UNIT-1 - NARSIMHA REDDY ENGINEERING COLLEGE

QUESTION BANK MULTIPLE CHOICE QUESTIONS

UNIT-1

1. A semiconductor is formed by ……… bonds.

A. Covalent

B. Electrovalent

C. Co-ordinate

D. None of the above

ANS:- A

2. A semiconductor has ………… temperature coefficient of resistance.

Positive

Zero

Negative

None of the above

ANS:- C

3. The most commonly used semiconductor is ………..

Germanium

Silicon

Carbon

Sulphur

ANS:- B

4. A semiconductor has generally ……………… valence electrons.

2

3

6

4

ANS:- D

5. The resistivity of a pure silicon is about ……………

100 O cm

6000 O cm

3 x 105 O m

6 x 10-8 O cm

ANS:- B

6. In a semiconductor, current conduction is due to ……..

Only holes

Only free electrons

Holes and free electrons

None of the above

ANS:- C

7. The static V-I curve for the SCR is plotted for a) Ia (anode current) vs Ig (gate current), Va (anode – cathode voltage) as a parameter

b) Ia vs Va with Ig as a parameter

c) Va vs Ig with Ia as a parameter

d) Ig vs Vg with Ia as a parameter Answer: b

8. The static V-I curve for the SCR is plotted for a) Ia (anode current) vs Ig (gate current), Va (anode – cathode voltage) as a parameter

b) Ia vs Va with Ig as a parameter

c) Va vs Ig with Ia as a parameter

d) Ig vs Vg with Ia as a parameter

Answer: b

9. The two transistor model of the SCR can obtained by

a) bisecting the SCR vertically

b) bisecting the SCR horizontally

c) bisecting the SCRs top two & bottom two layers d) bisecting the SCRs middle two layers

Answer: d

10. The di/dt rating of an SCR is specified for its (a) Decaying anode current

(b) Decaying gate current

(c) Rising gate current

(d) Rising anode current

Answer: D

11. A forward voltage can be applied to an SCR after its

(a) Anode current reduces to zero

(b) Gate recovery time

(c) Reverse recovery time

(d) Anode voltage reduces to zero

Answer: B

SHORT QUESTIONS

1. What is the two transistor model of SCRs?

2. What is a forced commutation? What are the advantages of forced commutation for AC-DC

converters? 3. List out at least two merits of IGBT over MOSFET.

4. Why trains of narrow gate pulses are required to turn on a thyristor? And why thyristor is called as

a semi controlled device? 5. Sketch static V-I characteristics of IGBT and mark the region in which the device is

operated as a switch.

6. Define the ratings of SCR (i) Average ON state current (ii) Forward break over voltage. 7. What losses occur in a thyristors during working conditions?

8. What is the difference between power diode and signal diode?

9. Define Latching and Holding currents.

10. What is the importance of line commutation?

11. How the SCR is protected from high di/dt and dv/dt values?

12. How the line commutation is happens in a half wave controlled rectifier?

13. What are the conditions under which a transistor operates as a switch? 14. How the secondary breakdown occurs in Power BJT? Show it on I-V characteristics

of Power BJT.

10 MARK QUESTION 1. Draw and explain the necessity of static and dynamic equalizing circuit for series connected SCRs?

Derive relations used for determining the values of shunt resistor R and capacitor C in this circuit.

2. What will happen if one of the SCR has large delay time in parallel SCRs? Explain the convenient

method of triggering parallel connected SCRs.

3. Draw and explain the simultaneous triggering circuit of series connected SCRs.

4. Discuss the need for parallel connections of SCRs with necessary diagrams. 5. Discuss various protections circuits of a thyristor.

6. A thyristor is triggered by a train of pulses of frequency 1 KHZ and of duty cycle 0.4. Calculate the

pulse width if average power dissipation is 5 W. Estimate the maximum allowable gate power loss.

7. With neat circuit diagram explain how UJT firing circuit will generate pulse for an SCR.

8. Explain the two-transistor analogy of SCR. 9. What are problems encountered when SCRs are operated in (i) series (ii) parallel. Derive an expression

to find the value of resistance to be connected across each thyristor for voltage balancing. 10. Design RC firing circuit with following specifications:

AC input voltage: 115 V Thyistor ratings: Vg(min) : 2.5 V , Vg(max) : 5V, Ig(min) : 1 mA ,

Ig(max) : 5 mA, Load: 15 ohms resistance

11. Explain the operation of IGBT with VI and switching characteristics.

12. Give the constructional details of SCR with the help of schematic diagram and circuit symbol.

13. Describe the different modes of operation of a thyristor with the help of its V-I characteristics.

14. Two thyristors having a difference of 4mA in latching current are connected in series in the circuit.

Voltages across the devices are 450V and 300V. Calculate the required equalizing resistance and

capacitance, if the permissible difference in blocking voltage is 10V and the difference in the recovery charge is 5μC.

15. Draw the switching characteristics of SCR and explain.

16. Draw output and transfer characteristics of MOSFET and explain the terms

i. pinch off voltage (ii) threshold voltage and (iii) trans-conductance. 17. What is a MOSFET? Explain its V-I characteristics briefly. Also write its advantages

over other switches.

18. Briefly explain the V-I characteristics of an IGBT. 19. Describe the turn-on methods of SCR. 20. Explain the dynamic characteristics of power IGBT.

21. What is the importance of snubber circuit in protection of SCR?

UNIT-2

SHORT QUESTIONS

1. What are the advantages of Freewheeling diode?

2. What is meant by overlapping period in phase controlled converters?

3. What is the effect of connecting freewheeling diode across R-L load in controlled rectifiers?

4. Write down general expression for average voltage of p- pulse fully controlled rectifier

5. Draw average output voltage versus triggering angle characteristics of a single phase semi-converter for

R-load.

6. How power flow can be controlled in a single phase fully controlled converter between source and load

for R load and RL load?

7. What is meant by input power factor in controlled rectifier?

8. What is symmetric-angle control of converters? [2]

9. Does the input power factor of converters depend on the load power factor?

10. What are the applications of dual converters?

10 MARKS

11. Explain the operation of single phase fully controlled converter with RL load. Derive the output voltage

and current expressions for firing angle of 45 degrees.

12. A single phase fully rectifier is used to supply power to load having impedance 200 ohms and 150 mH,

from 230V, 50Hz, ac supply at a firing angle of 90 degrees. Calculate

Average values of output voltage and current

RMS values of output voltage and current.

13. Explain the operation of three phase bridge type full converter with RL – load with neat waveforms.

14. Explain the operation of single phase half controlled bridge rectifier with R-L-E load. Derive the

expression for (i) Average output voltage (ii) RMS value of output voltage.

15. A fully controlled rectifier is used to charge a 115 V battery. The battery is already charged to 60 V. The

source voltage of bridge is 230 V at 50 Hz. Find the range of firing angle possible.

16. Draw the output voltage waveform of 3-phase fully controlled rectifier for a firing angle of 60 degrees.

Indicate firing sequence. Also derive expression for output voltage.

17. A 3-phase fully controlled bridge rectifier is operating from a 400V, 50 Hz supply. The load is highly

inductive and current constant and continuous. Find the load voltage at firing angle of 45 deg.

18. A three phase half wave SCR converter delivers constant load current of 20A over the firing angle range

of 0 to 60 deg. At these two firing angles, compute the power delivered to load for an ac input voltage of

300V from a delta star transformer.

19. Derive the expression for the RMS load voltage of six pulse converter with R load .

20. In a single phase midpoint converter turns ratio from primary to each secondary is 2. The source

voltage is 230V, 50 Hz. For a resistive load of 5Ω, calculate the maximum value of average output

voltage and load current and the corresponding firing and conduction angles.

21. Describe with neat circuit diagram and associated waveforms, operation of a 1- Ф half wave controlled

converter with Inductive load.

22. A 1- phase full bridge converter using four SCRs feeds power to RLE load with R=10 Ω, L = 100mH, and

E = 100V. The ac source voltage is 230 V at 50Hz. Assuming continuous conduction; determine the

average value of load current for firing delay angle 450.

23. A 1- phase semi-converter delivers power to RL load with R= 5 Ω, L = 10 mH. The a.c. supply voltage is

230 V, 50 Hz. For the continuous conduction, find the average value of output voltage and current for

the firing angle of 450.

24. Explain the operation of 3- phase half-wave converter for resistive load with necessary waveform and

circuit diagram.

25. A single phase semi converter delivers to RLE load with R=5Ω, L =10mH and E =80V. The source

voltage is 230V, 50Hz. For continuous conduction, Find the average value of output current for firing

angle α=50.

