LEVEL # 1 - Bothra Classes

131BOTHRA CLASSES EMI-TOPICWISE

LEVEL # 1Questionsbased on Magnetic flux

Q.1 A flux of 1m Wb passes through a strip havingan area A = 0.02 m2. The plane of the stripis at an angle of 60º to the direction of auniform field B. The value of B is-

(A) 0.1 T (B) 0.058 T

(C) 4.0 mT (D) none of the above.

Q.2 A small loop of area of cross section 10–4 m2

is lying concentrically and coplanar inside abigger loop of radius 0.628m. A current of 10. Ais passed in the bigger loop. The smaller loopis rotated about is diameter with an angularvelocity . The magnetic flux linked with thesmaller loop will be(A) 10–7 sint (B) 10–7 cost(C) 10–9 sint (D) 10–9 cost

Q.3 A coil of N turns and area A is rotated at therate of n rotations per second in a magneticfield of intensity B, the magnitude of themaximum magnetic flux will be :

(A) NAB (B) nAB(C) NnAB (D) 2nNAB

Q.4 The number of turns in a long solenoid is500. The area of cross-section of solenoid is2 × 10–3 m2. If the value of magneticinduction, on passing a current of 2 amp,through it is 5 × 10–3 tesla, the magnitudeof magnetic flux connected with it in weberswill be

(A) 5 × 10–3 (B) 10–2

(C) 10–5 (D) 2.5

Questionsbased on Induced EMF & current

Q.5 The instantaneous flux associated with aclosed circuit of 10 resistance is indicatedby the following reaction = 6t2 – 5t + 1,then the value in amperes of the inducedcurrent at t = 0.25 sec will be:

(A) 1.2 (B) 0.8

(C) 6 (D) 0.2

Q.6 A cylindrical bar magnetic is lying along theaxis of a circular coil. If the magnet is rotatedabout the axis of the coil then –

(A) e.m.f. will be induced in the coil

(B) Only induced current will be generated inthe coil

(C) No current will be induced in the coil

(D) Both e.m.f. and current will be induced inthe coil

Q.7 When a coil of area 2 cm2 and having 30turns, whose plane is normal to the magneticfield, is drawn out of the magnetic field, acharge of 1.5 × 10–4 coulomb flows in thecircuit. If its resistance is40 ohm, then themagnetic flux density in tesla will be –

(A) 10 (B) 0.1

(C) 1 (D) 0.01

Q.8 When a magnet is being moved towards a coil,the induced emf does not depend upon-(A) the number of turns of the coil(B) the motion of the magnet(C) the magnetic moment of the magnet(D) the resistance of the coil

Q.9 A wire carrying current I, lie on the axis of aconducting ring. The direction of theinduced current in the ring, when I isdecreasing at a steady rate is-(A) clockwise(B) anticlockwise(C) alternatively clock andanticlockwise(D) no induced current flow in the ring

Q.10 A magnet is brought towards a fixed coil rapidly.Due to this induced emf, current and chargeare E, I and Q respectively. If the speed of themagnet is doubled, then wrong statement is -

(A) E increases(B) increases(C) Q remains unchanged(D) Q increases

I

BOTHRA CLASSES EMI-TOPICWISE 132

Q.11 A field of 5 x 104/ ampere-turns/metre acts atright angles to a coil of 50 turns of area 10-2 m2.The coil is removed from the field in 0.1 second.Then the induced emf in the coil is-(A) 0.1 V (B) 80 KV(C) 7.96 V (D) none of the above

Q.12 A coil having n turns and area A is initially placedwith its plane normal to the magnetic field B. Itis then rotated through 180º in 0.2 sec. The emfinduced at the ends of the coils is-(A) 0.1 nAB (B) nAB(C) 5 nAB (D) 10 nAB

Q.13 A conducting circular loop is placed in a uniformmagnetic field B = 40 mT with its planeperpendicular to the field. If the radius of the loopstarts shrinking at a constant rate of 2mm/s,then the induced emf in the loop at an instantwhen its radius is 1.0 cm is-(A) 0.1 V (B) 0.2 V(C) 1.0 V (D) 1.6 V

Q.14 Two plane circular coils P and Q have radii r1 andr2, respectively, (r1 < < r2) and are coaxial asshown in fig. The number of turns in P and Q arerespectively N1 and N2. If current in coil Q isvaried steadily at a rate x ampere/sec then theinduced emf in the coil P will be approximately-

(A) 0 N1 N2 r21. (B) 0 N1 N2 r21 x(C) 0 N1 N2 r21 x / 2r2 (D) 0

Q.15 The rate of change of magnetic flux denistythrough a circular coil of area 10–2 m and numberof turns 100 is 103 Wb/m2/s. The value ofinduced e.m.f. will be –(A) 10–2V (B) 10–3V(C) 10V (D) 103V

Q.16 A long solenoid contains 1000 turns/cm and analternating current of peak value 1A is flowing init. A search coil of area of cross-section 1 × 10–

4 m2 and having 50 turns is placed inside thesolenoid with its plane perpendicular to the axisof the solenoid. A peak voltage of 22 × 10–2Vis produced in the search coil. The frequency ofcurrent in the solenoid will be –(A) 50 Hz (B) 100 Hz(C) 500 Hz (D) 1000 Hz

r2r1

P Q

N1

N2

Q.17 A coil of cross-sectional area 5 × 10–4 m2 andhaving number of turns 1000 is placedperpendicular to a magnetic field of 10–2 T. Thecoil is connected to a galvanometer ofresistance 500. The induced charge generatedin the coil on rotating it through an angle of radian will be –(A) 10 C (B) 20 C(C) 50 C (D) 100 C

Questionsbased on Lenz law & application

Q.18 Lenz's law is consistent with law of conservationof -(A) current (B) emf(C) energy (D) all of the above.

Q.19 The north pole of a magnet is brought neara coil. The induced current in the coil asseen by an observer on the side of magnetwill be(A) in the clockwise direction(B) in the anticlockwise direction(C) initially in the clockwise and then

anticlockwise direction(D) initially in the anticlockwise and then

clockwise direction.

