the field excitation of the motor is increased, the field flux will become strong and Eb will increase. As a result Eb will exceed V and the motor will be called an over excited motor.

16. Define pullout torque.

The pullout torque is the torque, beyond which the synchronous link between field poles and resultant flux wave is severed and the machine falls out-of-slip.

17. What is meant by the subtransient period?

The initial period of decay of the short circuit current is called the subtransient, in which the current decay is governed mainly by the damper winding constant.

UNIT-III

1. What are types of 3- phase induction motor?

i. Squirrel cage induction motor

ii. Slip ring induction motor

2. Why the rotor slots of a 3-phase induction motor are skewed?

The rotor slots of a three -phase induction motor are skewed

i. To make the motor run quietly by reducing the magnetic hum

ii. To reduce the locking tendency of the rotor

3. Why the induction motor is called asynchronous motor?

Since the induction motor runs always at a speed lesser than synchronous speed, it is called asynchronous motor.

4. What are slip rings?

The slip rings are made of copper alloys and are fixed around the shaft insulating it.

Through these slip rings and brushes the rotor winding can be connected to external circuits.

5. State the difference between slip ring rotor and cage rotor of an induction motor.

Slip ring rotor has 3-phase windings. Three ends of which are stared and the other three ends are brought up and connected to 3 slip rings mounted in the shaft. Extra resistance can be added in the rotor circuit.

Squirrel cage rotor has short-circuited copper bars. Extra resistance can’t be added as slip ring rotor.

6. Write an expression for the slip of an induction motor.

Percentage slip = (Ns -Nr) / Ns * 100.

Ns=Synchronous speed Nr=Rotor speed

7. What is cogging of an induction motor?

When the number of stator and rotor teeth’s is equal or integral multiple of rotor teeth, they have a tendency to align themselves exactly to minimum reluctance position. Thus the rotor may refuse to

accelerate. This phenomenon is known as cogging.

8. Explain why the no load current of an induction motor is much higher than that of an equivalent transformer.

In induction motor, due to the presence of the air gap, the magnetizing current that is required to set

up the flux is much higher. The working component of the current has to meet the hysteresis loss,

eddy current loss, friction and windage losses. Hence the no load current of induction motor is higher.

9. State the effect of rotor resistance on starting torque.

Starting torque increases with increase in value of rotor resistance.

10. What are the advantages of cage motor?

Since the rotor has very low resistance, the copper loss is low and efficiency is high

On the account of simple construction of rotor, it is mechanically robust.

Initial cost is less.

Maintenance cost is less.

Simple stating arrangement

11. Give the conditions for maximum torque for 3-phase induction motor.

The rotor resistance and rotor reactance should be equal for developing maximum torque i.e. R2 = s X2 where s is the slip –under running conditions. R2 = X2 under starting conditions

12. What is reason for inserting additional resistance in rotor circuit of a slip ring induction motor?

Introduction of additional resistance in the rotor circuit will increase the starting torque as well as running torque. Also it limits the starting current, improves the power factor.

13. List out the methods of speed control of cage type 3-phase induction motor.

a) By changing supply frequency

b) By changing the number of poles

c) By operating two motors in cascade

14. Mention different types of speed control of slip ring induction motor.

a) By changing supply frequency

b) By changing the number of stator poles c) By rotor rheostat control

d) By operating two motors in cascade

15. What are the advantages of 3-phase induction motor?

a) It was very simple and extremely rugged, almost unbreakable construction

b) Its cost is very low and it is veryreliable

c) It has been sufficiently high efficiency .No brushes are needed and hence frictional losses are reduced

d) It requires minimum of maintenance.

16. What does crawling of induction motor mean?

Squirrel cage type, sometimes exhibit a tendency to run stably at speeds as low as 1/7 the of their synchronous speed, because of the harmonics this phenomenon is known as crawling

17. State the application of an induction generator.

a) Used in windmill for generating electric power.

b) Used in regenerative breaking places like traction.

UNIT-IV

1. What are the types of starters?

Stator rheostat starter

Autotransformer starter

Star to Delta starter and

Rotor resistance starter.

2. List out the methods of speed control of cage type 3-phase induction motor?

a) By changing supply frequency

b) By changing the number of poles

c) By operating two motors in cascade

3. Mention different types of speed control of slip ring induction motor?

i) By changing supply frequency

ii) By changing the number of stator poles

iii) By rotor rheostat control

iv) By operating two motors in cascade

4. State the advantages of capacitor start run motor over capacitor start motor.

i) Running torque is more;

ii) Power factor during running is more.

5. What is Universal motor?

A Universal motor is defined as a motor, which may be operated either on direct current or single- phase ac supply.

6. State some application of universal motor.

Used for sewing machines, table fans, Vaccum cleaners, hair driers, blowers etc

7. Explain why single-phase induction motor is not self-starting one.

When the motor is fed from a single phase supply its stator winding produces an alternating or pulsating flux, which develops no torque which is explained in Double revolving field theory.

8. What type of motor is used for ceiling fan?

Capacitor start and capacitor run single-phase motor is used for ceiling fans.

9. What is the type of induction motor used in wet grinders?

Capacitor start capacitor run single-phase induction motor.

10. What kind of motor is used in mixie?

Single-phase ac series motor is used in mixie.

11. What is the application of shaded pole induction motor?

Because of its small starting torque, it is generally used for small fans, toys, instruments, hair driers, ventilators, electric clock etc.

12. In which direction does a shaded pole motor run?

The rotor starts rotation in the direction from unshaded part to the shaded part.

13. Why single-phase induction motor has low power factor?

The current through the running winding lags behind the supply voltage by a very large angle. Therefore power factor is very low.

14. Diffrentiate between “capacitor start “and “capacitor start capacitor run “induction

motor?

In capacitor start motor, capacitor is connected in series with the starting winding. But it will be disconnected fro m the supply, when the motor picks up its speed. But in capacitor start capacitor

run motor the above starting winding and capacitor are not disconnected, but always connected in the supply .so it has high starting and running torque.

15. State the application of an induction generator?

Used in windmill for generating electric power.

Used in regenerative breaking places like traction.

16. What do you mean by residual EMF in a generator.

The EMF induced in the armature conductor only due to the residual flux in the field poles is known as residual EMF

17. State the effect of rotor resistance on starting torque?

Starting torque increases with increase in value of rotor resistance.

18. How can varying supply frequency control speed?

We know that

Ns = 120f

P From the equation it is clear that by varying frequency speed can be varied it is vary rarely.

19. How is speed control achieved by changing the number of stator poles?

Here change in stator poles is achieved by having two or more independent stator windings in the same slot. Each winding gives different number of poles and different speeds. At a time only one winding is used and other is closed.

20. What are the main disadvantages of rotor rheostatic control?

The speed can be decreased by increasing the rotor resistance, but increases I2R loss and hence decreases efficiency.

Speed depends on load also and so used for small periods only.

21. What are the methods of speed control preferred for large motors?

Kramer system

Scherbius system

22. What is an induction regulator?

An induction regulator is used to obtain the constant voltage at the feeder end. Varying the range between the magnetic axes of the primary and secondary windings controls the voltage; it may be a single phase. Rotor is moved usually by a maximum of 180 degree.

23. Define-Slip frequency.

The relation motion of the stator flux and the rotor conductors induces the voltage of frequency Sf called slip frequency.

24. Define- Asynchronous torque.

When stator and rotor fields are stationary with respect to each other, a steady torque is produced and rotation is maintained. Such a torque existing at any mechanical speed other than synchronous speed is called as an asynchronous torque.

25. What is the main use of squirrel cage winding in synchronous motor starting?

When a squirrel cage winding called the amortissuer or damper winding is inserted in the rotor pole faces, the rotor comes up to the synchronous speed by induction motor action with the field winding unexcited.

26. What is breakdown torque?

From the torque verses slip charactertics, we can infer that as the torque increases, slip increases upto a maximum torque developed is called a breakdown torque.

27. What is the function of rotary converter? Where it is used?

Rotary converter converts low slip ac power. It is used in Kramer system, which is for the speed control of three-phase induction motor.

28. What are the advantages of Kramer system of speed control?

Any speed with in the working range can be obtained

When rotary converter is overexcited, it will take leading current, compensates with the lagging current drawn by the motor, thus improving power factor.