UNIT-3

SHORT QUESTIONS

1. Draw the equivalent circuit of a cyclo-conveter.

2. What are advantages and disadvantages of cyclo-converter as compared to ac voltage controllers?

3. What are the two types of cyclo-converters?

4. What is meant by step-up and step-down cyclo converters and what are the applications

of cyclo converter.

5. What are the steps involved in determining the output voltage waveforms of three phase bidirectional

controllers? [

6. What are the advantages and disadvantages of cycloconverters?

7. What is an AC voltage controller?

8. What kind of commutation is required for step-up cyclo-converter?

9. What is the difference single phase ac voltage controller and single phase cyclo-converter.

10. Draw the basic structure of TRIAC and its circuit symbol.

11. Define AC voltage controller.

10 MARKS

12. Distinguish between an ac voltage controller and a cyclo-conveter with respect to operation and control

aspects.

13. Derive an expression for rms value of output voltage of single phase bridge type ac voltage controller.

14. Draw the circuit of single phase voltage controller with antiparallel connection of two thyristors and an

R-L load. Explain its working. Sketch load voltage and load current waveforms. Derive an expression for

output voltage.

15. What is an Ac voltage controller? List some of its industrial applications. Enumerate its merits and

demerits.

16. A single-phase voltage controller has input voltage of 230 V, 50 Hz and a load of R=15 Ω. For 6 cycles on

and 4 cycles off, determine r.m.s output voltage, b) input pf c) average and r.m.s thyristor currents.

17. Draw and explain the control circuit block diagram for a cycloconverter with non-circulating current

mode.

18. A three phase resistive load is to be controlled by three Triacs from a 415V supply. If the load is 15 kW,

determine the required ratings of Triacs. If thyristors were used instead of Triacs, determine their rating.

19. Describe the control scheme for a cycloconverter using voltage sensing principle of converter group

selection. Also, draw and discuss the various voltage waveforms of a control scheme.

20. A single phase half wave AC voltage controller, using one SCR in antiparallel with a diode. Feeds

1kW,230V heater. Find the load power for a firing angle of (i) 00 (ii) 1800 (iii) 700.

21. Explain the operation of a single phase mid-point step up cyclo converter with the help of circuit

diagram and waveforms.

22. A single phase voltage controller with resistive load has the following data: supply

mains: 230V, 50 Hz, R = 5Ω. Calculate the firing angle at which the greatest forward or

reverse voltage is applied to either of the thyristors and the magnitude of these voltages

23. Explain the operation of a single phase bridge type step down cyclo converter with the help of circuit

diagram and waveforms

24. Describe the operation of a single phase AC voltage controller with a neat circuit diagram and output

wave forms with respect to source voltage waveforms at α = 600 for R-load.

25. A single phase voltage controller has input voltage of 230 V, 50 Hz and a load of R = 15 Ω. For 6 cycles

on and 4 cycles off, determine. (i) rms output voltage (ii) input pF and (iii) average and rms thyristors

currents.

26. Describe the working principle of 1-phase to 1-phase step-down midpoint type cyclo-converter with

associated waveforms for R load

27. A 1-phase a.c voltage controller has a resistive load of R = 5 Ω and the input voltage is Vs = 208 V, 60

Hz. If the desired output is PO = 2 kW, Compute i) delay angle, α and ii) input power factor, PF.

28. Explain the various modes of operation of TRIAC with the help of equivalent circuits and relevant

waveforms.

29. Describe the operating principle of single-phase to single-phase step-up cycloconverter with the help of

mid-point and bridge type configuration. Illustrate your answer with appropriate circuit and waveforms.

30. A single phase half wave AC voltage controller has a resistive load of R = 40 ohms and the input voltage

is Vs = 230V, 50Hz. The Delay angle of thyristor is 50 degrees. Determine

The rms value of output voltage V0,

The input power factor,

The average input current.

31. A single phase voltage controller with RL load has the following data:

Supply mains: 230V, 50 Hz, Z = (3+j4) Ω. Calculate the control range of firing angles and the maximum

value of RMS load current.

UNIT-4

SHORT QUESTIONS

1. Write few applications of choppers.

2. What is meant by Time Ratio Control?

3. Draw the output voltage waveform of single phase AC chopper.

4. A Class B turn-off circuit commutates an SCR. The load current is constant at 10Amps. Dimension the

commutating components L and C. The supply voltage is 100V dc. Turn off time spec of SCR is 20

micro sec.

5. What are the advantages and disadvantages of a boost converter?

6. What is the discontinuous mode of operation of a regulator?

7. List out the disadvantages of Frequency modulation control of dc-dc converter.

8. What is an AC chopper?

9. What are the different kinds of power losses in Choppers?

10. What is meant by Duty cycle?

11. Write down the expressions for average output voltage for step down chopper and step up chopper.

10 MARKS

12. Draw the circuit of class-B commutation circuit. Explain how thyristor is commutated in class-B

chopper. What are disadvantages of this commutation circuit?

13. A class-A chopper circuit has a load resistance of 100 ohms, capacitance of 10 micro farads and

inductance of 10 mH. Find the time for which thyristor will remain in ON state. What will be the turn

ON time if the load resistance is decreased to 25 ohms.

14. Derive expressions for minimum and maximum values of load current in a step down chopper with R-L-

E load.

15. A step-up chopper has a source of 250 V (dc) in series with inductance of 0.1 H. If the semiconductor

switch is operated with different values of duty ratio, plot output voltage vs duty ratio.

16. What is time ratio control in dc choppers? Explain the use of TRC for controlling the output voltage in

choppers.

17. A step-up chopper has input voltage of 220V and output voltage of 660V. If the conducting time of

thyristor-chopper is 100μs, compute the pulse width of output voltage. In case the output-voltage pulse

width is halved for constant frequency operation, find the average value of new output voltage?

18. Describe the Morgan chopper with associated voltage and current waveforms.

19. Enumerate the merits of Morgan chopper compared to Jones chopper.

20. Explain the operation of a step down chopper with RLE load. Derive the necessary output voltage and

current expressions.

21. A step-down chopper is fed from a 220 V DC source to deliver a load voltage of 100 V. If the non-

conduction time of transistor is 100μs. The required pulse width would be?

22. Write short notes on i) Jones chopper and ii) current limit control of dc-dc converter.

23. With the circuit diagram and output voltage waveforms, explain the working of Jones chopper.

24. A dc on-off chopper operating at 1 kHz and duty cycle of 10% is supplied from a 200V source. If the load

inductance is 10mH and resistance 10Ω. Compute the maximum and minimum circuit in the load.

25. Draw a schematic diagram of a single phase ac chopper and discuss in brief with output voltage and

current waveforms.

26. Explain in brief how average voltage across the load is made more than dc supply voltage using chopper.

Derive the expression for the average voltage.

27. Explain in detail about the time ratio control.

28. A step down chopper is fed from 200V DC and its duty cycle is 0.6. Calculate the RMS value of output

voltages for fundamental and third harmonic components.

29. Derive the expression for the output voltage of step up chopper.

30. A chopper fed from a 200V DC source, is working at a frequency of 50 Hz and is connected to an RL load

of R = 4Ω and L = 30 mH. Determine the value of duty cycle at which the minimum load current will be

(i) 5 A (ii) 10 A

31. What is chopper and how they are classified. Explain the working of A.C chopper.

32. A dc chopper is supplying a resistive load. If the input and output voltages are 200V and 120V and the

chopping frequency is 800Hz, find the periods of conduction and blocking in each cycle.

33. Enumerate the merits of Morgan chopper compared to Jones chopper.


UNIT-5

SHORT QUESTIONS

1. Write the application of inverter.

2. Draw the circuit diagram of parallel inverter.

3. What assumptions are considered for the operation of inverters?

4. Classify inverters according to connections.

5. What type of commutation is used in basic series inverter? How frequency of output can be controlled in

series inverter?

6. How can a PWM control signal be obtained using a carrier wave and reference wave with the help of

diagram?

7. What do you mean by Harmonics?

8. How quality of an inverter output voltage can be measured?

9. What is sinusoidal PWM technique?

10. What are the applications of parallel inverter?

11. What are the advantages of parallel resonant inverters?

12. What are the effects of eliminating lower order harmonics?

10 MARKS

13. Explain the operation of single pulse modulation of inverter with neat diagram.

14. Draw and explain the operation of three-phase series-inverter circuit.

15. Explain in detail about 180 deg Conduction Mode of 3 – Ø Voltage Source Inverters.

16. Explain the operation of single phase bridge inverter with the help of load voltage and load current

waveforms for R-L Load.