Q.20 A magnetic f ield is directed normallydownwards through a metallic frame asshown in the figure. On increasing themagnetic field

(A) plate B will be positively charged(B) plate A will be positively charged(C) none of the plates will be positively

charged(D) all of the above

Q.21 Two coils P and Q are lying a little distanceapart coaxially. If a current I is suddenly setup in the coil P then the direction of currentinduced in coil Q will be –

P

I

Qobserver

(A) clockwise (B) towards north(C) towards south (D) anticlockwise


Q.22 A system S consists of two coils A and B. Thecoil A carries a steady current I while the coil Bis suspended near by as shown in fig. Now if thesystem is heated so as to raise the temperatureof two coils steadily then-

BA

( )

(A) the two coils show attraction

(B) the two coils show repulsion

(C) there is no change in the position of the twocoils

(D) induced currents are not possible in coil B.

Q.23 Consider the situation shown in fig. If the currentI in the long straight wire XY is increased at asteady rate then the induced emf's in loops Aand B will be-

A

BI

(A) clockwise in A, anticlockwise in B.

(B) anticlockwise in A, clockwise in B

(C) clockwise in both A and B

(D) anticlockwise in both A and B

Q.24 A conducting ring is placed around the core of anelectromagnet as shown in fig. When key K ispressed, the ring-

(A) remains stationary

(B) is attracted towards the electromagnet

(C) jumps out of the core

(D) none of the above

Q.25 A copper ring having a cut such as not to form acomplete loop is held horizontally and a barmagnet is dropped through the ring with itslength along the axis of the ring. Then accelerationof the falling magnet is- (neglect air friction)

(A) g (B) less than g(C) more than g (D) 0

Q.26 The north pole of a magnet is brought away froma coil, then the direction of induced current will be

(A) in the clockwise direction(B) in the anticlockwise direction(C) initially in the clockwise and then

anticlockwise direction(D) initially in the anticlockwise and then

clockwise direction.

Q.27 A metal sheet is placed in a variable magneticfield which is increasing from zero to maximum.Induced current flows in the directions as shownin figure. The direction of magnetic field will be -

(A) normal to the paper, inwards(B) normal to the paper, outwards.(C) from east to west(D) from north to south

Q.28 A square loop PQRS is carried away from acurrent carrying long straight conducting wireCD. The direction of induced current in the loopwill be

D P Q

C S R(A) anticlockwise(B) clockwise(C) sometimes clockwise some times

anticlockwise(D) current will not be induced


Q.29 A thin sheet of conductor, when allowed tooscillate in a magnetic field normal to the sheet,then the motion is-(A) damped due to air friction(B) damped due to eddy currents(C) accelerated due to eddy currents(D) not effected by induced currents

Q.30 P and Q are two circular thin coils of same radiusand subjected to the same rate of change of flux.If coil P is made up of copper and Q is made upof iron, then the wrong statement is-

(A) emf induced in the two coils is the same(B) the induced current in P is more than that in Q(C) the induced current in P and Q are in the

same direction(D) the induced currents are the same in both the

coils.

Motional EMI

Q.31 A wire of length 4 m placed normal to the

magnetic field of )j4i2(

tesla is moving

with a velocity )k8j6i4(

m/s. The emf

induced across the ends of the wire will be–

(A) 4 V (B) 8 V(C) 16 V (D) 32 V

Q.32 A rectangular loop of resistance R, and sides Iand x, is pulled out of a uniform magnetic field Bwith a steady velocity v. The necessary force Frequired for maintaining uniform velocity ofwithdrawal is-

(A) R

vB 2l(B)

R

vB 22 l

(C) R

vB 222l(D) 0

Q.33 A small conducting rod of length l, moves witha uniform velocity v in a uniform magnetic field Bas shown in fig-

V

× × × × × ×× × × × × ×× × × × × ×

× × × × × ×

× × × × × ×

Y

X

(A)Then the end X of the rod becomespositively charged

(B) the end Y of the rod becomes positivelycharged

(C) the entire rod is unevely charged(D) the rod becomes hot due to joule heating.

Q.34 A conductor ABOCD moves along its bisectorwith a velocity of 1 m/s through a perpendicularmagnetic field of 1 Wb/m2, as shown in fig. If allthe four sides are of 1m length each, then theinduced emf between points A and D is-

(A) 0 (B) 1.41 volt(C) 0.71 volt (D) none of the above

Q.35 A circular coil of radius r is placed in a uniformmagnetic field B. The magnetic field is normal tothe plane of the coil, as shown in fig. Now if thecoil is rotated at an angular speed of , about itsown axis, then the induced emf in the coil is-

(A) BA2

(B) B (2r)

(C) 0 (D) None of the above


Q.36 An electric potential difference will be inducedbetween the ends of the conductor shows in fig,when conductor moves in the direction-

(A) P (B) Q(C) L (D) M

Q.37 A square conducting loop of side L andresistance R is moving with a uniform velocityat right angles to one of the sides in its ownplane. On applying a uniform magnetic field atright angles to its plane as shown in the figurethe induced current in the loop will be –

(A) Zero

(B) R

BLV in anticlockwise direction

(C) R

BLV in clockwise direction

(D) R

BLV2 in clockwise direction

Q.38 A circular copper disc of radius 25 cm isrotating about its own axis with a constantangular velocity of 130 rad/s. If a magneticfield of 5 × 10–3 Tesla is applied at rightangles to the disc, then the induced potentialdifference between the centre and the rim ofthe disc will approximately be –

(A) 20 × 10–3 V (B) 20 × 10–6 V

(C) 20 × 10–9 (D) Zero

Q.39 A 1.2m wide railway track is parallel tomagnetic meridian. The vertical componentof earth’s magnetic field is 0.5 oersted. Whena train runs on the rails at a speed of 60Km/hr, then the induced potential differencebetween the ends of its axle will be –

(A) 10–4 V (B) 2 × 10–4 V

(C) 10–3 V (D) Zero

Q.40 A conducting wheel in which there are fourrods of length is rotating with angularvelocity in a uniform magnetic field B. Theinduced potential difference between itscentre and rim will be –