29. Write the expression for concatenated speed of the set.

Cumulative mode (Nsc) = 120f

Pa + Pb

Differential mode (Nsd) = 120f

Pa – Pb

Pa – no of poles of motor A

Pb – no of poles of motor B

Unit -V

1. Name the two windings of a single-phase induction motor.

i. Running winding

ii. Starting winding.

2. What are the various methods available for making a single-phase motor self-starting?

i. By splitting the single phase into 2 phases

ii. By providing shading coil in the poles.

3. What is the function of capacitor in a single-phase induction motor?

i. To make more phase difference between the starting and running winding.

ii. To improve the power factor and to get more torque.

4. Give the names of three different types of single-phase motor.

i. Split phase motor

ii. Shaded pole motor.

iii. Single phase series motor.

iv. Repulsion motor.

5. What is the use of shading ring in a pole motor?

The shading coil causes the flux in the shaded portion to lag behind the flux in unshaded portion of pole. This gives in effect a rotation of flux across the pole face and under the influence of this moving flux a stating torque is developed.

6. State any four use of single-phase induction motor.

Fans, Wet grinders, Vacuum cleaners, small pumps, compressors, drills

7. State any 4 use of single phase induction motor?

Fans, wet grinders, vacuum cleaner, small pumps, compressors, drills.

8. Why single phase induction motor is not a self-starting one?

When motor fed supply from single phase, its stator winding produces an alternating flux, which doesn’t develops any torque.

9. What kind of motors used in ceiling fan and wet grinders?

Ceiling fan # Capacitor start and capacitor run single phase induction motor,Wet grinders #

Capacitor start capacitor run single phase induction motor.

10. What is the application of shaded pole induction motor?

Because of its small starting torque, it is generally used for small toys, instruments, hair driers, ventilators.etc.

11. In which direction a shaded pole motor runs?

The rotor starts rotation in the direction from unshaded part to the shaded part.

12. Why single phase induction motors have low PF?

The current through the running winding lags behind the supply voltage by large angle so only single phase induction motor have low PF.

13. Differentiate between “Capacitor Start” & “Capacitor Start Capacitor Run” single phase induction motor?

Capacitor start – capacitor is connected series with starting winding, but it will be disconnected from supply when motor pick up its speed.

Capacitor start capacitor run # starting winding and capacitor will not be disconnected from supply even though motor pickup its speed.

14. What are the principal advantages of rotating field type construction?

Relatively small amount of power required for field system can easily supplied to rotating system

using slip rings and brushes, more space is available in the stator part of the machine to provide more insulation, it is easy to provide cooling system, stationary system of conductors can easily be braced to prevent deformation.

15. Why an induction motor never runs at its synchronous speed?

If it runs at synchronous speed then there would be no relative speed between the two, hence no rotor emf, so no rotor current, then no rotor torque to maintain rotation.

16. What are the advantages of cage motor?

Since the rotor has low resistance, the copper loss is low and efficiency is very high. On account of simple construction of rotor it is mechanically robust, initial cost is less; maintenance cost is less,

simple starting arrangement.

17. Why an induction motor is called as rotating transformer?

The rotor receives same electrical power in exactly the same way as the secondary of a two winding transformer receiving its power from primary. That is why induction motor is called as rotating transformer.

18. What is the use of shading coil in the shaded pole motor?

In shaded pole motors the necessary phase –splitting is produced by induction. These motors have salient poles on stator and a squirrel cage type rotor. The poles are shaded ie each pole carries a

copper band one of its unequally divided part is called shading band. When single phase ac supply is given to the stator winding due to shading provided to the poles a rotating magnetic field is generated.

19. Why capacitor –start induction motors advantageous?

In capacitor start induction motors capacitor is connected in series with the auxiliary winding. When speed of the motor approaches to 75 to80%of the synchronous speed the starting winding gets

disconnected due to the operation of the centrifugal switch. The capacitor remains in the circuit only at start. The starting torque is proportional to phase angle ά and hence such motors produce very high starting torque.

20. List out 4 applications of shaded pole induction motor?

Shaded pole motors have very low starting torque, low power factor and low efficiency. The motors are commonly used for small fans, toy motors, advertising displays, film projectors, record players, gramophones, hair dryers , photocopying machines etc

21. What are the drawbacks of the presence of the backward rotating field in a single phase induction motor?

Due to cutting of flux, emf gets induced in the rotor which circulates rotor current .the rotor current produces rotor flux. This flux interacts with forward component φf to produce a torque in one particular direction say anticlockwise direction. While rotor flux interacts with backward component φb to produce a torque in the clockwise direction. So if anti clock wise torque is positive then clockwise torque is negative thus net torque experienced by the rotor is zero at start.

22. Why is hysteresis motor free from mechanical and magnetic vibrations?

The stator of hysteresis motor carries main and auxiliary windings to produce rotating magnetic field

or of shaded pole type also. The rotor is smooth cylindrical type made up of hard magnetic material.

The torque in this motor is constant at all speeds it runs at synchronous speed. There is not relative

motion between stator and rotor field so the torque due to eddy current vanishes. Only hysteresis torque is present which keeps rotor running at synchronous speeds .the high retentivity ensures

continuous magnetic locking between stator and rotor. Hence it is free from magnetic vibrations.

23. What types of motor is used in computer drives and wet grinders?

For computer drives permanent magnet dc motors are used while in wet grinder’s universal motor may be used.

24. Give two advantages and two applications of stepper motor.

Advantages:

*These motors are compatible with digital equipment and are flexible in operation.

*The dynamic response is fast

Applications:

Stepper motors are widely used in computer peripherals such as serial printers tape drives, floppy disk drivers. They are also used in control of machine tools. Robotics.

25. List some applications of linear induction motor.

They are used in machine tool industry and in robotics .They are used in trains operated on magnetic levitation; reciprocating compressors can also be driven by linear motors

26. What are the specific characteristic features of the repulsion motor?

Repulsion motors give excellent performance characteristics. A very high starting torque of about

300 to350% of full load can be obtained with starting currents of about 3 to 4 times the full load

current. Thus it has got very good operating characteristics. The speed of the motor changes with

load .with compensated type of repulsion motor the motor runs with improved power factor as the

quadrature drop in the field winding is neutralized. Also the leakage between armature and field is reduced which gives better regulation.

27. Discuss the features of single phase series motor.

* To reduce the eddy current losses, yoke and pole core construction is laminated *The power factor can be improved by reducing the number of turns. But this reduces the field flux.

But this reduction in flux increases the speed and reducing the torque. To keep the torque same it is necessary to increase the armature turns proportionately. This increases the armature inductance.

28. What are the demerits of repulsion motor?

very expensive

speed changes with load

on no load speed is very high causing sparking at brushes*low power factor on no load

29. List four applications of reluctance motors.

This motor is used in signaling devices, control apparatus, automatic regulators, recording instruments, clocks and all kinds of timing devices, teleprinters, gramophones 27.

30. What is a universal motor?

There are small capacity series motors which can be operated on dc supply or single phase ac supply of same voltage with similar characteristics called universal motors. The construction of this motor

is similar to that of ac series motor

December 2018

1. Write down the equation for frequency of emf induced in an alternator. (Nov 2018)

F = PN / 120 Hertz Where P = No. Of poles N = Speed in rpm.

2. Which type of synchronous generators are used in Hydroelectric plants and why? (Nov 2018)

As the speed of operation is low, for hydro turbines used in hydroelectric plants, salient pole type

synchronous generators are used. These allow better ventilation and also have other advantages over smooth

cylindrical type rotor.

3. Why a 3-phase synchronous motor always run at synchronous speed?

A synchronous motor always run at synchronous speed because of the magnetic locking between the stator and rotor

4. What is synchronous condenser? (Dec 2018) (April 2018) An over-excited synchronous motor under no load ,used for the improvement of power factor is called as synchronous condenser because, like a capacitor it takes a leading current.

5. What are types of 3- phase induction motor? i. Squirrel cage induction motor ii. Slip ring induction motor

6. Define pullout torque?

The pullout torque is the torque, beyond which the synchronous link between field poles and resultant flux wave is severed and the machine falls out-of-slip.

7. Name the two winding of single phase induction motor?(Dec 2018) Running and starting winding.

8. State any 4 use of single phase induction motor? (Dec 2018)

Fans, wet grinders, vacuum cleaner, small pumps, compressors, drills.

9. What type of motor is used for ceiling fan? (Dec 2018)

Capacitor start and capacitor run single-phase motor is used for ceiling fans.