17. A 3-phase bridge inverter is fed from a dc source of 200 V. If the load is star connected of 10 ohms /

phase, determine rms value of load current and required current rating of thyristors.

18. Discuss various voltage control techniques employed in inverter circuits.

19. Describe the operation of 3-phase bridge inverter circuit diagram with resistive load in 120deg

conduction mode

20. A 3-phase bridge inverter is fed from a d.c. source of 200 V. If the load is star-connected of 10 Ω /phase

resistance, Estimate the RMS load current, the required RMS current rating of the thyristors and the

load power for i) 120 deg firing and ii) 180 deg firing.

21. The square-wave inverter of 1-phase full bridge type has Vdc = 125 V, an output frequency of 60 Hz, and

a resistive load of 12.5 Ω. Sketch the currents in the load, each switch, and the source, and determine

the average and rms values of each.

22. With the help of neat circuit diagram and associated waveforms, explain operation of 1-phase full bridge

voltage source inverter with RL load.

23. Draw the circuit diagram of a single phase half bridge inverter and explain its operation.

24. A three phase bridge inverter delivers power to a resistive load from a 400V DC source.

25. For a star connected load of 8Ω per phase, determine RMS value of load current and RMS value of

thyristor current for 120 deg conduction mode of operation.

26. Explain the 180 deg conduction mode of operation of three phase inverters with necessary circuit


27. A single phase bridge inverter is fed from a 200 DC. In the output voltage wave, only fundamental

component of voltage is considered. Determine the RMS current ratings of an SCR and a diode of the

bridge for a resistive load of R = 5Ω.

28. Explain the single phase PWM, transformer connection, multiple commutation and filter methods used

for reduction of harmonics in inverter output.

29. Draw and explain the operation of the time sharing inverter circuit. Also draw the related voltage and

current waveforms.

30. A single phase half bridge inverter may be connected to a load consisting of (i)R (ii)RL and RLC over

damped (iii) RLC under damped. For all these loads, draw the load voltage and load current waveforms

under steady state operating conditions. Also, indicate the conduction of the various elements of the

inverter circuit.

31. Give the detailed design aspects of series inverter.

32. Discuss the following: a) Single pulse Modulation b) SPWM Technique

NARSIMHA REDDY ENGINEERING COLLEGE (Sponsored by Jakkula Educational Society)

Approved by AICTE & Permanently Affiliated to JNTUH, Accredited By NAAC With A-Grade

ISO 9001:2008 Certified Institute

SY.NO:518, MAISAMMAGUDA (V), Medchal (M), R.R.DIST. HYDERABAD

ASSIGNMENT 1 QUESTIONS

1. Explain the construction, working, V-I characteristics and switching characteristics of SCR. Also

derive the two transistor model of SCR.

2. Explain the construction, working, V-I characteristics and switching characteristics of MOSFET.

3. Explain the operation 1φ fully controlled converter RL Load with Rectification and inversion

mode. Also derive the performance.

4. Explain the operation of three phase bridge type full converter with RLE– load with neat

waveforms.

5. Draw the circuit of single phase voltage controller with antiparallel connection of two thyristors

and an R-L load. Explain its working. Sketch load voltage and load current waveforms. Derive an

expression for output voltage.

NARSIMHA REDDY ENGINEERING COLLEGE (Sponsored by Jakkula Educational Society)

Approved by AICTE & Permanently Affiliated to JNTUH, Accredited By NAAC With A-Grade

ISO 9001:2008 Certified Institute

SY.NO:518, MAISAMMAGUDA (V), Medchal (M), R.R.DIST. HYDERABAD

ASSIGNMENT 2 QUESTIONS

1. Describe the operating principle of single-phase to single-phase step-up cyclo-converter with

the help of mid-point and bridge type configuration. Illustrate your answer with appropriate

circuit and waveforms.

2. With neat circuit and waveform, Derive expressions for minimum and maximum values of load

current in a step down chopper with R-L-E load.


4. With the help of neat circuit diagram and associated waveforms, explain operation of

1-phase half bridge and full bridge voltage source inverter with R and RL load respectively.

5. Draw and explain the operation of series-inverter circuit.

DEPARTMENT OF EEE III-B.TECH II SEMESTER – I MID EXAMINATION

SET - A

SUBJECT: POWER ELECTRONICS DATE: 18/02/2019

MAX. MARKS: 10 TIME: 02:30-04:00 PM

ANSWER ANY TWO QUESTIONS 2*5=10M

1. Plot the I-V characteristics and turn-on and turn-off characteristics of SCR.

2. Explain the operation of IGBT with VI and switching characteristics.

3. Explain the operation of single phase half controlled bridge rectifier with R-L-E load. Derive the expression for (i) Average output voltage (ii) RMS value of output voltage.

4. Explain the operation of three phase full bridge converter with RLE – load with neat waveforms.

5. Derive an expression for rms value of output voltage of single phase bridge type ac voltage controller.

DEPARTMENT OF EEE

III-B.TECH I SEMESTER – I MID EXAMINATION

SET - B



ANSWER ANY TWO QUESTIONS 2*5=10M 1. Describe the different turn-on methods of SCR.

2. What is a MOSFET? Explain its V-I characteristics briefly. Also write its advantages over other

switches.

3. Explain the operation of single phase fully controlled converter with RL load. Derive the output

voltage and current expressions for firing angle of 45 degrees. 4. A single phase semi converter delivers to RLE load with R=5Ω, L=10mh, E=80V. the source voltage is

230V, 50HZ for continuous conduction, find the average value of average output voltage, average

output current, rms output current, rms output voltage, displacement factor, form factor, ripple

factor, rectification efficiency, active power and reactive power.

5. Draw the circuit of single phase voltage controller with anti-parallel connection of two thyristors and

an R-L load. Explain its working. Sketch load voltage and load current waveforms. Derive an expression for output voltage.

DEPARTMENT OF EEE

III-B.TECH II SEMESTER – II MID EXAMINATION

SET - A




1. Explain with relevant waveform, the use of TRC and CLC for controlling the output voltage

in choppers.

2. A simple DC chopper is operating at a frequency of 2KHZ from a 96V DC source to supply a

load resistance of 8Ω. The load time constant is 6ms. If average load voltage is 57.6V, find

(i) ON time (ii) RMS load voltage (iii) Average load current (iv) Inductance (v)

Minimum and Maximum value of load current

3. Explain the 180 deg conduction mode of operation of three phase inverters with necessary circuit


4. Draw and explain the operation of parallel-inverter circuit.

DEPARTMENT OF EEE

III-B.TECH I SEMESTER – II MID EXAMINATION

SET - B




1. Describe the working principle of 1-phase to 1-phase step-down midpoint type cyclo-converter with

associated waveforms for R load

2. Explain the operation of a step down chopper with RLE load. Derive the necessary output

voltage and current expressions.

3. With the circuit diagram and output voltage waveforms, explain the working of Jones

chopper.

4. Discuss the pulse width modulation in detail with necessary waveforms.

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f.toott" Slr,o\hTft*,L' 'rir"AotLos ' &-- (/C^'jo'"'* #o* F"'4. '<:----

L=> fz - sft)t At-)-tTti PL

lbfu t '. fT+x +" dn

htl

?

' ,,4t ,Lh' 'Yw&n- ' / ;t la'fu4' & '9o

/ihtf , it d":ai1'o't- f't' u*m uY hU

t+* f;^* 6l,uu, Tt T4 qk-a drhf-d

ffrr, Vo = -V<f , : +w '

Ts T4 ' F''B

@6G) -. T3 -+ R L -->

L* tA*fV, s +wP - +wt10 r

Ta - nF)

L dischs-^k>a Yto q T2 asw "*d"0

arnur* k*w P"-t'

pL --+ T^4 *) fr(+ ) -> 13(

-) --+ D -+ R t-

Y6 = *WQolO = -w

n.f

[*

I

kolb 4 : d rr da, "l rlt N

r&

itq

,'Y \$\*e\$

8ft+xl

I

o

n

rT

t

,i

P"

tvb) @") (w)

tlt dulb

\0 Lf

:oVrrl

- rT+

= fu (-ur-o'lr\ L )n

,

/: *v,nIta6n*)-TL

o(p

tfi+Vo=L (

n)0L

*,

: * [-*4- *"4

Vu = .?V, ca4t€n -->o

V,rt*^

q ,4^ vdcL')v =- * 6s*d-,' 4 -*fT fi'.