(A) 0 (B) B2

(C) B2 (D) 2

B 2

Q.41 A small straight conductor PQ is lying at rightangles to an infinite current carrying conductorXY. If the conductor PQ is displaced on metallicrails parallel to the conductor XY then thedirection of induced e.m.f. in the PQ will be –

(A) From Q to P

(B) From P to Q

(C) Vertically downwards(D) Vertically upwards

Q.42 A straight conductor carrying current i and aloop closed by a sliding connector of resistanceR lie in the same plane. The connector slidestowards right with a uniform velocity v. Theinduced current generated in the loop in termsof distance r of the connector form the straightconductor will be –

(A) r2

vi0

(B) r2

i0

(C) rR2

vi0

(D) None of these

Q.43 The spokes of a wheel are made of metal andtheir lengths are of one metre. On rotating thewheel about its own axis in a uniform magneticfield of 5 × 10–5 tesla normal to the plane ofwheel, a potential difference of 3.14 mV isgenerated between the rim and the axis. Therotational velocity of the wheel is

(A) 63 rev./s (B) 50 rev./s(C) 31.4 rev./s (D) 20 rev./s


Q.44 A metal rod completes a circuit as shown in thefigure. The circuit is normal to a magnetic fieldB = 0.15 T. If the resistance of the circuit is 3ohm then the force required to move the rodwith a constant velocity of 2 m/s will be –

(A) 3.75 × 10–3 N (B) 3.75 × 10–2 N(C) 3.75 × 102 N (D) 3.75 × 10–4 N

Self & Mutual induction andcombination of coils

Q.45 The significance of self inductance L is thesame as of that of ........ in the linear motion-

(A) mass (B) velocity(C) acceleration (D) displacement

Q.46 On making a coil of copper wire of length and coil radius r, the value of self inductanceis obtained as L. If the coil of same wire, butof coil radius r/2, is made, the value of selfinductance will be-

(A) 2L (B) L(C) 4L (D) L/2

Q.47 Out of the two coils placed near each other,when a current of 2 amp is passed in one, aflux of 6 × 10–5 weber passes through theother. If the number of turns in the secondarycoils is 20, the value of coefficient of mutualinduction in the coils will be-

(A) 6H (B) 6mH(C) 0.6H (D) 0.6mH

Q.48 The coefficient of mutual induction betweentwo coils is 4H. If the current in the primaryreduces from 5A to zero in 10–3 second thenthe induced e.m.f. in the secondary coil willbe-

(A) 104 V (B) 25 × 103 V(C) 2 × 104 V (D) 15 × 103 V

Q.49 The coefficient of mutual induction betweentwo closely lying coils does not depend upon-

(A) their mutual orientation(B) the permeability of their core material

(C) their structure(D) the current flowing in them

Q.50 The number of turns in a coil of wire of fixedradius is 600 and its self inductance is 108mH. The self inductance of a coil of 500 turnswill be-

(A) 74 mH (B) 75 mH(C) 76 mH (D) 77 mH

Q.51 The value of the self inductance of a coil is 5 H.If the current in the coil changes steadily from 1Ato 2A in 0.5 seconds, then the magnitude ofinduced emf is-(A) 1V (B) 10 V(C) 100 V (D) 0.1 V

Q.52 An inductance stores energy in-(A) electric field (B) magnetic field(C) resistance of coils (D) all of the above

Q.53 A thin copper wire of length 100 metres is woundas a solenoid of length l and radius r. Its selfinductance is found to be L. Now if the samelength of wire is wound as a solenoid of length lbut of radius r/2, then its self inductance will be-(A) 4L (B) 2L(C) L (D) L/2

Q.54 The coefficient of coupling between two coil ismaximum when the two coils are-(A) placed at right angles(B) placed parallel at close distance(C) wound around a common ferromagnetic core

and insulated from it.(D) placed at an angle of 45º with each other.

Q.55 Two coils of self inductances L1 and L2 aretightly wrapped one over the other. The maximummutual inductance of the combination will be-(A) L1 + L2 (B) L1 L2

(C) L L1 2 (D) L L

L L1 2

1 2

Q.56 The coefficient of mutual inductance of the twocoils is 5 H. The current through the primary coilis reduced to zero value from 3A in 1 milli second.The induced emf in the secondary coils is-(A) 0 (B) 1.67 KV(C) 15 KV (D) 600 V

Q.57 The value of coefficient of mutual induction intwo coils can be increased by-

(A) placing the coils mutually perpendicular.

(B) keeping the coils near to each other.

(C) keeping the coils considerably apart.

(D) winding the core on the common ironmagnetic material and insulating them.


Q.58 The current is reduced from 3 amp to zero in0.001 sec. in the primary coil. It induces an emfof 15000 volts in the secondary. The value ofcoefficient of mutual inductance in henry will be-

(A) 5 (B) 0.5(C) 4.5 (D) 50

Q.59 A solenoid having a core of cross-section 4 cm2,half air and half iron (relative permeability = 500),is 22 cm long. If the number of turns on it is 103

its self inductance is-

(A) 570 H (B) 57 H(C) 5.7 H (D) 0.57 H

Q.60 The coefficients of self induction of twoinductance coils are 0.01H and 0.03Hrespectively. When they are connected inseries so as to support each other, then theresultant self inductance becomes 0.06Henry. The value of coefficient of mutualinduction will be-

(A) 0.02 H (B) 0.05 H(C) 0.01 H (D) zero

Q.61 Two identical solenoid coils, each of selfinductance L are connected in series. Theirturns are in the same sense, and the distancebetween them is such that the coefficient ofcoupling is half. Then the equivalent inductanceof the combination is-

(A) L (B) 2L(C) 3L (D) L/2

Q.62 If two coils of negligible mutual induction andhaving coefficient of inductances L1 and L2(L1>L2) are arranged in parallel, the value of theequivalent self-induction will be-

(A) L1 L2 / (L1 – L2) (B) L1 L2 / (L1 + L2)

(C) (L1 + L2) / L1 L2 (D) (L1 – L2) / L1 L2

Questionsbased on Growth & decay of current in coil

Q.63 The self inductance and resistance of a coilare 5H and 20 respectively. On applying ane.m.f. of 100 V on it, the magnetic potentialenergy stored in the coil will be-