10. List some applications of linear induction motor? (Dec 2018) They are used in machine tool industry and in robotics .They are used in trains operated on magnetic

levitation , reciprocating compressors can also be driven by linear motors

April 2018

1. Two reaction theory is applied only to salient only to salient pole machines. State the reason. In cylindrical rotor has uniform air gap and therefore, its reactance remain same, irrespective of the

spatial position of rotor. In salient pole non uniformity of the reluctance of the magnetic path, mmf divided into two components such as direct and quadrature component. These facts from the basis of the two reaction

theory applied to salient pole machines

2. What are the advantages of salient pole type of construction used for synchronous machines? (April 2018)

They allow better ventilation.

The pole faces are so shaped radial air gap length increases from the pole center to the pole tips so that flux distribution in the air gap is sinusoidal in shape which will help to generate sinusoidal emf.

Due the variable reluctance, the machine develops additional reluctance power, which is independent of excitation.

3. What is synchronous condenser? An over-excited synchronous motor under no load ,used for the improvement of power factor is called as synchronous condenser because, like a capacitor it takes a leading current.

4. How does a change of excitation affect its power factor? (April 2018)

An over-excited synchronous motor under no load ,used for the improvement of power factor is called as synchronous condenser because, like a capacitor it takes a leading current.

Under excited synchronous motor under no load condition, it takes a lagging current.

5. Why an induction motor never runs at its synchronous speed? If it runs at sy.speed then there would be no relative speed between the two, hence no rotor emf, so no rotor

current, then no rotor torque to maintain rotation.

6. Explain why an induction motor, at no load, operates at a very low power factor (April 2018)

In induction motor, due to the presence of the air gap, the magnetizing current that is required to set up the

flux is much higher.

7. What is the need of starter for induction motor?

When a 3 phase induction motor is switched on at normal supply voltage, heavy current will flow through the

motor (usually five to seven times of full load current) because; at the time of starting there is no back emf. This initial inrush of excessive current is objectionable. Due to this starters are used for starting the three

phase induction motors.

8. What are the advantages of slip power scheme?

In slip power recovery scheme, slip power can be recovered and fed back to the supply of an additional

equipment which is mechanically coupled to the main rotor. This improves the overall efficiency of the system.

The speed of the slip ring induction motor can be controlled both in the sub synchronous and super

synchronous region. This is called cascade connection.

9. What are the methods available for making a single phase motor self starting?

Split phase motor , capacitor – start motor, capacitor – run motor, capacitor – start capacitor -run

motor , shaded pole motor.

10. What is the principle of reluctance motor?

Reluctance motors operate on the principle that forces are established that tend to cause iron poles carrying a

magnetic flux to align with each.

16 Mark Questions:

Unit –I

1. Describe with neat sketches the constructional details of a salient pole type alternator.(Hydraulic

turbines and diesel engines)(April 2018, Dec 2016, Dec 2014)

2. Draw a neat sketch showing the various parts of a synchronous machine. State the type of

synchronous generator used in nuclear power stations (Steam turbines).(Dec 2014)

3. Discuss briefly the load charactertics of alternator for different power factor.

4. Explain any one method of predetermining the regulation of an alternator.

5. Explain why the potier reactance is slightly higher than leakages reactance.(April 2018)

6. Explain dark lamp method of synchronizing an alternator with the bus bar.

7. Explain Blondel’s two-reaction theory,(Dec 2015)

8. Explain how will you determine the d and q axes reactance of a synchronous machine in your

laboratory.(Dec 2017, April 2015, May 2014 )

9. Derive an expression for synchronizing power.

10. For a salient pole synchronous machine, derive an expression for power developed as a function

of load angle.

11. Explain the operating principle of three-phase alternator.(Dec 2018)

12. Explain the constructional details of a three-phase alternator, which is used for slow speed

operation.

13. What is meant by synchronizing?. State requirements for paralleling alternators.(Dec 2017)

14. Derive the equation of induced emf for an alternator.(Dec 2018,Dec 2017,Dec 2016,Dec 2014 )

15. Why voltage regulation value obtained using mmf method is considered as optimistic?(Dec

2018, Dec 2017,Dec 2016)

16. Explain step by step method of potier method of determining the regulation of analternator(April

2017)

17. Explain the concept of armature reaction and mention the methods to reduce this effect (May

2016)

Unit –II

1. Explain why a synchronous motor does not have starting torque.

2. Explain the starting methods of synchronous motor.(Dec 2015, May 2016, Dec 2016, Dec 2017)

3. Why does the power factor of industrial installation tend to be low? How can it be improved?

4. Does the change in excitation affect the p.f of the synchronous motor?(May 2014, Dec 2015, May

2016, April 2018)

5. An over excited synchronous motor is called a synchronous condenser. Explain.(Dec 2017)

6. Mention some specific applications of synchronous motor.

7. Explain what happens when the load on a synchronous motor is changed.(Dec 2015)

8. What is meant by constant power circle and constant excitation circle for synchronous

motor?(Dec 2014,Dec 2017)

9. What is meant by hunting in a synchronous motor? Why is it undesirable? What is done to minimize it? (April 2015)

10. Explain V-curves and inverted V-curves.(Dec 2014, May 2016, Dec 2016,April 2017, Dec 2018)

11. Draw the power angle diagram of a synchronous machine.

12. Explain briefly the principle of operation of three-phase synchronous motor.(Dec 2017, Dec

2018)

13. Describe the effect of varying the excitation on the armature current and power factor of a synchronous motor when input power to the motor is maintained constant.(May 2015)

14. Derive the expression for power delivered by a synchronous motor in terms of load angle(April 2017)

Unit –III

1. Develop the equivalent circuit for 3-phase induction motor? (May 2016, Dec 2016, April 2018)

2. Explain the different speed control methods of squirrel cage induction motor.

3. Describe the principle of operation of synchronous induction motor. (Dec 2014)

4. Explain any one method of speed control of three- phase induction motor.

5. Draw the slip-torque characteristics for a three-phase induction motor and explain. (Dec 2014, Dec 2016, April 2017,Dec 2018)

6. Explain how a rotating magnetic field is produced in a three-phase induction motor.

7. Draw and explain the equivalent circuit of a three-phase induction motor. (Dec 2015)

8. Describe with a neat diagram, the principle of operation of induction generator

9. Draw and explain the torque/slip curves of a three-phase induction motor for different values of rotor resistance.

10. Starting from the first principles, develop the equivalent circuit of a 3- phase induction motor.

11. Explain the procedure of drawing the circle diagram of an induction motor. How arethe performance characteristics obtained from it?( May 2016, April 2017)

12. Explain the operation of induction generator.( Dec 2016, Dec 2017)

13. Explain the construction and working principle of a 3 phase induction motor (Dec 2014, Dec

2017, April 2018)

14. Draw the equivalent circuit and derive expressions for maximum torque and power of a three

phase induction motor (April 2015)

15. Derive the expression for torque slip and draw speed torque characteristics of 3 phase induction

motor. Obtain the expression for maximum torque(May 2016, Dec 2017)

16. Explain the speed torque characteristics of the double cage induction motor with neat

diagram(Dec 2016)

17. Explain the concept of crawling and cogging of induction motor in detail (Dec 2018, May 2014)

Unit-IV

1. Develop the equivalent circuit for 3-phase induction motor.

2. Explain the different speed control methods of squirrel cage induction motor.

3. Explain the methods of starting of induction motor. (May 2016,Dec 2016)

4. Explain the characteristics features of alternator on load.

5. Explain what is crawling and cogging.

6. Describe Kramer system of speed control for 3-phase induction motor with a neat diagram. (Dec 2017)

7. Explain in detail autotransformer method of starting a squirrel cage induction motor.

8. How adding an external resistance in the rotor circuit controls the speed?

9. Briefly explain the V/F control of an induction motor. (Dec 2017)

10. Explain the working of following starters with help of neat circuit diagram.

i. Stator resistance starter

ii. Star- Delta starter (Dec 2014, Dec 2017)

iii. Direct On Line Starter

iv. Rotor resistance Starter

v. Autotransformer Starter (May 2014, Dec 2015, Dec 2016, April 2018)

11. Explain the pole amplitude modulation method.

12. Explain the supply voltage method. Why this method rarely used in practice.

13. With neat diagrams. Explain the slip power recovery schemes as applied towound rotor induction motors (Dec 2014, April 2015, April 2017)

14. Describe the method of speed control of 3 phase squirrel cage induction motor by changing the number of stator poles and state the application of this method.(Dec 2014, Dec 2017)