** [o' i, I sa ) , +t'n :- /^*d * uT (sn /."

flew- t>or nood'-' Y o7u"^i* qlLP- P**'ebgon+,oLk) 6;rdf rtac'h'fas fi"T ttu ;>eu-<h '%'t' e"

t wrrznfu ee^ 0&" "^ e:/*aa o;'4 eh^ov) .

w\ail N"d 1

f r+& 2- lY'=

f * : o- si^ 'n) o"')

l' ,t:n 1 1.

"l n; ( '-'nu,*o I

lF ) 2 a"it*J

- rl+x )'/'--Ivi f,or-*in"Q I) - I - _)*

J(*" L

:- [o; f C'rn) - sb2t^:9(a" L 2-

A

=)y: I ^r/ - r* -f +

)-tL,A (

: [# rsi''"

*"*

Vu.t ied .

& -ry"#rL

hvrtxt "io* M^ods- '

.gwLinq tf* in,t ,"vq-!4

Olx:anb

b^n .

& atla fr< -

,t*9

fufPU

N 4ato ,n-l-.&n"

ISou,tQ le d c lel ,

*fu v,: tlo,+,d

AC

b

at tt.t- ,(*^rl

,. . ?o wt-r

eyurxns u a.

g.*4)r;*" r*ad" '

8l N > 1o , ft'h-o vtkay at nfr' 'to'C i<n*ins/' h -'n '

-0/1lr-e:a,f-rw-r tl,, pc uuea $"x )-"'rY- C" "'fu

+D &L 'i atn +

A"^* fl.-t Le\^"$Ltej ofe'^tu a's k lY W'

8" tftl, mpok foo+'z* ;a t"^ t@ad lo so urLQQ '

BotL ryfV vttta-y

.', Peuuzn #** f,*n

,tL" fnft.,,Nwl

Vj z -we

7h-a "Load

fi"fkn .

8rA rftLL

N.'fa .fi, i

vs d- *yp|AC rl$LLrLLa "

-fvt r

ac ,+id< tD dt ,t",oa rt. o"t'*'r'&"

i

n 'lD fr+q

h*t J4 = +t<t

Yrailux gomt-ofr,r^ft "- q fh ,*uW /, n"

ntt po tue't /'[*ul f'e'

1Lr*^ l-'ci", ql^.t"-^ C, i"kL,*;rrqA

Iu

ffo,*a t*^.u-ch-liax .

F"lll G,,*'.Bilee B*'iy Br*'l*o ff rc ba0

v., r*1

l,la& l: (u de n) 'rtr.' 1i,., t cy t A

f,412 wiU lutrr* 4 , Vr\eu

%=\& Vs

=e. btTS)RLE%+A.

4 ?ourut + 9ot*rt ue lp ,bod .

r4ia*r* ,/o^e fnluotot"t l' A'fL

Dun lo /f,;-s, ,!uqr(. eurl',u'Lt i: ca'lfn'-'*t

Nvt fiifpll

fr, ,t"A a a,wunJf dD ,.8< o ElF b?n,urA!^t E ,i /f* hd c;,ra;"t ,"t

V#T E,nart,fu &t lo a- batr'!^1frn tt--

,baol ;*rrrit @l rna.y ,lR frlutAfud 4 *o(t nolw .

fa-oda t'. (o: i" 1T.+@)

&fL ,lru=-uo

IEIJ,

:I*w b'

CT

L J,,

8J

A+Tt -'r R tE ->72 + 4 , V" 'fuu*s ) gouttu fo bad

Ho& 3: (n+x) tu ,nr

Vs

qE

a

%

"Jry'ftt

NilW til 4 wtt u'-+'ou'r b'Irf coruwtri+rt

&fith RLE bad '

(u*,.ou,- eYex-u'#"*)

olA2t

A*y dt "oTrn*ryvd,

= * I vm atiot

0a

: -V,n fr* G+x) - ^ n-l7LJ

Votc = & Ym @5 tL

n

?t L Joc

fuY ,lead auu,hujtb

Ia" = W -8,

P

QUS olr

Vu*

tj'"

10

;-t_)

Y*'J'x

3n dxJ /

',/v,

J+:

/uA Yarl

,6 /l

5"*rr/fr^ mnde .t ,f4* t'P Wft uut oUrA bil-df ernn(fet-e Al

hr o(r?oo, ole w Vs t)

q "ilra ,tua.d orrrr*Lt % E lJ

,tunuz/ + ,rrim x71oo, tf'u'Molc,+aur(ct E u,"U N Pouot

b*e* fu Ac &ott?1u.

uti t+ o(tqo"

eyus-lio"

'(A; ffen4a'* ,t t',ll cnlAxnfrl1

ti knnwn 4's ir"xxluz

k

L

F

W

|Udelt' r/- ta fi

\rs - twL - +\^4

POgXtt t f,-C ,rlA,uct

ain t:r*,fl 41o" ;t ,"i/"t

lnwl<tt '

Lotl.rt

t dfrst

:d,k-/

/"11 L

NUmrn*t,

ftu

ryrfr"rn- @wr

lo olc ,|ot/,,tu .

HNab L: ,t dD fi+*,

Vg - tlt4

?s - t/r4

Peutttr -> dc to atswu'

*Xn

* Vrr irwtnWn

* bu,r K,LryM,a t*' *3#fit"-ll '&1

,oCorVWfr't oYOw+tW ' fe fielt F

Va

E

y dc &outtcz ib ac "hrff? V*

daw/*tm ^ ti ry,bnlmlhtr ry csw'&zfrA

w;'lf1 Rte /roa ( f".or*t* €Pet$'f;r/t)

t\ -/\

\t -r ''zf

I

i

Sr* pts,tt- au,ieeru,vxA"/ n*t1 ,ail,ot,hul o*'* fuclirt"ett/ * A'''a

ta-wnka '

Jaricorr,uu,l*q u)&, a t i xlt t* "l d;ootu + lfi;'lolr 'ilenct

+fur& *iU ,lu e ,fuf;lcl Lm/f?o( oa'q''t rt'. /,'Nl ( dc a/e

lt.e o[f wttV,c a*rd afihAt ;, q/il"f Po&7h'w '

I |/arbs$ Mt '

\ ,4flM,,ilrbrlul " r

,f t\il cead,oLud ry "*e'fu o?'tfi R /'^"(ot'tl-d' *T u--1-''vqt61r'4

G**t + ^l

e,^:0rrrafr'0r,)

(e*il b''dtL e ftu

Mnrt"m't WM't'dr%Ara .

SW fre P,r,[* 'it aou/

lo faig2ttt 'Hs dCn t,'tfnu ll't

crJt*d;"q .t 8 u-t * ,_h"ffTi Dt - FB

(orbr, +R+Dt+b-)

1t''e'

,k cA!il

-r^Y

-V3 = Vnein-eol

[-lo,fu L i' trr< br cil,l" (x lu n )

Ju

"^l

A* aJL =fi , ba,ot

to et| atab dila to

t,

Pafi"

Ys

oto

g"'"^t tfu+we.

+w

v*'tyvo + io tusolat lv

t" hr""l cqn "rno"l'bil '

W, tf,A/, Tt + D, fuol

'ry "-!q!_. l!.ri!4Ellr

l-lptuar$+x) lo Jn

A

b

Tz Ds cenfu&

Pqh , ,t o.ot aa*utfI g+Tt-+R-+92+A

plrnil vo ' +w

tL+w

.\

Af J fi , f2 | g, c;Tuqs fo 'ffi *tafu at'*! lo tlaj'^hsl btntnafah'u

',flr,1go

o.a,rUfir t"

"o

@

t0,t+o( wt St+eirii

uJ,L

b0t

\

\fo

(+)

, (vou) t*txry ,/" d, we*tfu)AwV De

Vok : flrt yR

n

* | v* sin ut otnt

*)

- Vm f -cos,^riln-;L J*

' -Vrrt ( cun - @|r(.f-'JtrL

i -Ya (- t - brdT- l- J. n L

4L

*T ry

v,nu,qi" *l'- f vs=vms&,",/

= kit'^q*l lr"* ''# I

= 'r lrtn'*, n*rf"" t- )(^! ].lV (,_*LLot o_)''-[; ): *'J

= [ u*' fio, - si^zot)\ 7 '''

G4, l*- v-w'1vve

/ Ltan ( . J* I(^\ZJ

= [nr- [ n - t;""ry - Nt sil :tAl'LL""L 2- "ll=lv; /n-^,, o

tJ

* 0-" n'tuflo = kfn-*r'bJ'

RHs l"rd.