(A) 62.5 Joule (B) 62.5 erg(C) 62.5 × 10–3 Joule (D) zero

Q.64 The energy stored in an inductance is 1 joulewhen a current of 0.1 A is established in it. Theself-inductance of the coil is-(A) 25 H (B) 50 H(C) 200 H (D) 2.6 H

Q.65 The growth of current in an L - R circuit in timet = L / R is equal to about-(A) 37% of maximum (B) 63% of maximum(C) 57% of maximum (D) 67% of maximum

Q.66 The current in an L - R circuit in a time t = 2L / Rreduces to-(A) 36.5% of maximum(B) 13.5% of maximum(C) 0.50% of maximum(D) 63.2% of maximum

Q.67 A coil of 10 H inductance has a 5 resistanceand is connected to a 5 volt battery in series. Thecurrent in ampere in the circuit 2 seconds afterthe circuit is switched on is-(A) 1 amp (B) (1 – 1/e) amp(C) (1 – e) amp (D) 1/e amp.

Q.68 A coil of resistance R and inductance L isconnected to a battery of E volt e.m.f. This finalcurrent in the coil is-(A) E/R (B) E/L

(C) E R L/ 2 2 (D) E L R L/ 2 2

Q.69 Calculate the ratio of power desipatted bythe bulb at t = 1 sec and t = 2 sec afterclosing the switch-

L=200HV=200 voltP=100 watt

(A) 1e

e4

2

(B)

)1e(

e2

2

(C) 1e

1e4

2

(D) None of these


Q.70 Calculate the ratio of current flowing throughthe battery at t = 0 and t = . (t = 0 is thetime of closing of switch)

V=20volt

5

5

2µF 2 H

5

t=0

(A) 1 (B) 2

(C) 2

1(D) 0

Q.71 Plot the variation of emf across the inductorwith respect time

LR

E

(A)

t

(B)

t

(C)

t

(D)

t

Questionsbased on Transformer & AC generator

Q.72 To transmit electrical energy from a generatorto distant consumers-

(A)high voltage and low current aretransmitted

(B)high voltage and high current aretransmitted

(C) low voltage and low current are transmitted

(D) low voltage and high current are transmitted

Q.73 A transformer transforms 220 volts to 11 volts.If the current strength in the primary coil is5 amp. and that in the secondary, 90 amp,what is the efficiency of the transformer -

(A) 90 % (B) 100 %(C) 211 % (D) 150 %

Q.74 A step up transformer operates on a 230 volt lineand supplies a load of 2 amp. The ratio of primaryand secondary windings is 1 : 25. Determine theprimary current-(A) 12.5 amp (B) 50 amp(C) 8.8 amp (D) 25 amp

Q.75 A transformer is used to light 140 watt 24 voltlamp from 240 volt AC mains, the current in themain cable is 0.7 amp. The efficiency of thetransformer is-(A) 63.8% (B) 84%(C) 83.3% (D) 48%

Q.76 In a step-up transformer, in comparison with thesecondary the primary coil has-(A) less voltage and high current(B) high voltage and less current(C) less voltage and less current(D) high voltage and high current

Q.77 In the secondary coil of step-up transformer, thenumber of turns are-(A) more and the copper wire is thicker(B) more and the copper wire is thinner(C) less and the copper wire is thicker(D) less and the copper wire is thinner

Q.78 A dynamo-(A) creates electrical energy(B) converts mechanical energy into electrical

energy(C) converts electrical energy into mechanical

energy(D) creates mechanical energy.


× × × × × × ×× × × × × × ×× × × × × × ×× × × × × ×× × × × × ×× × × × × ×× × × × × × ×× × × × × × ×

××O

Rim

Spoke

Q.1 The coefficient of mutual inductance of twocircuits A and B is 3mH and their respectiveresistances are 10 ohm and 4 ohm. How muchcurrent should change in 0.02 second in thecircuit A. So that the induced current in B shouldbe 0.006 ampere-(A) 0.24 amp (B) 1.6 amp(C) 0.18 amp (D) 0.16 amp

Q.2 The coefficient of self inductance is 5 mH. If theemf of the cell in the circuit is 1.1 volt and at anyinstant the rate of increase of current is 6ampere/second, then at that instant, the result-ant e.m.f. in the circuit will be-(A) 1.13 V (B) 0.13 V(C) 1.07 V (D) 1.4 V

Q.3 The phase difference between the flux linkageand the induced e.m.f. in a rotating coil in auniform magnetic field is-(A) (B) /2(C) /4 (D) /6.

Q.4 A dynamo is sometimes said to generate elec-tricity. It actually acts as a source of-(A) charge (B) magnetism(C) e.m.f. (D) energy

Q.5 In a step-down transformer the number of turnsin-(A) primary are less(B) primary are more(C) primary and secondary are equal(D) primary are infinite.

Q.6 An inductor coil stores 32 J of magnetic fieldenergy and dissipates energy as heat at the rateof 320 W, when a current of 4 A is passedthrough it. The time constant of the circuit whenthis coil is joined across an ideal battery will be-(A) 0.2 s (B) 0.3 s(C) 0.4 s (D) 0.5 s

Q.7 A solenoid of inductance 50 mH and resistance10 is connected to a battery of 6 V. The timeelapsed before the current acquires half of itssteady-state value will be-(A) 3.01 s (B) 3.02 s(C) 3.03 s (D) 3.5 ms

Q.8 An inductor - resistance battery circuit is switched

LEVEL # 2on at t = 0. If the emf of the battery is E. Thecharge which passes through the battery in onetime constant will be-(A) i0 /e (B) i0 e/.(C) e/i0 (D) i0 e

Q.9 Two conducting circular loops of radii R1 and R2are placed in the same plane with their centrescoinciding. The mutual inductance between themassuming R2 < < R1 , will be-

(A) 0 2

2

12

R

R (B) 0 2

2

12

R

R

(C) 0 2

12

R

R (D) 0 2

2

122

R

R

Q.10 A conductor rod ABmoves parallel to X-axis in a uniform mag-netic field, pointing inthe positive Z-direc-tion. The end A of therod gets-(A) positively charged(B) negatively charged(C) neutral(D) first positively charged and then negatively

charged.