15. Explain the different speed control methods of induction motor. (Dec 2015, April 2018)

16. Explain the methods of starting of slip ring induction motor. (April 2015, May 2016)

17. Describe Scherbius system of speed control for 3-phase induction motor with a neat diagram. (May 2016)

18. Explain the DC dynamic braking ofa 3 phase induction motor (Dec 2017)

Unit-V 1. Explain the operation of a single-phase induction motor using double revolving field theory. (May 2014, Dec 2014, Dec 2015, April 2015, Dec 2016,April 2017, Dec 2017)

2. Describe the constructional features and operating charactertics of single- phase shaded pole motor.

3. Explain the construction and principle of working of stepper motor. (May 2014, Dec 2017, Dec

2018)

4. Explain the principle of operation and applications of reluctances motor.

5. Explain the principle of operation and constructional details of linear induction motor.

6. Write brief notes on hysteresis motor. (Dec 2014, April 2015,Dec 2015, May 2016, Dec 2016,

April 2017, Dec 2017, April 2018)

7. Write brief notes on A.C.series motor. (Dec 2014, April 2015, Dec 2015, May 2016, Dec 2016,

April 2017, April 2018)

8. Explain the methods of making single-phase induction motor self-starting.

9. Write short notes on linear induction motor. (May 2016)

12. Write notes on permanent magnet DC motor.

14. With neat diagram, explain the construction and operation of shaded

pole motor.(Dec 2016, Dec2017)

15. Explain the speed control of universal motor.

15. What is a universal motor? Draw its phasor diagram and discuss its operation. Bring out the effects of various emf induced in the armature.

16. Explain the no load and blocked rotor test for obtaining the equivalent circuit parameters of single phase induction motor (Dec 2014, Dec 2017)

17. Write notes on Repulsion motor (Dec 2015)

18. Explain why single phase induction motor is not self starting? (Dec 2015)

19. Explain in detail the operation of capacitor start and run induction motor (May 2016)

20. Give the classification of single phase motors. Explain any two types of singlephase induction motor.( April 2018)

TRANSMISSION AND DISTRIBUTION

UNIT I TRANSMISSION LINE PARAMETERS

PART-A

1. Why is electrical power preferably to be transmitted at a high voltage? [April/May15]

Electric power is preferably transmitted at a high voltage because it improves transmission

efficiency, reduces percentage line drop and reduces the cost of conductor material.

2. Give reason why the transmission lines are three phase 3 wire circuits while distribution lines

are three phase 4 wire circuits.[Nov/Dec -13]

The transmission is at very high voltage level and such a balanced three phase system does not

require neutral conductor. Hence the transmission line circuits are 3 phase 3 wire circuits. While

distribution, it is necessary to supply single phase loads along with the three phase loads. For single

phase distribution a neutral conductor is must. Hence distribution lines are 3 phase 4 wire circuits.

3. List out the advantages of high voltage A.C transmission. [Nov/Dec‘11] [May/June‘16]

Reduction of current and losses

Reduction of volume of conductor material

Improvement in voltage regulation

Increase in transmission efficiency

Reduction in %line drop.

4. List the various elements of power system.[April/May‘14]

The various elements of power system are generators, transformers, transmission lines, bus bars,

circuit breakers, isolating switches, feeders, distributors, service mains etc.

5. State the practical transmission and distribution voltage levels commonly used. [Apr/May05]

Generating station: 6.6kV, 11kV or 22kV

Primary transmission: 11kV/132kV/220kV/400kV

Secondary transmission: 11kV/22kV/33kV

Primary distribution: 6.6kV/3.3kV/11kV

Secondary distribution: 400V/230V.

6. What is the highest a.c transmission voltage we have in India?[April/May‘10]

The highest a.c transmission voltage we have in India is now 1200kV in Madhya Pradesh.

7. What is skin effect and its consequence?[Nov/Dec -12][Nov/Dec‘10]

Skin effect is defined as the tendency for the alternating current (AC) to flow mostly near the outer

surface of a conductor which causes non-uniform distribution of current. Thus the current density

is largest near the surface of the conductor and decreases with greater depths inside the conductor.

The effect becomes more and more apparent as the frequency increases.

Due to reduction in effective area of cross section offered to the flow of current through the

conductor, the resistance of conductor increases.

8. What is proximity effect? [May/June‘13] [April/May‘11] [April/May-15] [Nov/Dec‘15]

Due to non uniform distribution of current, the current density is non uniform which increases the

effective resistance of the conductor. As the distance between the conductor goes on reducing, the

distribution of current becomes more and more non uniform. This is known as proximity effect.

9. A three phase transmission line has its conductor at the corners of an equilateral

triangle with side 3m. The diameter of each conductor is 1.63cm. Find the inductance

per phase per km of the line.[Nov/Dec -13] [April/May-15][A]

The expression for the inductance of a conductor. A in a three phase line with spacing D

between the conductors and r‘ as the effective radius (GMR) is given by

10. Deduce an expression for capacitance of three phase transmission line with

unsymmetrical spacing. (Transposed conductors)[10][Nov/Dec‘13]

The capacitance of the 3 phase unsymmetrically spaced transmission lines is given by,

11. What are the advantages of using bundled conductors?[Nov/Dec‘11]

Reduction in corona loss

Minimization of interference with communication circuit.

Reduction in voltage drop which increases circuit capacity and boosting ofoperating

voltage.

Low reactance, increase in capacitance and surge impedance loading.

12. Distinguish between self and mutual GMD.[Nov/Dec‘15]

Self GMD Mutual GMD

The denominator of argument of log, which is the m2 root of m2 distances, the distances of the various conductors from one conductor and the radius of the same conductor, is called geometric mean radius (GMR also called self GMD) and denoted by Ds.

The numerator of argument of natural log mndistances between m conductors of wire-A and n conductors of wire-B) is called geometric mean distance(GMD, often called GMD) and denoted by Dm.

13. Mention the advantages of transposition of conductors. [Nov/Dec‘15]

Transposition of Conductors refers to the exchanging of position of conductors of a three

phase system along the transmission distance in such a manner that each conductors occupies

the original position of every other conductor over an equal distance. When conductors are not

transposed at regular intervals, the inductance and capacitance of the conductors will not be

equal. When conductors such as telephone lines are run in parallel to transmission lines, there

is a possibility of high voltages induced in the telephone lines. This can result in acoustic

shock or noise. Transposition greatly reduces this undesired phenomenon.

14. What are the factors to be considered while designing a transmission line?

various factors to be considered while designing a transmission line are

Type and size of conductor

Voltage level

Power flow capability, stability and efficiency of transmission

Line regulation and control of voltage

Power system structure

Economic aspects

15. What are the advantages of double circuit lines?

The advantages of double circuit lines are

(i) Continuity of supply is possible

(ii) More reliable.

(iii) Less spacing of conductors required

(iv) Less inductance and reactance.

(v) Efficiency is enhanced as compared with single circuit lines.

16. Write the expression for a capacitance of a 1ᴓ transmission line. [Nov/Dec ‗12][R]

Capacitance of the line per unit length is given by

17. What is meant by transposition of line conductors?[April/May‘11]

Transposition is the periodic swapping of positions of the conductors of a transmission line, so

that each conductor occupies the original position of every other conductor over an equal

distance so as to achieve balance in the three phases.

18. What are the advantages of using bundled conductors?[Nov/Dec‘11]

a. Reduction in corona loss

b. Minimization of interference with communication circuit.

c. Reduction in voltage drop which increases circuit capacity and boosting of operating voltage.

d. Low reactance, increase in capacitance and surge impedance loading.

19. What are the advantages of double circuit lines?

The advantages of double circuit lines are

(i) Continuity of supply is possible

(ii) More reliable.

(iii) Less spacing of conductors required

(iv) Less inductance and reactance. Efficiency is enhanced as compared with single

circuit lines.

UNIT II MODELLING AND PERFORMANCE OF TRANSMISSION

PART-A

1. Write down the classification of overhead transmission line Short transmission line

Medium transmission line

Long transmission line

2. What is mean by Short transmission line? If the transmission line length is about 50 km and the line voltage is low i.e. is 20kv or less than

that the line is treated as short transmission line.

3. What is mean by medium transmission line?

When the transmission line length is about 50 to 150 km and the line voltage is 20kv to

100kv than that the line is treated as short transmission line.

4. What is mean by long transmission line?

When the transmission line length is about 150 km and the line voltage is Above 100kv than that

the line is treated as short transmission line.