V,*r^

fu,. =b(t+cu*)nP

ki"y Centw+b-A b*idfl *rt*l*n fi?ffi R U"a (da"tr*'n*'ieo-l

C*#f--h'|"0

I^ Ad"/r"*rhfc"l,*ftn*fon,#?atef4 ^ l"rrhffu c;a u':h aP't>

,ltl ltJL.r-A , '

3o lt4A,t tf'.L U"d'*ein'

tonrnind' of fiu t*Yt'ttton ';(! k

.

';ifuW dtrk car'd/"1 ohh Yto'tHa& t'

BG)

si;fz

laod" ry,,+y+il,u,t1irAl *fi,^r,s,lt*t. *

@rrdil€Jh ot"rriet-t Offd"r ry

-t

.f\&

Hso&-ll & to n

ft Dt cPndlch

A(4-7T7+R+DzaVo - tt/Q- 7o - -Fe

R"p^q

Ltglb.-A,, n td to at

tz 9, @r1&toL

1(1) '-> Dr "a & '+ Tz r A (-)

Vo fu'e

oio I v'L

AP

fu;1

w&rys ryvb?

,/t r; earunxtn '

Wot*,pw

o[c #pad v*LtV ,

h *iril,n h

A/"r* ttlq r ,h/t 'fi*E rnod,e .L (? I )rrqoh I (rr g, )

:II

rf

Vs

'ptLfitrVo

AIT-

'll

ba?dw-H eLl unhroll-z-d, cr^r*1""

Ia y" &L Loaa (.)y*",*i c*l anp,V**"t:w

7A! ,yalra ,t inarUunu'l-' h

a.rturrud ,to ,fu lat'rfi ' ,to 'tf"et

tfri a.6*r4f W "t eoool

wf ! ,/r1 conlfn totot .

Hw,n /oad ethrrA,a % h ia*ut

h ,1* coutunt '

\ 9t - Fo

1q(+) -a fr -+ LR +Dt +B?)

Vo +w

fo +u4

flnola t : o( *o ^

MeazA: n h fi+*

AT

S"f,py vAfV,< fieuln*t bia'ut I r 4

luru,i ?t ,ti ' 'D z F o

7Ar*t t1,L /oaA '+, W

,firt*f LR 1 Dz+f1 ; Lrz

fz D, Fo

bGL rz + Lf? 4 Dt- a A(-)l

L

tR-

rnodl- s :ft + 'e) fo rn

l.odc 4 : l-rt +o (tn +x)

Ad,,v"wty

At-xaX* d,c

Va" @) Va

t"rryry& DL -RB

tM.Dr-F8.

LR+D1 )Tt +lR

No nutt ,t oder'fforr-ol FJ,z hnze/rfl -do&- ,

/o"/ ut tttr4ul l'wuilar/A tfrr-,r/"

q e/p wnt*

fr.c"&R

t

t-.,

t" vm sfn.l,t otz't

d.

tttJd

= -yg f cean-crtnJL

n

Va, = u! (t+ t*sx)n

wYarru

eM"e o[p *bf U*)=[*

Y^sin*'r*)1t/a-

= frrt ? ,-cr'..ov ot"ot(l;) --- lL&

=[y^ b'-'g:]':"=Hb-*r[r0n

u t

t

*?railYLr-l

&_J

tlh Hili@^fu\"l.kJ ,*u,if **rttb* ulib Rr Laaot (A'hfr*b';c"lC*,,ik"N'")

tht corlet*attfl Pwbo( -t

Wvu I ahao' wu 'l)ler#r,",,

L't'o&/e ry3o ,ted' ,rrt*;il contin"^o'u tl

*o ;f k hkcn "to ,'Az cwrta'rlt'

t"ln,ck'z i 9l to n+*

.1;rl_

l,ter6 r .. ( ,* fo * )

Tt Dy -fr)

AF) + Tr 1t R + 9t+ oG)

rre-(+Ix f o-ft) r,q

t,l*lol-e- 3". (n+rc) tD 'z-rt

$(+)

gtD, FB

L&i9zt Dr

vs- tw

H-od' 4 "' "2w '

]l

+ LR-

tos - +tx

to (arr * x)

L

r&bQ

-OrOtf PHs o/f ,ril .i, Adrnz titu lff"'ehfl'|el WAv7 o[e wl

f+"q"

n A+ot --- Irr ZIfr8yn c*t Cot,lhrr,,sr;w,

nz3 rL.D1

,t\ r\+x

aq,

+rcnt

*:ar

Qb

db

Tz.

tf t4at eonn**A *"tif* \"

Ynodtt> xlPll

T,D' f B

A+ -+ Tt) Rte + Dr -+ B

Yo = +r^4

io z fw'

B* +'lz4 (t-t -l 0.+A?o = 4w

rcA,F ,,(""a @d lrto t&l"zrl;n*.D^'@/L

(Sy^^*;*l c"('yaeO

bart ?nfutrJancx i' '+s"''*d

.to /'e Mry *r,t

utos"t c",x,w* ,it

Cw*irtcto<*t

'/t't tfi'l/'htvrr u'iT f' t*4^bioud firlrln rr'l'-' 't'"n* t'+ltvf W

aktrd) io, Vs t E

nwob a: ff h rr roa

fr D,- *X, FD f6/^)atL4 a'"'>z/

1lu d"*4 A'bA' conlttc'h to

f*rO tr* htf'*'17 rt @'* tt* ?nd/L:j;4^e lodd '

Vo = @ tr'-- twRLt + F9 .+ R.LE

mnd.a 4 '.' o2. n to &rl+N)

h!

rz Dz - "tFLE T

tl

I:li

(

tE

F,

L

fr

Let - Fg

Vo = +\8

lrwd,! 3 ? rf+a- lo A-^

f D -ta'F

Ys

F

ffl'

tt,

ItlO

,t*dc 9rr+&

ED D

,t /t$oc ztt 2n+* 3^ Sfr**

A:t-t*f dt

Vo:

n[f wLlvry0

,t

' (v,tutt^J

s

&fr

fiJd'n

= Y [- c*t'"El -T L re

3 -vm | *n- cosoLfrL )

=Htn-Erq

(t+ cux)Vo = u-n,

n

vr*,r = l*I(v" s"wr,,st)"

RM3

Sb &n*wlltA c,oywuat?h^8' r

o^f trt- - *fry at lk ot'c 'l<"*';na/" t''|'j-l'bh i't ^"

wdrino*' tru

-/tw*|*w , a lrrr*rfiJ^fl h,aAdet b hlc'Q-rttuV tt zn--etd'n ffa

e/r' v'otr"f ' .^ r f r r:* .r.-,i tfr-L

7f, ,urA q ^"*"ru"f can LI"l- w';'; r";r4d o/

f: ffi* ptu tru c^o*vu,.tnh tq/,.&rns "

fi-^* Pa*t' 't1* 'tr **f rub' f^ *'-T*q

,fr**+Bb u"l""t $u' '

rf rudf* c*t' il1e wd Y +Y f* Wff&*'

q.,rt;cahnr: , Af cont'oLhJ cel1^Nhf,P'u

) 3- pott'tt U'rv"$'tuas

e)a Ptu co*fl,ai*4

UruW)lfu'Js) tz- 1''""W

S-pil* ct"N$'fu1-' CI'a'a *1" **'Dun * O##;tr-grt ,hl'A S- Put't-t UrwAfu-1 ho'/'l-

o*,fu err* *.f f rf ,"1""1

;;-; ; k"ut rr'si trry w+D* 'r7uia/ /"yve-t (

d.c *^%"hi t-,tn ,;; rr""fu n' dc

Agre t'fuI

, f,ndn"clantz /q/;-/ ?" u't"u b C"t+.;d4hnl'? ,otudJrCal

3f WU cwrut'TP&'t tilW cen*xtu'

9ir, - 7r,Ltz Whl<rra t tMV My co*,*a*pl v

tf,oru" - p,alx can*qlran

t *^**l*t*n

$ O*u+an mtbueh- rtrlu'

ffv A--c' ,,;r(]

Aa:"n*i"-' ,

*;!A

;, ,tudAud 01"2 .tT tf,,t *rP*Lctr.sn ;"f,t rn d!- **T

ftE-,.J

t.L

-it! /âd k P $i* & lcl ry" uu*e urwlctlh 't 6YU tfr

n PWq t/^nr.t r vto ru^Lb"At e"îl ru?"*q'

He** fhe'u'e\tnl cp^t'LLr:"'t b oytiw*'

Ne..â*en, l* 'uet,"*'h % nlf il*" *"f'Pry f*'" '| or t* kWwtp m

lw*t""'*^ k la &L a'vn-n'z-c]<-d

U ?t k ffirrsrE€L r w ,.1^rt;ff:u-rl,rLQ-cl*rt &, do//^ b"+ fu

-; *-*k* f*,, rt* c'xu''l*n'V pan tr' J'd Ao'n'o'ic u*'t""/t.'