Q.11 A closed coil of copper whose area is 1m × 1mis free to rotate about an axis. The coil is placedperpendicular to a magnetic field of 0.10 Wb/m2.It is rotated through 180º in 0.01 second. Theinduced e.m.f. and induced current in the coil willrespectively be-(The resistance of the coil is 2.0 )(A) 20 V, 10A (B) 10 V, 20 A(C) 10 V, 10 A (D) 20 V, 20 A

Q.12 A bicycle wheel of radius 0.5 m has 32 spokes.It is rotating at the rateof 120 revolutions perminute, perpendicularto the horizontal com-ponent of earth's mag-netic field BH= 4 x 10-5 tesla. The emf induced between therim and the centre of the wheell will be-(A) 6.28 × 10–5 V (B) 4.8 × 10-5 V(C) 6.0 × 10–5 V (D) 1.6 × 10–5 V

A

B

v

X

Y


Q.13 The current in a coil varies w.r. to time t asI = 3t2 + 2t. If the inductance of coil be 10 mH,the value of induced e.m.f. at t = 2s will be-(A) 0.14 V (B) 0.12 V(C) 0.11 V (D) 0.13 V

Q.14 If circular coil with N1 turns is changed in to a coilof N2 turns. What will be the ratio of self induc-tances in both cases-

(A) N

N1

2(B)

N

N2

1

(C) N

N12

22 (D)

N

N1

2

Q.15 A solenoid has an inductance of 50 mH and aresistance of 0.025 . If it is connected to abattery, how long will it take for the current toreach one half of its final equilibrium value ?(A) 1.34 s (B) 1.2 s(C) 6.32 s (D) 0.23 s

Q.16 5.5 × 10-4 magnetic flux lines are passingthrough a coil of resistance 10 ohm and numberof turns 1000. If the number of flux lines reducesto 5 × 10–5 in 0.1 sec. The electromotive forceand the current induced in the coil will berespectively-(A) 5V, 0.5 A(B) 5 × 10–4 V, 5 × 10–4 A(C) 50 V, 5 A(D) none of the above.

Q.17 A closed coil consists of 500 turns on a rectan-gular frame of area 4.0 cm2 and has a resistanceof 50 ohm. The coil is kept with its planeperpendicular to a uniform magnetic field of 0.2weber/meter2. The amount of charge flowingthrough the coil if it is turned over (rotatedthrough 180º) will be -(A) 1.6 × 10–19 C (B) 1.6 × 10–9 C(C) 1.6 × 10–3 C (D) 1.6 × 10–2 C


LEVEL # 3Q.1 A coil of area A = 0.5m2 is situated in a uniform

magnetic field B = 4.0 wb/m2 and makes anangle of 60° with respect to the magnetic fieldas shown in figure. The value of magnetic fluxthrough the area A would be equal to -

(A) 2 wb (B) 1 wb

(C) 3 wb (D) 2

3 wb

Q.2 A conducting loop is pulled with a constantvelocity towards a region of uniform magneticfield as shown in the figure then the currentinvolved in the loop is (d > r) -

(A) Clockwise while entering

(B) Anticlockwise while entering

(C) Zero when partially outside

(D) Anticlockwise while leaving.

Q.3 A conducting loop of resistance R and radius rhas its centre at the origin of the coordinatesystem in a magnetic field B, When it is rotatedabout y-axis through 90°, net charge flown inthe loop is directly proportional to -

(A) B-1 (B) R

(C) r2 (D) r

Q.4 A small conducting circular ring of area 2 mm2

is placed coplanerly with a long straight currentcarrying wire at a distance of 10 cm from it. Itcurrent through the wire decreases from 4 A tozero in 0.1s, the average value of emf inducedin the ring.

(A) 1.6 x 10-10 V (B) 2.0 x 10-10 V

(C) 3.2 x 10-10 V (D) Zero.

Q.5 A conducting square loop edge length a andresistance R is in a uniform magnetic field B,perpendicularly. Two opposite corners of the loopare pulled apart as shown in fig., till it becomesstraight, the charge flown through the loop willbe -

(A) R

Ba2

(B) R

Ba2 2

(C) R2

Ba2

(D) Zero

Q.6 A wire is bent to form a semicircle of radius a.The wire rotales about its one end with angularvelocity . Axis of rotation being perpendicularto the plane of the semicircle. In the region, auniform magnetic field B exist along the axis ofrotation as shown in fig.

The emf induced in the wire.

(A) 2

aB 2(B) 2aB

(C) 2aB2 (D) 4

aB 2


Q.7 A circular coil of radius a and having N turns isplaced at centre of a long solenoid, coaxially.The solenoid has radius b (b >> a) and numberof turns per unit length is n. Their coefficient ofmutual inductance will be -

(A) 220 anN (B) 2

0 anN

(C) 220 aNn (D) 222

0 aNn

Q.8 In the circuit shown in fig.. Time constant andsteady state current will be -

(A) 0.25 s, 0.75 A (B) 0.75 s, 0.25 A

(C) 0.25 s, 0.25 A (D) 0.5 s, 0.5 A

Q.9 Through an induction coil of L = 0.2 H, an a.c.current of 2A is passed first with frequency f1and then with frequency f2. The ratio of the

maximum value of induced emf 2

1

e

e in the coil

in the two cose is -

(A) 1

2

f

f(B) 2

1

22

f

f(C) 2

2

21

f

f(D)

2

1

f

f

Q.10 Two coils have mutual inductance 0.005H. Thecurrent charges in the first coil according to

equation I = 0I tsin , where A10Io and

s

rad100 . The maximum value of emf in

the second coil (In volts) is -

(A) 2 (B) 5 (C) (D) 4

Q.11 When the current in a coil charges from 2A to4A in 0.05 s, emf of 8 volt is induced in the coil.The coefficient of self induction of the coil is -(A) 0.1 H (B) 0.2 H (C) 0.4 H (D) 0.8 H

Q.12 A large coil of 10 turns has resistance 2 . It iskept in a magnetic feild of 0.5T. If the coil ispulled out of the magnetic field uniformely suchthat its area coming out of the magnetic feild is

200 cm2/s, the induced current in its is -

(A) zero (B) 500 A (C) 50 mA (D) 5A

Q.13 Consider the situation shown in fig. the wire ABis slide on the fixed rails with a constant velocity.If the wire AB is replaced by a semicircular wire,the magnitude of induced current will be -

(A) Increase

(B) decrease

(C) remain the same

(D) May increase or decrease depending on whether the semicircle bulges towards the resistance or away from it.