5. What are the types of medium transmission line?

End condenser method

Nominal T method

Nominal π method

6. Define voltage regulation. The difference in voltage at the receiving end of the transmission line at the no load and full load

is termed as voltage regulation expressed in terms of percentage of receiving end voltage % voltage regulation = (Vnoload – Vfull load / Vfull load ) X100

7. Define transmission efficiency.

The ratio of power obtained at the receiving end to the power at sending end is called transmission efficiency of the line.

8. What is meant by disruptive critical voltage?[Nov/Dec -13][Nov/Dec‘11]

The potential difference between conductors, at which the electric field intensity at the surface of

the conductor exceeds the critical value and generates corona is known as disruptive critical voltage

9. What is corona?[May/June‘16]

The phenomenon of corona (a sort of electric discharge around the high tension line)

produces a hissing noise which is audible when habitation is in close proximity. At the towers

great attention must be paid to tightness of joints, avoidance of sharp edges and use of earth

screen shielding to limit audible noise to acceptable levels.

10. Define: Visual critical voltage. [May/June‘13]

Experimental investigations have revealed that visual corona does not occur when the electric

intensity becomes equal to critical value Eo but starts at a higher value of intensity Ev. This is

because the dielectric breakdown of air requires a finite volume of over stressed air. In other

words, a finite amount of dielectric energy is necessary to cause visual corona. The empirical

relation for calculating Ev is

Where r is the conductor radius in meter and mv is the surface factor is calculating visual

critical voltage. mv is generally called irregularity factor.

11. How will you reduce the corona loss?[Nov/Dec‘15]

a. Increasing the conductor size.

b. Increasing the conductor spacing

c. Using hollow and bundled conductor.

12. What are the factors to be considered while designing a transmission line? The

various factors to be considered while designing a transmission line are

Type and size of conductor

Voltage level

Power flow capability, stability and efficiency of transmission

Line regulation and control of voltage

Power system structure

Economic aspects

13. What is mean by corona effect?[April/May‘08]

It can be noticed that near the overhead lines there exists is hissing noise and sometimes a faint violet glow. The effect due to which such phenomenon exists surrounding the overhead lines is called corona effect.

14. What are the factors affecting corona?[April/May‘12]

Electrical factors such as supply frequency

Line voltages

Atmospheric conditions like pressure, temperature etc.

Size of the conductor

Surface conditions whether rough, smooth, dry or wet

Shape of the conductor

Spacing between conductors

Number of conductors per phase

Clearance from ground.

Load current.

15. What are the disadvantages of corona loss?[April/May‘05]

The corona power loss is the biggest disadvantage which reduces the

transmission efficiency.

The third harmonic components produced due to corona makes the current non

sinusoidal. This increases the corona loss.

The ozone gas formed due to corona chemically reacts with the conductor and

can cause corrosion.

16. What is the range of surge impedance in case of underground cables?[Nov/Dec -12]

The approximate value of surge impedance for underground cables is 40Ω while typically it is in

the range of 40Ω to 60Ω.

17. What is the range of surge impedance of an OH transmission line?[May/June‘13] The

approximate value of surge impedance for overhear lines is 400Ω while typically it is in

the range of 400Ω to 600Ω.

18. Distinguish between attenuation and phase constant.[Nov/Dec‘11]

Attenuation constant Phase constant

It is the real part of the propagation constant γ.

It is the imaginary part of the propagation constant γ.

It is denoted by the symbol α. It is denoted by the symbol β.

It is measured in nepers per unit length It is measured in radians per unit

Length.

It represents the attenuation of an

electromagnetic wave propagating through a

medium per unit distance from the source.

It represents the change in phase

per meter along the path travelled

by the wave at any instant.

19. Draw equivalent circuit and phasor diagram for short

transmission line.[May/June‘16]

20. What is power circle diagram?

The real and reactive powers at sending and receiving end can be computed mathematically

and the transmission line characteristics can be represented graphically. By taking sending

end or receiving end voltage or current as a reference, these characteristics can be plotted

which represent circle and the corresponding diagram is called circle diagram. The real

power is plotted on X axis while the reactive power is on Y axis.

21. Draw the nominal π representation of a transmission line.

22. Draw the nominal T representation of a transmission line.

23. What are the factors which govern the performance of a transmission line?

The transmission line performance is mainly governed by its four parameters series resistance

and inductance, shunt capacitance and conductance where the shunt conductance is often

neglected as it is very small. All these parameters are distributed over the length of the line.

Based on these parameters measures of transmission lines are the transmission efficiency and

voltage regulation both expressed as percentage.

24. What is mean by Surge impedance?

In the power system network the characteristic impedance is sometimes referred as surge

impedance. It is defined as square root of Z/Y.

Where,

Z = series impedance of line

Y = Shunt admittance of line.

22. Write down the various factors on which transmission line capability.

Thermal limits of conductor

Transient and steady state stability

Transmission line capability depends on over voltage at the capacitor terminals of series compensated line.

UNIT III MECHANICAL DESIGN OF LINES

PART-A

1. Mention the insulating materials used in insulators.[May/June -13] Porcelain

Glass

Synthetic resin

steatite

2. What are the methods of improving string efficiency?[May/June‘13][Nov/Dec‘15]

By using longer cross arms to reduce the ratio of shunt capacitance to self capacitance

By grading the insulators

By using a guard ring

3. How does guard ring improve string efficiency? [Nov/Dec -13]

The use of guard ring increases the capacitance between the metal plate of insulator and the line. These

capacitors are greater for the lower units. Due to this the voltage across these units is reduced. Hence

uniform voltage distribution can be obtained which improves the string efficiency

4. What are the causes of failure of insulators?[April/May‘11]

Due to lightning strokes

Due to mechanical stresses

Due to cracking of insulating material

Due to porosity in the insulating material

Due to defective insulating material

Improper glazing on the insulator surface due to which moisture sticks on the surface

causing flashovers.

Due to overheating caused by flashovers

Due to short circuits.

5. Define string efficiency.[Nov/Dec‘10][Nov/Dec‘15][May/June‘16]

The ratio of voltage across the whole string to the product of number of discs and the voltage

across the disc nearest to the conductor is known as string efficiency.

6. What is the main purpose of armouring? [April/May -15]

Armoring is a layer consisting of galvanized steel wires which provide protection to the cable

from the mechanical injury.

7. What are the tests performed on the insulators?[May/June‘16]

a. Mechanical tests

b. Electrical insulation tests

c. Environmental tests

d. Temporary cycle tests

e. Corona and radio interference tests

8. What is dielectric stress?[April/May‘14]

The insulation of a cable is subjected to an electrostatic force under operating condition which

is called dielectric cable.

9. What is shackle insulator?[April/May‘14]

The insulator used at the dead end of the aerial wire of service connection to a house or a

factory to reduce the excessive tension is called shackle insulator. It is also used if distribution

line changes its angle.

10. What are the properties of insulators?[Nov/Dec‘10]

a. High mechanical strength

b. High insulationresistance

c. High relative permittivity

d. Should not be affected by temperature changes

e. It should be non porous

f. It should be flexible

g. It should be non-inflammable

11. Why the potential distribution across the string of insulators

is not uniform?[Nov/Dec‘06]

Due to different shunt capacitors, the charging currents through them are different. Hence the

potential distribution across the string of insulators is not uniform.

11. Define sag.[May/June‘16][Nov/Dec‘13]When a conductor is suspended between two

points then it takes the shape of parabola or catenary and sags down. The difference in levels

between the point of support and the lowest point on the conductor is called sag.

12. What is meant by sag template?[Nov/Dec‘15]

For normal spans and for standard towers, the sag and the nature of the conductor curve are

calculated under excepted load conditions and plotted on a thin stiff plastic sheet. Such a graph

is called sag template.

13. What is the economic value of span of 400kV transmission line?[April/May‘10]

The span must be between 200m to 400m. For river and ravine crossing exceptionally long

spans up to 800m or so is sufficient.

14. Give two factors which affect the sag in transmission line. [Nov/Dec‘12]

Ice coating on the conductor which increases weight of the conductor

Wind pressure due to which the conductor gets subjected to the additionalforces.

15. Define factor of safety.

The ultimate stress which conductor can sustain without fail is called breaking stress. The normal tension

in the conductor is called working stress. The ration of breaking stress to the working stress is called the

factor of safety denoted as Sf.

16. Classify the types of insulators.

There are several types of insulators but the most commonly used are pin type, suspension type,

strain insulator and shackle insulator.