.', 1l* d"d 0\rl- rto'nn+onie c,u;,t*nh 'q- nol' a1ap"fu@-fi" ff't

ua-hich ;" 0,n *r"*ru:

.3f Wrt w.fu&l)"t t';V'**ry utitfr. P-- -lDo'd. .

t-IIt*

ft*t,

bI

It

*

*

).4

% 2 flsuf,a

P^d bl

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,ff 1- *"/p7 */t--f

- w ,*-rf d.r*i u-t alLe- h,,''uaot 'on afun #'L "ry'f| vo/rya ala*W.

% S$g,tut ,fl* ck+ r^'uA'w*fi

, oZ

lf* wrr.- ff^" ;. o\d'Lh fro (emtn'ncl

Ypu ottttt 0^l erw ( 'tt* '1""'e*A)+rf\ ,

dt*rl. furtu ,tl^r-ld ,[r" fW at a d"be"l

Isc"t" JC-e cAn c,ani-,' ut lr4 t\oo '

cu,1"h2nt-,t-lg9t flL q "4"'0

;.

fr*"^f,*fd

gcfu rna,tt Jr, trfryr,rrl U tf12 &Lfuua^& f,,'-fr,93 'f4 ''G + E

,hx plv,* a*Qt fuJ'tttt^ ff* tfrff**V T ?1'ro 4"* seen b 6o'"

d+ */ irufa'nt , fw.o sCR, can unfuct 6,^t tf,u,l a*2 SucA 6 7iu,l '

U, rt) ,0, ,rz) , Lrz b), U3 rq) (r+ tq) d (r' '

)

+.-b>

<rt3 -\1 r 1'ltl*I q,i.Ot,)r"P

^* "f -t^a

,r1,ffi

3p

Tir't

71,-Q- &t v',ru1*oN

0

u

*vq f**f otn ui *' o,\-a

+\ao .

tw f*-fl,-w f@u,

'l/_L

N'&-

,/U

q sctu , *|Q fl*f ? -*fr*Y.Tr,fbd-T5f4,T6 lTz

hornzrl - a-n aA-en

w@rt FaA 3 CR wnfu& h t pa.&".,t + , ee*dL [rt:* a-ond.,, & f* ,u".

* Vt L fru@*;fl rcrt ry ff'! .*""V 'fe'? 4

I;rr*rf, ?Larynca " I ctu .

8.No

col f,n*îr*se;- U "4*ru

Oufio;r,il

3ct"

y'Ele- wlau,W dfu

t,

2

3

4

6

6

ls;r *

I to' *x

l,* rnl,o **

l,,o r o

33o+x

Tt

Tz

tr3

f4

T5

f6

fo ?t

fi Tz-

'fr- T3

,Dq

f4 fD

GT6

lGl"l"z94

Vat

Vo.,

Va,

Vto

1t*Vu

W h LfPfu

a.ch.*t4 ttu tn"-d'

to

a -oI A' ,, , o Lb ,Al^r"A fu 6?t,"

cr*d*oh"rt atub , hat k hi';"'fl i^-t<xn'(/*t r'--- b u

\/ahtry & ;" a- 6Yu/-u./t* glf v*t**X,e *"*if^ Y *7 Yq/u''L X a

wwê w;fl, " n^frrJ* #qF*V db seo fi'\'

t/OL-a,n lwo .9cx,o ah-L ezrrdr*clinX , ;2, ottt W

t*- -\ê , fr*k- ,**rffufl l'fru *Y*

fi/:

Gnlirunul aorrl*c*iott rn-ode ( o = x a [; )

&=3o'Nht^ t?a .Ao*et (n-e1 L @lb$.d to e**d&ut a* x benwu,

0 to nlS , 7t cp^jirrrru to cnr,/rta* &y 6o' tnL-"'" A, phq^"Ag

"L fio,--A 't-E

YAA cr"l"rcn:Drt [' flA:U Pd4v1 s c T6 +o T2-,' : _ .

T6 & orllru,r.,-ba bil fL N'tvlu& - w4hy -t P** + B su'P1lff'

Pfitr

$-

o

S*

frB Ae geb,euUnBAeBe6+ ltL -gm 4n 4 f:6-6: 6 t Yl L-vz-

*.,!i

fuV , d.< 6d Catirurpv-t W=,";v-' (tah*'fi),t

6t tl a\43\34\/fqg+x

Vtr x ' 60" bnttruout "rr'*jf"n'E - 3, *d*l

,f

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C)7 "* PLnqA +

da**'*,rh bLh-o'r aco'ut1 "

'11,..e- ol.tLrun,"

-y*"r

b IN fi,e

"lA" $tyyl" i, fr^"

h**v* * *,-i"Yl^k i^ tw"^ f^

/*^/tr,, "

b-A

l,:"^t,

tf-t fn?nefyJ-e q

b[$ 1",r*ru-*/ Ci

v

v

v

v

v

\/

v

\--

v

" 'Y'o

f tcA:o c"truyy,u N

\/Loi lh

v

-*

%nw..

%,,^

trll"t#t i

NLt li'*it LN

Lo.tko'nl: '[i* "

*tt",n L""rt''J-*l-

tl*sA L*t

"1"h1

"tl* to o,*ea t, ,)rooif t l-Lj

h pn*-|& d;tf'Lt) ui th cô'rdf l4'QA Pr

li,ni t- b'rLt'"'e/ rt tt-*zol fiL?

ury e.l"rrr-^rt -

va,Lul alLt

Itlruh*tu

rtlrl Luôl t"'\'hz/Lt

*u*YT

*t r***

ul-zn ffu "

\-/

\v

04 teô(- v

\v,

v

"tt* aL*o^/4

3t"* , l'f,-L C,trpyu 6fur*tu

Ct? ,rruif Cld .- ,

,t;/";tt ,

birr f,o rnaa + ?- *;r', obc;/- ffr-' s"slfcA'"'w-r

cavt Le ,q"d"tz/

tinaltu

d t+,-Q fia,er".--,

,rra. h,L,^j

ohyy<x *W^,/ W t,"rt fr*

\..-

jl

\l

3./5S.ilctinS modo_ W

8)e funw+kj's an ,&-s & 4d a4 **ry'mole *7'M- h

Corwzx,E q- 4:_ tA , noo,*ry elYlil4fd , h aL rreyl**<a d,c e/r v*"

.tlu)lL ah-p . 4 l**fc /"Nf!)

) Aock *tX@*

4 B,v*

Bud< WtrL

i&d, r : @rom

is,L -L+-++

ve

% /.,r,1k ry ruf&lefs44

,) Buck * l,aetb ***4 &,k-.-_fM

;;& +VorV*

a-v? Yt' 'vâ't h ' h b"4 /n,^"' tf'e

" bccck ' .

*Ct-i,

tMc L, &4f

+

fr, a. butck "ff"W ' lb

i lp v&'t , Vs

"lt^r. cW

4- Jrêne--, tr^- \r1e-N\e-

uy*u^-h* cs'L -M off,i 't'd f n-to tu'o "'fre"' '

,ru 'rY!^vn &r ;' ,,*;54'ad 'am wt F ='o '

|",-oot? t 'l*7,ru*th.t tr Lh a rid, ni*, , Sl*wt *l"ae* f,'tku r"ndû-st l-'

H t+,u cf c , + Jerrl /L!'rb R '

l\oo;z ,&r4",') dL'm At 't a'u"it-c'la''l'tr et *=tr'a

lt^-L WhilL4 df",la D m DyLoLl-c,E 'lrla r,c **W ,/D.LC ", fl\

' inAr*Cte< ; ,t',1 fnd.nCna q (o*fi"nun-2 ,6t &;o nl4. 9n .

oTuu

'Lhl_ traut* q l*W^ un*il Uf b ,*ui*c,tn t

1[* wou,W-Lr,,4 F fre e4^ ,ah^outa. '* tV P e.

tbwtfrute-vtt q W A

w-1. + ctTt

f ,*kurn I .

(-. oJ-t vu q-fUrm-zoi

:

I P eperrot;"1 tfrn ,,a,tJ

1 +hr Tndrx,tu c4 @"il

*/* a1 *,&,u I W,,lfq . "v

""4rrl*y Y"1, , t Llrrx inpfutana ,4 uVa citant.

t6 ., €t=Lab-rEi ati--.'