Q.14 A coil having inductance and L and resistanceR is connected to a battery of emf at t = 0. Ift1 and t2 are time for 90% and 99% completion

of current growth in the circuit, then 2

1

t

t will be-

(A) 1 : 2 (B) 2 : 1

(C) 2

10loge (D) 10log2 e

Q.15 Two circular, similar, coaxial loops carry equalcurrents in the same direction. If the loops arebrought nearer, what will happen -

(A) Current will increase in each loop.

(B) Current will decrease in each loop.

(C) Current will remain same in each loop.

(D) Current will increase in one and decrease in the other.

Q.16 A rectangular coil of 20 turns and area of cross-section 25 cm2 has a resistance of 10 ohm. If amagnetic field which is perpendicular to the planeof the coil changes at a rate of 1000 tesla persec, the current in the coil is -(A) 1 ampere (B) 50 ampere(C) 0.5 ampere (D) 5.0 ampere


Q.17 A solenoid ha 2000 turns wound over alength of 0.3m. The area of its cross-section is1.2x10–3 m2. Around its central portion a coil of300 turns is wound. If an initial current of 2 ampin the solenoid is reversed in 0.25 sec, the e.m.f.induced in the coil is equal to -(A) 6x10–4 V (B) 48 mV(C) 6x10–2V (D) 48 kV

Q.18 A step-down transformer transforms a supplyline voltage of 2200 volt into 220 volt. The primarycoil has 5000 turns. The efficiency and powertransmitted by the transformer are 90% and 8kilowatt respectively. Then the number of turnsin the secondary is -(A) 5000 (B) 50(C) 500 (D) 5

Q.19 The coil of a dynamo is rotating in a magneticfield. The developed induced e.m.f. changes andthe number of magnetic lines of force alsochanges. which of the following conditions iscorrect -(A) Lines of force minimum but induced e.m.f.

is zero.(B) Lines of force maximum but induced e.m.f.

is zero.(C) Lines of force maximum but induced e.m.f.

is not zero.D) Lines of force maximum but induced e.m.f.

is also maximum.

Q.20 An inductance L and a resistance R are firstconnected to a battery. After some time thebattery is disconnected but L and R remainconnected in a closed circuit. Then currentreduces to 37% of its initial value in -

(A) RL sec (B) (R/L) sec

(C) (L/R) sec (D) (1/LR) sec

Q.21 An ideal coil of 10 henry is joined in series witha resistance of 5 ohm and a battery of 5 volt.Two seconds after joining, the current flowingin ampere in the circuit will be -(A) e–1 (B) (1–e–1)(C) 1-e (D) e

Q.22 An e.m.f. of 15 volt is applied in a circuitcontaining 5 henry inductance and 10 ohm

resistance. The ratio of the current at time tand t=1 second is -

(A) 1e

e2/1

2/1

(B)

1e

e2

2

(C) 1e1 (D) 1e

Q.23 The number of tuns in the coil of an AC generatoris 5000 and the area of the coil is 0.25 m2 ; thecoil is rotated at the rate of 100 turns per secondin a magnetic field of 0.2 weber/m2. The peakvalue of the e.m.f. generated is nearly -(A) 786 kV (B) 440 kV(C) 220 kV (D) 157.1 kV

Q.24 In an inductor of self-inductance L=2 mH, currentchanges with time according to relation -

t2etI

At what time e.m.f. is zero ?(A) 4s (B) 3 s (C) 2 s (D) 1 s

Passage type question :-A conducting bar is slide at a constantvelocity v along two conducting rods. The rodsare separated by a distance and connectedacross a resistor R. The entire apparatus isplaced in an external magnetic field B directedinto the page.

× ××

× ×v

×

××

× ×

××

×

× ××

×

R

Bin

Q.25 Which of the following represents thecurrent i generated by the apparatus.

(A)

i

t

(B)

i

t

(C)

i

t

(D)

i

t

Q.26 If rod is replaced by a semicircular and conductingwire of diameter . Then current in R -(A) increase(B) decreases(C) remain same(D) may increase or decrease.


Q.27 The current in closed loop will be -

(A) clockwise

(B) anticlockwise

(C) may be clockwise or anti clockwise(D) none of the these

Statements type question :

Each of the questions given below consist ofStatement – I and Statement – II. Use thefollowing Key to choose the appropriateanswer.(A) If both Statement- I and Statement- II are

true, and Statement - II is the correctexplanation of Statement– I.

(B) If both Statement - I and Statement - II aretrue but Statement - II is not the correctexplanation of Statement – I.

(C) If Statement - I is true but Statement - II isfalse.

(D) If Statement - I is false but Statement - II istrue.

Q.28 Statement I : A thin aluminium disc, spinningfreely about a central pivot, is quickly broughtto rest when placed between the poles of astrong U-shaped magnet.

Statement II : A current induced in a discrotating in a magnetic field produces a forcewhich tends to oppose the motion of the disc.

Q.29 Statement I : A step up transformer can alsoas a step down transformer.

Statement II : This is because p

s

p

s

n

n

E

E

Q.30 Statement I : When we consider mutualinduction of two coils, their self induction is takenas zero.

Statement II : Self induction and mutualinduction are effective simultaneously.

Q.31 Statement I : In a given situation, the directionof induced current given by Lenz's Law andFleming's right hand rule is the same.

Statement II : Statement of both the laws isthe same.

Q.32 Statement I : An inductor can not have zeroresistance.

Statement II : This is because inductor has tobe made up of some material, which must havesome resistance.