1 Pin type Insulators. Pin Type Insulator

2 Suspension Type. Suspension Type.

3 Strain Insulators. Strain Type Insulator

4 Shackle Insulators. Shackle Type Insulator

17. Classify the types of towers.

Types of towers

Waist-type tower. This is the most common type of transmission tower. ...

Double-circuit tower. This small-footprint tower is used for voltages ranging from 110 to 315

kV.

Guyed-V tower. This tower is designed for voltages ranging from 230 to 735 kV. ...

Tublar steel pole. ...

Guyed cross-rope suspension tower. ...

Crossings.

18. What is the reason for the sag in the transmission line? (Nov2013)

While erecting the line, if the conductors are stretched too much between supports then there

prevails an excessive tension on the line which may break the conductor. In order to have safe tension in

the conductor a sag in the line is allowed.

19. What are the methods ofTesting Of Insulators?

Following are the different types of tests that are carried out on overhead line insulators.

Flashover tests

Performance tests

Routine tests

20. What is the purpose of insulation test?

Insulation tests on low voltage circuit breakers are performed to ensure acceptable levels of insulation resistance between phases and from phase to ground. Test equipment is used to apply an overvoltage to test the integrity of the insulation.

UNIT IV UNDER GROUND CABILITYS

PART-A

1. Define grading of cables.[Nov/Dec -12][Nov/Dec‘15]

The process of obtaining uniform distribution of stress in the insulation of cables is called

grading of cables.

2. Mention any 4 insulating materials for cables.[May/June‘13]

a. Poly vinyl chloride(PVC)

b. Paper

c. Cross linked polythene

d. Vulcanisedindia rubber (VIR)

3. Why loss angle of a cable should be very small?[April/May‘11]

The dielectric loss in a cable is given by,

W=V2ωtanδ

where δ = Loss angle Smaller the loss angle δ, smaller are the dielectric losses. Hence the loss angle of cable should be very

small.

4. What are the methods of grading of cables?[Nov/Dec‘11]

i. Intersheath grading

ii. Capacitance

5. What is the main purpose of armouring? [April/May -15]

Armouring is a layer consisting of galvanized steel wires which provide protection to the cable

from the mechanical injury.

6. Classify the cables used for three phase service.[May/June‘16]

1. Belted cables — upto 11 kV

2. Screened cables — from 22 kV to 66 kV

3. Pressure cables — beyond 66 kV.

7. What is dielectric stress?[April/May‘14]

The insulation of a cable is subjected to an electrostatic force under operating condition

which is called dielectric cable

8. What is the economical core diameter to give minimum value of maximum stress? The

core diameter must be ½.718 times the sheath diameter D so as to give the minimum value of

the maximum stress

9. What is bedding?

The metallic sheath in a cable is covered by a layer called bedding which fibrous material like

jute cloth which protects the armouring from the atmospheric conditions.

10. Write down the various parts of cables.

(i) Core (ii) Insulation (iii) Metallic sheath (iv) Bedding (v) Armouring (vi) Serving

11. What are the types of cables?

(i) Low tension cable

(ii) High tension cable

(i) belted cable (ii) super tension cable (iii) extra tension cable

12. What are the advantages of separate lead sheath cables?

(i) Due to individual lead sheath core to core fault possibility gets minimized

(ii) The electrical stress are radial in nature

(iii) Bedding of cable is easy

(iv) Increases the current carrying capacity

13. What are the types of super tension cable?

(i) Oil filled cables (ii) Gas pressure cables

14. What are the advantages of oil filled cables?

(i) Thickness of insulation is less (ii) The thermal resistance is less (iii) The possibility

of voids is completely eliminated (iv) Reduced earth fault

15. What are the disadvantages of oil filled cables?

(i) The initial cost is very high (ii) The long length is not possible (iii) The laying of cable

is difficult (iv) Maintenance of cable is difficult

16. What are the advantages of gas pressure cables?

(i) Maintenance cost is small (ii) The nitrogen in the steel tube helps in quenching any fire

or flame (iii) No reservoirs or tanks required (iv) The power factor is improved

17. What is mean by grading of cables?

The process of obtaining uniform distribution of stress in the insulation of cables is called

grading of cables.

18. What is mean by capacitance grading?

The grading done by using the layers of dielectrics having different permittivity between the

core and the sheath is called capacitance grading

19. What are the types of suspension type insulator? (i) Cemented cap type (ii) Hewlett or

inter linking type

20. What are the methods used to secure insulator to the bolt?

(i) The porcelain insulator has cement threads which are lined with a soft material like lead.

The pin is screwed into such cement screw

21. What are disadvantages of gas pressure cable?

The only disadvantage of this cable is very high initial cost

UNIT V DISTRIBUTION SYSTEMS

PART-A

1. Why is electrical power preferably to be transmitted at a high voltage? -[Nov/Dec‘15]

Electric power is preferably transmitted at a high voltage because it improves transmission

efficiency, reduces percentage line drop and reduces the cost of conductor material.

2. What is a feeder? [Nov/Dec -12][Nov/Dec‘15]

A feeder is a conductor which connects the substation or localized generating station to the

area where power is to be distributed.

3. List the types of HVDC links. [May/June‘13]

Monopolar HVDC system

Bipolar HVDC system

Homopolar HVDC system

Back to back HVDC coupling system.

4. Give reason why the transmission lines are three phase 3 wire circuits while distribution

lines are three phase 4 wire circuits.[Nov/Dec -13]

The transmission is at very high voltage level and such a balanced three phase system does not require

neutral conductor. Hence the transmission line circuits are 3 phase 3 wire circuits. While distribution, it

is necessary to supply single phase loads along with the three phase loads. For single phase distribution

a neutral conductor is must. Hence distribution lines are 3 phase 4 wire circuits.

6. State the disadvantages of HVDC transmission.[Nov/Dec‘10]

Converters at both ends though reliable they are much expensive than the ordinary

AC equipments and they have little overload capacity and needs supply of reactive

power locally.

Using HVDC becomes economically only for long distances

It is impossible to either step up or step down DC voltages directly so conversion is

required everytime-transformation is required.

The converters produce a lot of harmonics which may cause interference with

communication lines requiring filters which increase the cost.

Circuit breaking for multiterminal line is difficult.

7. List out the limitations of high transmission voltage.[Nov/Dec‘15]

More insulation is required for the conductors and towers

More clearance is required between the conductors and ground. So height of the

supporting tower increases.

More distance is required between the conductors. So length of the cross arms used

increases.

The transformers, switchgears and other terminal equipments should be designed to

handle such high voltages.

9. State the meaning of an electrical grid.[April/May‘09]

An electrical grid is a network in which the various generating, transmission and distribution

systems are interconnected with each other to supply electricity to the consumers.

10. List the various elements of power system.[April/May‘14]

The various elements of power system are generators, transformers, transmission lines, bus

bars, circuit breakers, isolating switches, feeders, distributors, service mains etc.

11. What is service mains?[April/may‘11]

The small cables used to connect the distributors and the actual consumer premises are called

service mains.

12. Explain the term regionalgrid.[Nov/Dec‘07] In order to achieve economy, reliability and continuity in the supply, individual power

systems generating electrical power are arranged in the form of electricity connected areas called

regional grid

13. List the types of substations[Nov/Dec 12][Nov/Dec‘10]

Indoor sub-station

Outdoor sub-station

Underground sub-station

Pole-mounted sub-station

14. Mention any 4 bus schemes in the substation. [May/June‘13]

Single bus single breaker scheme

Double bus double breaker scheme

Main transfer bus scheme

Ring main arrangement scheme

One and half breaker scheme

15. What is the function of isolators? [Nov/Dec‘13]

The function of isolators is to disconnect a part of power system for repair and maintenance and

operated after switching off the load by means of a circuit breaker.

16. What is the need of an earthing system?[Nov/Dec‘13]

In order to provide safety of personnel or human beings against electrical shocks (include

animals and plants), to reduce the possibility of getting electrical shocks and avoiding

accidents, to protect the equipments, buildings, machinery/appliances against lightning and

voltage surges, to reduce stress on the lines along with that on the equipment with respect to

earth under abnormal conditions earthing is required.

17. State the advantages of outdoor substation over indoor substation.[April/May‘11]

Following are the disadvantages of outdoor substation over indoor substation:

Time required for erection is less

Future expansion is easier

The capital cost required is less

All equipments are within view and the fault location is easier

The cost of switchgear installation is less and amount of building material

required is small.