)1 vsurf ach,-t': L q *en paniud ry /'fu sLr;ltA,u,0D l,

tf our^ V^-V - , ltnwx'2.-;r\,J-,o . t* | -^ -'*'' 1\n^)

Ys-vo " L /41)t'*)

Irn.!ar1Ly,r )

// e, /@4 L

;, t'l* nurE-ry

\.

flo"-, tilno u4,udl

un ofu*

*tu

It ^t

,/rt d) w*in uotr.,

o

U*y oLcA.e+t L *"U fW

Pt= Vo 3 L A4

Tyorn O )-+@

---.. *@

w: rlA-e\

V)Ar = y(%:,)

L

Wort @ g Ae = Lnt-tff) -+@

a-L

i-

i

L-

t

I

i-

\_

36

*L

il*ofs

I

I

I

T

(g' .@

Tofal *or,u- pQurps(

e4d.t (o +@

A(Y'",, -

rb*, Vs = Vo ( Lon * bril)

vo U \v* +\6,r+W)

I

^il(9

Af,1*IuoJ

"i

, (#,") ",(

LAEt",:l-)L0-

-r,)tl

T - t-rr 4<rlz.

Tz------+

@.

,fril. *f ,fr, ,"&4 ,/"r44 LL$ ,

Vr&'Vo%V.J.r i u36ya ( on'.%"v"s)

ry

Js't&?** Cd AI 5 r(ut -vo) vo

Lvs

,(ur-vsd) Yu S ur(r-l)J ButT=ir%

A2; Vr5 (,-b)

L

&f lt k ct ,r,

)-nr t fr- ,k

&54"r,*:"J ttu.

ff* inpLtcfa cf

l4e-m nfpp"tz

ft-e AV"c|/u C

oLb * (v=r)

Af t = AIc

Ic : AI

ckt- , i,

"tlq- efy"b

lead. crt it

6(ai la * la

Lrl

l4a'

112 *f tt7 fu''"1 tt,-'"etV't',

U* wi LuBu

A Vt,

AV" =

av.

=19BL

[-ur" = !L,I 8c t't

,Lt'u uy^cifa Crl,

Vc-* t- (,c l'.vo

;- r/" *Vr(84) e

lz'AC f t,

4Jo

*n/-at f t Ir- Joz+

\AL IrLt4L)

'r1.

L( r" dbe,o

J.e

-It-

:J-c

G)

lAv, : r- f vJ- L t:' t)l

8ct L t )Secb AL

+

\b

tsrTs n Vt Lrfi- d'tb 2nq

bwt W3*

htk +

ub, v*

t =Tu

&4"-!t tl t ;, ,ln;fteArrl W at L'b) 'fl&co

(*yV fu.UA il,A" tawil tn< lafruid aetu*L, C t l,t "l a"rd "d"a/, 3 n ,

a

%

n bae* , tl,,-L s(e ybl l, fr *" ff,sr1 +lra f/p N-

kwv tAl fts.r*- "b*ot".

"t h-? (kt ayex*rty b.n ,lr4 dr",lirt ,l t"to ArrD rrtadat .

Wda t ,/rei*,t u:!,,t-n fl, k A.; +eh"] Fn vLh t zQ ,)

"tl,.a- f lp L, , .wt

ich

l-tw&(- 1- Ll?;*'YAL Ch ++'s* DJa)

M fl"u+ 44r*'f

",;*, ffot* f?u4o,yt L + E,

71" L c.tt ,IALU **rt N ( & hlLrul w(0 ryrt ir, lfu ru4Lt

cy Lh' l lro n^*W "lD4erl , L L, +ft^vLtdlrtLto/ to ,fl,--e /.*^C

"tt',t u:a*a*<^t t* yo't d' c-4 &w ,'t4*ron t" f tr csn'iucot*"'

tiode t

n+

"th et7 t)ru-u oe1 W l;*Lrny.

\b

\tJ8-

--JI

IrII

II$

I;;

\-

\-/t-,

V

Je,.--f

l-

VUV ot!>It*y L

Va,( axhea t| /r^r*.il

V, -Vu , Vt

v. = LgL JI-

rN, *tr ) Y =L(ry#)rAE

"'^t ot1

'fo* . LoIVs

/\------+ L'

,a[r_*t ,

.r.e . -!N1,(g -Vo ->Cg.

@t-

*'rW

W a$a*t L q Toffi rt Tt

lron @A' = c"vs

-lr"rn @ A.T E. tV.e -vr) ---) @ ,

g,b

r Gt4

@'@ h+ =

GnVs = -Gkt Vs

vs (r- "W) =

v" = utr(

folat lirru prird 7 = To'n r rnil 7'n* C + @

r =r (#).n -'[ fi,.) ' ' '

- ' L^tlJ J.i1 \

"(vg us-vn'l

.. -

t/''

=rL Lz r/*41 E L'btr (:Y-L v" (us -r,)) \ v* (v-n 'il)

.i

T=L z Lryv-Y* \e (uo'vc)

ruA u, = +T ,.. r = r ap (*) 2 .L LL L+_ilt-

r(fr*)

r&)

Vu f*|-

ry:H) z,_ff I

*" L*t^,E

+----

V';rr(*)\)

ftnT

I

er\

u"ff) 9

-G4 Uo;v,)

_ LLt *_GO-r,

[::1t_, ]

\-

i-

-\1\-:

.

I

!-

,

,.\_

i

j

I

II

I

--.1

,rj ?r)

ffiUlttvl Y

** /t' '/''r ub+n 't'v-' Vs I

' 3 Vo fu

/sr,mr,

L AL

Vs&4-l=t-

-cJ

,A'54'L',rLtJff

Gy o-c? ia trel bn t , ; \ ^.-

*%- = + lr,**ve*;I .t-D^,^nrxc?t-.aoL4 i,"i+,'nil1*' L j

-L-* "'

u"' wo -o*r crwtiu;" crl*nilu' v

bn\/c -Yo Lv -.-o) a t J

,: olt -0 \*v

A \,, Y" tt

) f' 'db

v

o bon ^bw,.: | [a& = ef El". c J c L")o

O-

Or,.r,1r1 .rr, , capacitw 't, WW q +D toad. !, EA -

Av, z r, f rlo, +te_fc L J6 Zr--"'J

,/rwbatiiu,tt t"rr ) Lr,l".L Ia^tl€L ".),Mh A1 ) avc z + L- (yj)

c vs Lrf)

n_- %as-r -6

6Vc u ,"jcI

3-q

?ry ?a

, l&7ls

t

-*'*

I.lode z,,i

7

ofd

aO

b=L

L

:eVg.=-Vo

t

0mc

olc.

a

VD

Vs tn +rf$

V9oLt

a,

aroip

]z-

Tt

otc

-h

=T4

Io

AT-

I

I

I

-<-*

-

-

fG

\

t

fl4 &vck- bs* *N"^ l**;d- @,n e/p W' ffid,t 'r/ta4' lh' '/;r4"ia"n'--d

01 qr,ep[t^ fka/, .rf,t ",t, llil -k-nr- fuq ' t@rYL!- "b''tcl-- bw+t"; ff* o/f vb'/o

PWI ,;4 *tru;& rD that o( e* ifr v*l' :^;hh aya*u & od", knpun as an i"r^w+-v *rt**^ . u

7h4- ck4 "W* @r'd*l odidnd 'n't' tnpdp: ' \*

Du^;r* n^DdL t , & ; tun*ea. on 4. olfoalt Dm : tu;raun broztr ' L-

"**J i o- oo )4 v

'* 3Y: ;*.m ffij *o ?u* un) w*Y,/-t\

t wur!.ol !)Hrt +t^j,e"rt" )-' t' D' il't tnad \*?* ferl:-twv* f-' 0 , ,---,_lrnneol lo

Yht ,*ut. ,s4'',,A'tn L L"e''['l *" f**X'-'*t " +fu JP'o q fl

c, ureuL. W'unfi"l (hr 'a

',$'*'LJ ,,rL Y

"'4 tfu wxt cVcU ' '--:v

vpl arw.*s L \t t'(ot) eL = r & \v

Vb'.. eltLo-t^ L ' a'x*1 f6a1 "t 11 :

,U

!!=V, = tAL- \-+on \-,,+b"/t

''fri . L e!Vc

\/ol" @-cA-*vt L fbi4 q rl

Vo "-," =-L Aq

'"k6

>@

-----+ O

09 AI'

,AL =

+vr, --- @vL

bt (+)I

bU : -L LZOD

@q *=r@

-1,1.o=@

fi,to._l ,h"^,7*tool

Put " -v,r 5

7 =llnor*t,

' L.LL ,-\?IV,9 ,vo

- v.gt6

i

(9,\-7

=w (+)= - V / rrn\

t rrti)

: -% /_g\\r- *" )

:_yJ/ , \ ?

l*, -'l

l/YsthmL

!rvo

-/j (rr/

z L A'(* i)

: = r' L ai lU:"| t ,out)

vo

,7)

Ir)

.