LEVEL # 4(Question asked in previous AIEEE & IIT-JEE)

SECTION - AQ.1 When a rectangular loop pulled out from uniform

magnetic field. The induced current isproportional to - [AIEEE-2002]

(A) B

(B) –1

(C) R

(D) v2

Q.2 Resultant inductance of the circuit will be -[AIEEE-2002]

(A) 3 H

(B) 9 H

(C) 1 H

(D) 7.5 H

Q.3 Two coils are placed close to each other. Themutual inductance of the pair of coils dependsupon – [AIEEE-2003](A) Relative position and orientation of the two

coils(B) The materials of the wires of the coils(C) The currents in the two coils(D) The rates at which currents are changing in

the two coils

Q.4 When the current changes from +2A to –2A in0.05 second, an e.m.f. of 8 V is induced in acoil. The coefficient of self-induction of the coilis & [AIEEE-2003](A) 0.4 H (B) 0.8 H(C) 0.1 H (D) 0.2 H

Q.5 A coil having n turns and resistance R isconnected with a galvanometer of resistance4R. This combination is moved in time tseconds from a magnetic field W1 weber to W2weber. The induced current in the circuit is

[AIEEE-2004]

(A) – tnR5

)WW( 12 (B) –

tR5

)WW(n 12

(C) – tnR

)WW( 12 (D) –

tR

)WW(n 12

Q.6 In a uniform magnetic field of induction B a wirein the form of a semicircle of radius r rotatesabout the diameter of the circle with an angular

frequency . The axis of rotation is perpendicularto the field. If the total resistance of the circuitis R the mean power generated per period ofrotation is – [AIEEE-2004]

(A) R2

rB 2(B)

R8

)rB( 22

(C) R2

)rB( 2 (D) R8

)rB( 22

Q.7 A metal conductor of length 1 m rotatesvertically about one of its ends at angular velocity5 radians per second. If the horizontal componentof earth’s magnetic field is 0.2 × 10–4T, then thee.m.f. developed between the two ends of theconductor is – [AIEEE-2004](A) 5 µV (B) 50 µV(C) 5 mV (D) 50 mV

Q.8 A coil of inductance 300 mH and resistance 2is connected to a source of voltage 2 V. Thecurrent reaches half of its steady state value in

[AIEEE-2005](A) 0.05 s (B) 0.1 s(C) 0.15 s (D) 0.3 s

Q.9 The self inductance of the motor of an electricfan is 10 H. In order to impart maximum powerat 50 Hz, it should be connected to acapacitance of – [AIEEE-2005](A) 4µF (B) 8µF(C) 1µF (D) 2µF

Q.10 One conducting U tube can slide inside anotheras shown in figure, maintaining electricalcontacts between the tubes. The magnetic fieldB is perpendicular to the plane of the figure. Ifeach tube moves towards the other at a constantspeed V, then the emf induced in the circuit interms of B, l and V where is the width of eachtube, will be – [AIEEE-2005]

(A) BlV (B) –BlV(C) zero (D) 2BlV


Q.11 The flux linked with a coil at any instant 't' isgiven by = 10t2 – 50t + 250. The induced emfat t = 3 s is – [AIEEE 2006](A) 10 V (B) 190 V(C) – 190 V (D) – 10 V

Q.12 In an AC generator, a coil with N turns, all of thesame area A and total resistance R, rotates withfrequency in a magnetic field B. The maxi-mum value of emf generated in the coil is –

[AIEEE 2006](A) N.A.B.R. (B) N.A.B.(C) N.A.B.R. (D) N.A.B.

Q.13 An inductor (L = 100 mH), a resistor (R = 100) and a battery (E = 100 V) are initially con-nected in series as shown in the figure. After along time the battery is disconnected after shortcircuiting the points A and B. The current in thecircuit 1 ms after the short circuit is –

[AIEEE 2006]

(A) 0.1 A (B) 1 A(C) 1/e A (D) e A

Q.14 An ideal coil of 10H is connected in serieswith a resistance of 5 and a battery of 5V.2 seconds after the connection is made, thecurrent flowing in amperes in the circuit is -

[AIEEE 2007](A) (1 – e) (B) e(C) e–1 (D) (1 – e–1)

Q.15 Two coaxial solenoids are made by winding thin

insulated wire over a pipe of cross-sectional area

A = 10 cm2 and length = 20 cm. If one of the

solenoids has 300 turns and the other 400 turns,

their mutual inductance is (

0

= 4 × 10–7 T m A–1)

[AIEEE 2008]

(A) 4.8 × 10–4 H (B) 4.8 × 10–5 H

(C) 2.4 × 10–4 H (D) 2.4 × 10–5 H

Q.16 An inductor of inductance L = 400 mH and

resistors of resistances R1 = 2 and R2 = 2

are connected to a battery of emf 12V as shown

in the figure. The internal resistance of the

battery is negligible. The switch S is closed at

t = 0. The potential drop across L as a function

of time is – [AIEEE 2009]

(A) 6 e–5tV (B) t

12e–3tV

(C) 6 [1 – e–t/0.2) V (D) 12 e–5tV

SECTION - BQ.1 In a straight conduting wire a constant current

is flowing form left to reight due to a sourceof emf. when the source is switched off, thedirection of the induced current in the wirewill be – [IIT - 93](A) from left to right(B) form right to left(C) no current will be induce(D) none

Q.2 The magnetic flux through a coil varies withtime as = 5t2 + 6t + 9 . The ratio of emfat t = 3s to t = 0s will be – [IIT - 94](A) 9 : 1 (B) 1 : 6(C) 6 : 1 (D) 1 : 9

Q.3 Two inductances L1 and L2 are placed farapart and in parallel . Their combinedinductance is– [IIT- 94]

(A) L1+ L2 (B) (L1 + L2) 2

1

L

L

(C) (L1– L2) 1

2

L

L(D)

21

21

LL

LL

Q.4 Two different coils have self-inductance, L1 =8 mH, and L2 = 2 mH. The current in onecoil is increased at a constant rate. Thecurrent in the second coil is also increasedat the same constant rate. At a certianinstant of time, the power given to the twocoils is the same. At that time the current,the induced voltage and the energy stored inthe first coil are i1, v1 and w1 respectively.Corresponding values for the second coil atthe same instant are i2, v2 and w2respectively. Then [IIT- 94]