18. What are the objectives of earthing?[April/May‘11]

i. It should provide adequate safety of operating personnel/human being (including

animals and plants) against electrical shocks/hazards and avoid accidents

ii. It should provide an alternative path for the fault current to flow so as to reduce danger

of the user

iii. It should ensure that all the exposed conductive parts do not reach a dangerously high

potential and should reduce the stress on the lines along with that on the equipment with

respect to earth under abnormal conditions.

iv. It should be able to maintain the voltage at any part of an electrical system at a known

value so as to avoid excessive voltage on the appliances or equipment or over current

situation.

19. What are the various methods of earthing in substations?[Nov/Dec‘11]

The earthing in substations is carried out with the help of equipments such as electrodes,

driven rods, risers and grounding grid or mat consisting of number of meshes and connected to

several earth electrodes driven at intervals. The various methods adopted for earthing are

i. Solid or effective grounding

ii.Resistance grounding

iii. Reactance grounding

iv. Resonant grounding

20. State the disadvantages of HVDC transmission.[Nov/Dec‘10]

(i) Converters at both ends though reliable they are much expensive than the ordinary AC

equipments and they have little overload capacity and needs supply of reactive power locally.

(ii) Using HVDC becomes economically only for long distances

(iii) It is impossible to either step up or step down DC voltages directly so conversion is

required everytime-transformation is required.

(iv) The converters produce a lot of harmonics which may cause interference with communication lines requiring filters which increase the cost.

(v) Circuit breaking for multiterminal line is difficult.

21. List out the basic types of FACTS controller.[April/May‘11][R]

(a) Series controller

(b) Shunt controller

(c) Combined series-series controller

(d) Combined series-shunt controller

22. Definition of Kelvin's law.

A statement in electrical economics: the most economical cross-section area for an electric conductor is that for which the cost of energy lost in a given period equals the interest for

the same period of the capital involved.

23. What are the objectives of FACTS?[May/June‘16]

(i) Regulation of power flow is prescribed transmission routes

(ii) Loading of transmission lines nearer to their thermal limits

(iii) Contributing to emergency control without disconnecting more equipments from source

(iv) Improves system stability by damping oscillations.

24. State the advantages of FACTS.[April/May‘10]

It controls line impedance angle and voltage which helps in controlling the power flow in transmission lines.

The power flow in transmission lines can be made optimum.

It helps in damping out the oscillations and prevent the damage of equipments

It supports the power system security by increasing the transient stability.

It limits the overloads and short circuit currents

The reserve requirements for generators are considerable reduced.

The loading capacity of the line is greatly increased upto their thermal capabilities.

25. List out the various FACTS devices.[April/May‘08]

a. Static synchronous compensator(STATCOM)

b. Static synchronous generator(SSG)

c. Static VAR compensator (SVC)

d. Thyristor switched or controlled reactor.(TSR/TCR)

e. Static VAR generator(SVG)

f. Static VAR systems(SVS)

g. Thyristor controlled braking resistor.(TCBR)

h. Static synchronous series compensator(SSSC)

i. Interline power flow controller(IPFC)

j. Unified power flow controller (UPFC)

k. Interphase power controller(IPC)

l. Thyristor controlled voltage limiter(TCVL)

UNIT I

UNIT I TRANSMISSION LINE PARAMETERS

PART-B

1. Draw and explain the structure of electric power system indicating the voltage level in each transmission levels. [10][Nov/Dec‘13]

2. Derive an expression for capacitance of 3ᴓ unsymmetrically spacedtransmission

line.[16][Nov/Dec ‗12][May/June‘16]

3. Derive an expression for the inductance of a 3ᴓ over head transmission lines with

unsymmetrical spacing. Also spacing the concept of transposition of conductors.

[16][May/June‘13][Nov/Dec‘10]

4. Derive an expression for the capacitance of a 1ᴓ overhead transmission line.

[8][May/June‘13]

5. Find out the capacitance of a line 1ᴓ line 30km long consisting of two parallel wires each

15mm diameter and 1.5m apart. [8][May/June‘13]

6. A three phase circuit line consist of 7/4.75mm hard drawn copper conductors. The

arrangement of the conductors is shown in figure. The line is completely transposed.

Calculate inductive reactance per phase per km of the

system.[12][Nov/Dec‘13][Nov/Dec‘11][April/May‘15]

7. Derive an expression for capacitance of a three phase transmission linewith

asymmetrical spacing.[12][April/May‘11]

8. A 220kV, 50Hz, 200km long three phase transmission line has its conductors on the

corners of a triangle with sides 6m, 6m and 12m. The conductor radius is 1.81cm. Find

the capacitance per phase per kilometre.[4][April/May‘11]

9. Find the inductance per phase per km of double circuit 3 phase line shown in figure. The

line is completely transposed and operates at a frequency of 50Hz

10. A 220kV, 50Hz, 200km long three phase transmission line has its conductors on the

corners of a triangle with sides 6m, 6m and 12m. The conductor radius is 1.81cm.

11. Find the capacitance per phase per kilometre, capacitive reactance per phase. Charging

current and total charging Mega volt-amperes.[16][Nov/Dec‘10]

12. Determine the inductance per km of a double circuit 3ᴓ line as shown in Figure. The

transmission line is transposed within each circuit and each circuit remains on its own

side. The diameter of each conductor is 15mm.[16][May/June‘16]

13. A 460 kV bundled conductor transmission line has the conductor

spacing as shown below. ACSR conductors are used. Determine the inductance per

phase per km if the self GMD of each conductor is 0.9cm. Assume line regularly

transposed.[16][May/June‘16][A]

UNIT II MODELLING AND PERFORMANCE OF TRANSMISSION LINES

PART-B

1. A 15km long 3 phase overhead line delivers 5MW at 11kV at 0.8 lagging p.f line loss is

12% of power delivered. Line inductance is 1.1mH per km per phase. Find sending end

voltage and voltage regulation.[16][Nov/Dec ‗12]

2. Explain the following methods for medium transmission lines. (i) end condenser method.

(ii) nominal T method (middle condenser method) [16]

3. A three phase, 50Hz transmission line, 40km long delivers 36MW at 0.8 power factor

lagging at 60kV(phase). The line constants per conductor are, R=25Ω, L=0.1H.

C=0.25µF. Shunt leakage may be neglected. Determine the voltage, current, power factor,

active power and reactive voltamperes at the sending end. Also determine the efficiency

and regulation of the line using nominal π method.[16][Nov/Dec‘13][

4. Deduce an expression for the sending end and receiving end power of a line in terms of

voltages and ABCD constants. Show that the real power transferred is dependent on the

power angle and reactive power transferred is dependent on the voltage drop in the

line.[16][April/May‘11

5. A 200km long three phase over transmission line has a resistance of 48.7Ω/phase,

inductive reactance of 80.20Ω/phase and capacitance (line to neutral) 8.42nF per km. It

supplies a load of 13.5 MW at a voltage of 88kV and power factor 0.9 lagging. Using

nominal T-circuit, find the sending and voltage, current, regulation and power

angle.[16][April/May‘11]

6. A 3 phase line having an impedance of (5+j20)Ω per phase delivers a load of 30MW at a

power factor of 0.8 lag and voltage of 33kV. Determine the capacity of the phase

modifier to be installed at the receiving end if the voltage at the sending end is to be

maintained at 33kV. Assume the shunt admittance is neglected.[16][Nov/Dec‘11

7. Explain the real and reactive power flow in lines. Also explain the methods of voltage

control.[16][April/May‘15]

8. A 3ᴓ, 50Hz, 100 km line has the following constants. Resistance/phase/km=0.153Ω,

inductance/phase/km=1.21mH, Capacitance/phase/km=0.00958 µF. If the line supplies a

load of 20MW at 0.9 pf lagging at 110kV at the receiving end calculate sending end

current, sending end power factor, regulation and transmission efficiency using nominal

T method.[16][May/June‘16][

9. Draw the nominal T circuit of a medium length transmission line and derive expressions

for sending end voltage and current. Also draw the respective phasor

diagram.[16][Nov/Dec‘15]

10. Derive the power flow performance equation of a three phase transmission line in the

form of sending-end receiving-end complex power and voltages at the two ends of the

line.[08][May/June‘16][

11. Write a short note on the following: (i) concept and procedure to draw circle diagram (ii)

Power transfer capability of the transmission lines.[16][Nov/Dec‘15]