\$y

)

tLA

'IL

I

ItI

= Lx

r-$-€_ t+

-vs(*)

r -S

i-

3wb f =rar (*)

Lttt f t1[,, I

,ro4+nq adWL, r 6\,)c. : t1,"

,lo

AI=Vr6L-

AaatnunlU

b1,*&r*

ft.ld- uf^ 't' '41 Jo44

VsLs = -Vof,'o

/,u = /f'J+] r*/" t'-E)

olt * V" (t =o)

Vc * Vc U,=r)

av.. i

.lryr'

= J- ( t, ,'lt-c.)

o

*G,")c

.l 3 lr\.'-5 )

3,firy:

I

I

I

,,fuhatttu.f,z +^ A%=

h4h Af, Avo

AV" : P*t Ir= tL

+(lglC L %J

*ttw,J. I b \

" lr )Avu . -.& t"

c

\v:J

!

!

Crr* Rrf ib,h,r

oaculs et

*$&,, :

h

Nodz z :

v.el ib Lz 4 fr,Ct !-t

+44- -M"t+-<4

'Il,L ckt **T*t ,( ,th:

,/) ,*town &, fi '

ark ^y^-l* *,q poLue) gff

llla ,to *t.t- buck - booah r fhp. alk *Wfu p!t-'"(r,wv o[p t+l tfr.Ak '2, &v non H t *^k-, tf^An rr4l rlr ,oa , bwt- tl,-l-- otP.

w- pq ir ffytertl" +, t't^At vl tr^" iyp pM.

:CL

btCz

i*=+f "r

JI9r

,+w^

tohln il* i k vr-t A /uAntul an + q bl ,tuo? tc!,,2d % , sl,bcl" Dt"t

rt W hra-\el + cr; ry r^"VLU t,e*,4 ,ti* ftr*rfp|V*^'llu c*t vyrar*n?u cAll D&t ,l;*;d>i fn-ly .t- **"1-,bln fu t "$.4q*Li uolu-n &t ;t wrn*A fit o.Lf t = b ,

lavuttht q ^y, Lt nhu,

,Art ,Hr-L vto.mt- humt , #u Wl *t Lt ,fifrt;^e,, tt*d" Dot,...

tuwiua ir q

A,6fw

,h Ly. i, +&arupt&A

J,,Difd,\

Tf" drhrl* D,n

ora.lion.

f-6-t1 '

6y, = Lr !9_V3

--+ e)

D^*J

g.&D+s L

rqqWLW fr* lrr,r,Kt b S.,rh r * rey

7tt apacilwr Ct ntlacfilf k ,r*Ty ,to ,,eV C,kt @c1 t cz-,ffii ,loa-r, 4- LL.

\

fladr 2- erf;u atA-an @t D ,e * b -- bt. !..-'

fL ct i, "W fr*, tiw f t *fp? + ,tf"e u,Lr,ff.eorrL

tol1-ortod oL ,.7T't'/d'fi'Ela \-

'/he uValiru cr ,rt -fr,u -*d;-^ t- @ ""r31 rt"-*

ed-y \ wt bJi

Vs -= Lr

,,ffl *oltlt-L-z ,b tlurj'

,trfi Ar

Ve,l Ac,h-*V h

AT,

,fr tfu ,bad ,

4- &, lr*"rioW

dr^y ,W U t/s - vet

!.

-

3,|L1

O o af, t . Tdn VJ --+ @k

@ a Ar, s "y Ur, *\r)l_t

ft[4 :

--+@

-11 yr.e

-AJa)\y* - u", I

@ =@ + ry *tV eLeeLo4-4 uVncilot c )

A I, = Vs bDn = 0", *ur) tW

Vt ,t"n = Vo, +"t( - Vt fyl

W (r"" -+rfi) z W-, +"k

vet r url,*.]fr\\w)? -Gh)

t vr (*,)\7 t'/

\ r/

D.r"inq ,tonI

& t A2. : Zr,-orr z

O-l*t, ^(-2Ls-y4

L7

ct r,

\/e-t -Vet z Lz AZz

+.,

G,t ' AL2-L2- -+ @.uci + vo

,*ry Trtl q k',*"y,. tt* ta-LLa fr'x" D-rn-a,.r z +a ltofn z

|u - *Ly Ar\rd4

, *Lz Atu -* @,v0

AL, = W (vr,rr*)

/'z\e' =)

LL

A2, . -TILLuo* UU

L"4

fffi [Vgi ,v*)

-tft /

4-- Lttn_vt2

tll ft'"ro-Xr,, lL ilur4r #, * Zrnfnz /D fn,a1t 2

I

j

i

I

ai^-,

'otb

@+

z- -'?fr-:"L-y-Ly

Tanvet + fiyt Vo

vo (f* "W )

drti"y en p"i"d

z -frk va

2 *Toy Vc t

-uo (M,W)vcl =

frn'

3.tt'vo (*) l

-vo ( h\\ r/.-

Vcr =

-r@a

,'bE

6\*o (1,'

__*@

= +rn +du64

z 21 Af1 L -L1 bZ1

/'

,\

-W,)

i,il

V* -Yc

vs

* Ve_t

('n -

J-Vg

vu,

\4

i LtOr,(

z- Lt bf,t (

\t t*n, l\

'tr''cnn @ 4 @ vs /_:_)

[, , )

G,uiaufrtl

VJ

**b Vo

Ls

tarwt h:*- far*d p, Lr

\z - -V.i $vg u

-I -8

frt'L ry ;c i'4 tB+4 ['a't

E = - Vrtn '

ufs (*f, ) f.

E

Ir,T = L1 bf,t ,>v, 1

( r (v, (v, -v") J

=) bti i Yr(h -Vct)

vet L1

us (vt, *Vt)ALt :

bt* Ve-r * V:-

lP5

Vu Lr

Pea-k fD penk

Tot*l. [.",",-a *&t

ilpr"t" ,t in Lt

Lr T=T6a*W

hu.b Vci => AI,

afr : %6tr

.lt-tt

AT,

vs vslT:t )r(*)''

L" AlL

t+

49.

a-(

Vc

, Lz_

:l L-L l)_E+

"r = -12- 6fz vc I

v, (Vci +vr)**+ @.

3-t*

Pr"k l" f eAk/A@e)

*\t,h c, k, Ly

A9, z *Uo(ver*uo)

lrVer

suhA+(DArz.-[*.ff)]H

't*J

@_-/

*)7--)

iC +,r_lvtt-t r-5

f(#)vs(1",i-5

-)t

-LtI

: -lLzI

t*l.---n @

,,Ohen T( "a ffi , C,

fu *T.o qrt *** '7

f lr ch ** v- 'r'r$ '

2c =f4

lae^.K te pea* frprk *LiV - c1

Lcl

: =)-tz_ f

e *t*tre44(a*J0

,tb a J-LI

Aez = !:4L,,T

AVcr .

i

t_

\

\*

ur ( ''-.,

aq fq Lv'-/"),4.

SLb LD .,. AVC, :

/tu)o t ,l

Avcr-.$ Lr Art

vo)*-o % Vcr @

? *L Lt /)'tt

,, f ,, - Yr IL- t-U

. ALz f rlII

BCz L)

-crvspJ'l" ,-t )

V

H,G)

Afz ( 11I -l4 cz L.)

ot,CrL*Yt C2-

.t/zI ( Arz

cz ) Io

AVer = f,s L1 ('-t)

CtWE

Vet . -t* t ,- t)

CtI

*,)rb alt @

1 ,rt

Lt, '-' A.fCz-

iltz

fiaf le"/ fuf,nub, AScz +ff e)

*;rt'*'/2

I rrr.Jo

A-t+l,tW

.', A Itz

d"t

Pee-k

iJ-Cy

/r*sj\LJ )

AYez

i fJfr Lf,_II

r Vr5-

Lr

1' 8a b& rwn't"7aub

ev*^y 4"1f[, fu-uvwua f,ez

apadta (z oh;oh g-l'owz Y /t"rn-eq.. Att

If'2e-o.t l"

UNIT-1 - NARSIMHA REDDY ENGINEERING COLLEGE

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Transcript of UNIT-1 - NARSIMHA REDDY ENGINEERING COLLEGE