(A) 4

1

i

i

2

1 (B) 4i

i

2

1

*(C) 4w

w

1

2 *(D) 4

1

v

v

1

2


Q.5 A thin semicircular coducting ring of radius Ris falling with its plane vertical in a horizontalmagnetic induction B (figure). At the positionMNQ the speed of the ring is V, and thepotential difference develped across the ringis – [IIT- 94-96]

(A) Zero(B) BVR2/2 and M is at higher potential(C) RBV and Q is at higher potential(D) 2RBV and Q is at higher potential

Q.6 The network shown in figure is part of acomplete circuit. If at acertain instant thecurrent (I) is 5 A, and decreasing at a rate of103 A/s, then VB – VA = [IIT-1997]

A 1 15 V

I 5 mH

B

(A) 15 V (B) 10 V

(C) 5 V (D) 20 V

Q.7 A metal rod moves at a constant velocity ina direction perpendicular to its length. Aconstant, uniform magnetic field exists inspace in a direction perpendicular to the rodas well as its velocity . Select the correctstatement (s) from the following– [IIT-98]

(A) The entire rod is at the same electricpotential

(B) There is an electric field in the rod.

(C) The electric potential is highest at thecentre of the rod and decreases towardsits ends.

(D) The electric potential is lowest at thecentre of the rod, and increases towardsits ends.

Q.8 A small square loop of side is placed insidea large square loop of side L (>>). The loopsare coplanar and their centres coincide. Themutual inductance of the system isproportional to – [IIT-98]

(A) (/L) (B) (2/L)

(C) (L/) (D) (L2/)

Q.9 A circular loop of radius R, carrying currentI, lies in x-y plane with its centre at origin.The total magnetic flux through x-y plane is :

[IIT-1999]

(A) directly propotional to I

(B) directly proportional to R

(C) directly proportional to R2

(D) zero

Q.10 Two identical circular loops of metal wire arelying on a table without touching each other.Loop - A carries a current which increaseswith time . In response , the loop - B

[IIT-1999](A) Remains stationary

(B) Is attracted by the loop -A(C) Is repelled by the loop-A(D) Rotates about its CM, with CM fixed

Q.11 A coil of inductance 8.4 mH and resistance6is connected to a 12V battery. The currentin the coil is 1.0 A at approximately the time –

[IIT-1999](A) 500s (B) 20s(C) 35 ms (D) 1 ms

Q.12 A charged particle is released from rest in aregion of steady and uniform electric andmagnetic fields which are parallel to eachother. The particle will move in a :

[IIT 99]

(A) straight line (B) circle(C) helix (D) cycloid

Q.13 Two circular coils can be arranged in any ofthe three situations shown in the figure. Theirmutual inductance will be –

[IIT-2001]

(A) Maximum in situation (A)(B) Maximum in situation (B)

(C) Maximum in situation (C)(D) the same in all situation


Q.14 A metallic square loop ABCD is moving in itsown plane with velocity v in a uniformmagnetic field perpendicular to its plane asshown in the figure. An electric field isinduced – [IIT-2001](A) In AD, but not in BC(B) In BC , but not in AD(C) Neither in AD nor in BC(D) In both AD and BC

Q.15 As shown in the figure, P and Q are twocoaxial conducting loops separated by somedistance. When the switch S is closed, aclockwise current IP flows in P(as seen by E)and an induced current IQ, flows in Q. Theswitch remains closed for a long time. When

S is opened, a current 2QI flows in Q. Then

the direction 1QI and

2QI (as seen by E) are:

[IIT-2002]

(A) respectively clockwise and anti-clockwise(B) both clockwise(C) both anti-clockwise(D) respectively anti-clickwise and clockwise

Q.16 A small magnet is moving with constantvelocity along the axis of a coil as shown inthe figure. Then correct graph betweeninduced emf and time is - [IIT - 2004]

(A)

e

t

(B)

e

t

(C)

e

t

(D)

Q.17 A long holow cylindrical wire placed parallelto the direction of unifrom magnetic field whichis directed along + Z axis. Then inducedcurrent on the surface of cylinder -

[IIT - 2005](A) in the direction of magnetic field(B) 0(C) clockwise as seen from + Z axis(D) Anticlokwise as seen from + Z axis

Q.18 The figure shows certain wire segments joined

together to form a coplanar loop. The loop is

placed in a perpendicular magnetic field in the

direction going into the plane of the figure. The

magnitude of the field increases with time. I1

and I2 are the currents in the segments ab and

cd. Then- [IIT - 2009]

× × × × × ×

a × × × × × × ×

× × × × × × ×

× × × × × × ×

× × × × × × ×

b

d c

(A) I1 > I

2

(B) I1 < I

2

(C) I1 is in the direction ba and I

2 is in the direction

cd

(D) I1 is in the direction ab and I

2 is in the direction

dc


Q.19 Two metallic rings A and B, identical in shape

and size but having different resistivities A and

B, are kept on top of two identical solenoids as

shown in the figure. When current I is switched

on in both the solenoids in identical manner,

the rings A and B jump to heights hA and h

B,

respectively, with hA > h

B. The possible relation(s)

between their resistivities and their masses mA

and mB is (are) – [IIT - 2009]

A B

(A) A >

B and m

A = m

B

(B) A <

B and m

A = m

B

(C) A >

B and m

A > m

B

(D) A <

B and m

A < m

B


ANSWER KEY

LEVEL # 2

LEVEL # 1Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Ans. B D A A D C C D D D A D D C D A B C B A

Q.No. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40Ans. A A A C A B B B B D C B B B C D A A C D

Q.No. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60Ans. A C D A A A D C D B B B C C C C D A D C

Q.No. 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78Ans. C B A C B B B A B A C A A B C A B B

Q.No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Ans. D C B C B A D A A B A A A A A A C

Ques. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Ans. B B C A A C B A D B B C C A B D B C B C

Ques. 21 22 23 24 25 26 27 28 29 30 31 32

Ans. B B D C A C B A A D C A

LEVEL # 3

LEVEL # 4

SECTION-A

SECTION-B

Ques. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Ans. A C D A,C,D D A B B D C D A A D D D B D B,D

Ques. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Ans. A C A C B B B B C D D B C D C D

LEVEL # 1 - Bothra Classes

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Transcript of LEVEL # 1 - Bothra Classes