12. Explain the following with respect to corona. [Nov/Dec

‗12][April/May‘15]

a. Corona[2][R]

b. Effects[2][R]

c. Disruptive critical voltage[4][R]

d. Visual critical voltage.[4][R]

e. Corona power loss[4][R]

13. Explain the various factors affecting the corona loss.[8][Nov/Dec‘11]

14. Explain the phenomenon of ‗Corona‘ at EHV line. How can the corona effect be

minimized?[06][May/June‘16]

15. Determine (i) the critical disruptive voltage (ii) the visual critical voltage and (iii) the

corona loss under foul weather condition for 3-phase line, 160 km long, conductor

diameter 1.036 cm, 2.44 metre delta spacing. Air temperature 26.6ºC, corresponding to an

approximate barometric pressure of 73.15 cm of mercury, operating voltage 110 kV at

50Hz , surface irregularity factor is 0.85. Assume roughness factor is 0.72 and disruptive

voltage under foul weather=0.8 times of fair weather value.[10][May/June‘16]

16. Explain about interference between power and communicationcircuits.[04][Nov/Dec‘13

UNIT III MECHANICAL DESIGN OF LINES 1. Define ‗string efficiency‘ and calculate its value for a string of 3 insulators units if the

capacitance of each unit to earth and line be 20% and 5% of the self capacitance of the

unit. Derive any formula that might be used.[16][May/June‘13][

2. Why are insulator used with overhead lines? Discuss the desirable properties of

insulators.[6][Nov/Dec‘13]

3. An insulator string for 66kV lines has 4 discs. The shunt capacitance between each joint

and metal work is 10% of the capacitance of each disc. Find the voltage across the

different disc and string efficiency.[10][Nov/Dec‘13]

4. Explain briefly the different methods for improving string efficiency of an

insulator.[8][April/May‘11

5. An insulator string has three units each having a safe working voltage of 15kV. The ratio

of unit self capacitance to stray capacitance of earth is 10:1. Calculate the string

efficiency.[8][April/May‘11][U]

6. A 3 phase overhead transmission line is being supported by three disc insulators. The

potentials across top unit and middle unit are 9kV and 11kV respectively. Calculate

the ratio of capacitance between pin and earth to the self-capacitance of each unit.

the line voltage and (iii) the string efficiency.[16][Nov/Dec/11][A]

7. Discuss briefly on the following: (a) Pin type insulator (b) Suspension type

insulator.[16][Nov/Dec/10]

8. In a 3-unit insulator, the joint to tower capacitances is 20% of the capacitance of each

unit. By how much should the capacitance of the lowest unit be increased to get a string

efficiency of 90%? The remaining two units are left

unchanged.[16][April/May‘15][

9. What are the various properties of insulators? Also briefly explain about suspension type

and pin type insulators. Draw the schematic diagram[16][April/May‘15

10. A three unit insulator string is fitted with a guard ring. The capacitances of the link pins to

metal work and guard ring can be assumed to be a 15% and 5% of the capacitance of each

unit. Determine voltage distribution and string efficiency.[08][May/June‘16]

11. Discuss briefly on the following: (a) Pin type insulator (b) Suspension type

insulator.[16][Nov/Dec/10

12. In a 3-unit insulator, the joint to tower capacitances is 20% of the capacitance of each

unit. By how much should the capacitance of the lowest unit be increased to get a string

efficiency of 90%? The remaining two units are left

unchanged.[16][April/May‘15][

13. What are the various properties of insulators? Also briefly explain about suspension type

and pin type insulators. Draw the schematic diagram[16][April/May‘15]

14. A three unit insulator string is fitted with a guard ring. The capacitances of the link pins to

metal work and guard ring can be assumed to be a 15% and 5% of the capacitance of each

unit. Determine voltage distribution and string efficiency.[08][May/June‘16] A single

core cable used on 33 kV, 50Hz has conductor diameter 10 mm and inner diameter of

sheath 25 mm. The relative permittivity of insulating material used is 3.5. Find:

Capacitance of the cable per km

Maximum and minimum electrostatic stress in the cable.

Charging current per km.[08][May/June‘16]

15. The self capacitance of each unit in a string of three suspension insulators is C. The

shunting capacitance of the connecting metal work of each insulator to earth is 0.15C

while for line it is 0.1C. Calculate the voltage across each insulator as a percentage of the

line voltage to earth and string efficiency.[16][Nov/Dec‘15]

16. A transmission line has a span of 275 m between level supports. The conductor has an

effective diameter of 1.96cm and weighs 0.865kg/m. If the conductor has ice coating of

radial thickness 1.27cm and is subjected to a wind pressure of 3.9 gm/sq.cm of projected

area. The ultimate strength of the conductor is 8060kg. Calculate the sag if the factor of

safety is 2 and weight of 1 c.c of ice is 0.91gm.[16][May/June‘16]

17. Assuming that the shape of an overhead line can be approximated by a parabola, deduce

expressions for calculating sag and conductor length. How can the effect of wind and ice

loadings be taken into account?[16][Nov/Dec‘15]

UNIT IV UNDER GROUND CABILITYS

1. Describe the general construction of an underground cable with a neat

sketch.[8][Nov/Dec ‗12][May/June‘16][

2. State the classification of cables and discuss their general construction.[8][Nov/Dec12][

3. Explain the following with respect to cables. (i) capacitance grading (ii) Intersheath

grading. [16][May/June‘13]

4. Describe an experiment to determine the capacitance of a belted Cable.[10][Nov/Dec‘13]

5. A 33kV single core cable has a conductor diameter of 1 cm and a sheath of inside

diameter 4cm. Find the maximum and minimum stress in the insulation.[6][Nov/Dec‘13]

6. What is grading of cables? Discuss the two methods of grading of cables in

detail.[16][April/May‘11][Nov/Dec‘15]

7. With neat diagrams explain constructional features of various types of

cables.[16][Nov/Dec‘11]

8. Derive the expression for the insulation resistance, capacitance, electric stress and

dielectric loss of a single core cable.[16]

9. Explain the methods of grading of cables with neat diagrams and

equations.[16][May/June‘16]

10. Explain the role of static shielding in insulators.[06][Nov/Dec‘15]

11. Explain any four insulating materials used in manufacturing of cables.[06][Nov/Dec‘15

12. Find the economic size of a single core cable working on a 132 kV three phase system, if

a dielectric stress of 60 kV/cm can be allowed.[10][Nov/Dec‘15]

13. A single core cable used on 33 kV, 50Hz has conductor diameter 10 mm and inner

diameter of sheath 25 mm. The relative permittivity of insulating material used is 3.5.

Find:

Capacitance of the cable per km

Maximum and minimum electrostatic stress in the cable.

Charging current per km.[08][May/June‘16]

UNIT V DISTRIBUTION SYSTEMS

1. Explain the following. (i) solid grounding (ii) Reactance grounding (iii) Indoor substations (iv) Outdoor substations.[16] [May/June‘13

2. Find the ration of volume of copper required to transmit a given power over a given

distance by overhead system using (i) dc 2 wire and 3 wire system (ii) 3ᴓ, 3 wire AC

system.[16] [May/June‘13]

3. Explain the following system of distribution

(i) Radial system[4]

(ii) Ring main system [4] (iii) Interconnected system[4] (iv) Design consideration in

distribution system [4] [Nov/Dec‘13]

4. Write a short note on sub—station equipments.[10][Nov/Dec‘13]

5. A 3 wire d.c distributor is fed at one end at 220V between wires and middle wire as

shown in figure. The numbers between section indicate the resistance of the respective

section. Calculate the voltage between middle wire and outer at each load point.

6. Explain briefly the various types of bus bar arrangements in a substation.[16][Nov/Dec‘10]

7. Discuss briefly each of the following: (i) Feeders (ii) Radial distribution (iii) Ring main

distribution.[16][Nov/Dec‘10]

8. Write shorts on :

(i) sub mains (ii) Stepped and tapered mains (iii) Grounding[Apr/May‘15]

9. Explain the following: (i) Neutral grounding (ii) Resistance grounding.[16][April/May‘15]

10. Explain the methods of neutral grounding.[16][May/June‘16][Nov/Dec‘15]

11. Explain the reasons leading to the general practice of earthing the neutral point of a

power system. Discuss the relative merits of earthing it (1) solidly and (2) through a

resistance.[10][May/June‘16]

12. Write short notes on ‗earthing practices in a substation‘.[06][May/June‘16]