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Electromagnetic Induction and Alternating Currents

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Q 1. A metallic square loop ABCD is moving in its own plane with velocity v in a uniform magnetic field perpendicular to its plane as shown in figure. An electric field is induced

A

in AD, but not in BC

B

in BC but not in AD

C

neither in AD nor in BC

Explanation

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Q 2. In an AC generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency in a magnetic field B. The maximum value of emf generated in the coil is

A

{tex}N.A.B.R. \omega{/tex}

B

{tex} \mathrm { N } . \mathrm { A } . \mathrm { B } {/tex}

C

{tex} \mathrm { N } . \mathrm { A } . \mathrm { B } {/tex}{tex} . \mathrm { R } {/tex}

{tex}N.A.B.\omega{/tex}

Explanation

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Q 3. A thin circular ring of area {tex} A {/tex} is held perpendicular to a uniform magnetic field of induction B. A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is {tex} R {/tex} . When the ring is suddenly squeezed to zero area, the charge flowing through the galvanometer is

A

{tex} \frac { B R } { A } {/tex}

{tex} \frac { \mathrm { AB } } { \mathrm { R } } {/tex}

C

ABR

D

{tex} \frac { B ^ { 2 } A } { R ^ { 2 } } {/tex}

Explanation

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Q 4. A boat is moving due east in a region where the earth's magnetic field is {tex} 5.0 \times 10 ^ { - 5 } \mathrm { NA } ^ { - 1 } \mathrm { m } ^ { - 1 } {/tex} due north and horizontal. The boat carries a vertical aerial {tex} \mathrm { 2m } {/tex} long. If the speed of the boat is {tex} \mathrm { 1.50ms } ^ { - 1 } {/tex} , the magnitude of the induced emf in the wire of aerial is:

A

{tex} \mathrm { 0.75mV } {/tex}

B

{tex} \mathrm {0.50 mV } {/tex}

{tex} \mathrm {0.15 mV } {/tex}

D

{tex} \mathrm {1 mV } {/tex}

Explanation

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Q 5. A horizontal straight wire 20{tex} \mathrm { m } {/tex} long extending from east to west falling with a speed of 5.0{tex} \mathrm { m } / \mathrm { s } {/tex} , at right angles to the horizontal component of the earth's magnetic field {tex} 0.30 \times 10 ^ { - 4 } \mathrm { Wb } / \mathrm { m } ^ { 2 } {/tex} . The instantaneous value of the e.m.f. induced in the wire will be

3{tex} \mathrm { mV } {/tex}

B

4.5{tex} \mathrm { mV } {/tex}

C

1.5{tex} \mathrm { mV } {/tex}

D

{tex}6 \mathrm { mV } {/tex}

Explanation

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Q 6. The self inductance of a long solenoid cannot be increased by

A

increasing its area of cross section

B

increasing its length

C

changing the medium with greater permeability

increasing the current through it

Explanation

The self-inductance of a long solenoid From the above expression, it is clear that the self-inductance of a long solenoid does not depend upon the current flowing through it. i.e., the self-inductance of a long solenoid cannot be increased by increasing the current through it.

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Q 7. Lenz's law gives

A

the magnitude of the induced e.m.f.

the direction of the induced current

C

both the magnitude and direction of the induced current

D

the magnitude of the induced current

Explanation

The Lenz's law gives the direction of induced current.According to this law, the induced current opposes the cause that produces it.

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Q 8. A metal ring is held horizontally and bar magnet is dropped through the ring with its length along the axis of the ring. The acceleration of the falling magnet

A

is equal to g

is less than g

C

is more than g

D

depends on the diameter of ring and length of magnet

Explanation

A metal ring is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring. The magnet falls with an acceleration less than g As the magnet falls, the magnetic flux linked with the ring increases. This induces emf in the ring which opposes the motion of the falling magnet, hence a < g.

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Q 9. A metal rod of length 1 cuts across a uniform magnetic field B with a velocity v. If the resistance of the circuit of which the rod forms a part is r, then the force required to move the rod is

{tex} \frac { B ^ { 2 } l ^ { 2 } v } { r } {/tex}

B

{tex} \frac { \mathrm { B } l v } { r } {/tex}

C

{tex} \frac { \mathrm { B } ^ { 2 } l v } { r } {/tex}

D

{tex} \frac { \mathrm { B } ^ { 2 } l ^ { 2 } v ^ { 2 } } { r } {/tex}

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Q 10. The mutual inductance of a pair of coils, each of N turns, is M henry. If a current of I ampere in one of the coils is brought to zero in t second, the emf induced per turn in the other coil, in volt, will be

{tex} \frac { \mathrm { MI } } { \mathrm { t } } {/tex}

B

{tex} \frac { \mathrm { NMI } } { \mathrm { t } } {/tex}

C

{tex} \frac { \mathrm { MN } } { \mathrm { It } } {/tex}

D

{tex} \frac { \mathrm { MI } } { \mathrm { Nt } } {/tex}

Explanation

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Q 11. A magnet is moved towards a coil (i) quickly (ii) slowly, then the induced e.m.f. is

larger in case (i)

B

smaller in case (i)

C

equal to both the cases

D

larger or smaller depending upon the radius of the coil

Explanation

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Q 12. A circular wire of radius r rotates about its own axis with angular speed {tex} \omega {/tex} in a magnetic field B perpendicular to its plane, then the induced e.m.f. is

A

{tex} \frac { 1 } { 2 } B r w ^ { 2 } {/tex}

B

{tex} \mathrm { Br } \omega ^ { 2 } {/tex}

C

2{tex} \mathrm { Br } ( \mathrm { v } ) ^ { 2 } {/tex}

zero

Explanation

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Q 13. A conducting ring of radius 1{tex} \mathrm { m } {/tex} kept in a uniform magnetic field {tex} B {/tex} of {tex} 0.01 T , {/tex} rotates uniformly with an angular velocity 100{tex} \mathrm { rad } \mathrm { s } ^ { - 1 } {/tex} with its axis of rotation perpendicular to {tex} B {/tex} . The maximum induced emf in it is

A

1.5{tex} \pi \mathrm { V } {/tex}

{tex}\pi V{/tex}

C

2{tex} \pi \mathrm { V } {/tex}

D

0.5{tex} \pi \mathrm { V } {/tex}

Explanation

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Q 14. A magnetic field of {tex}2\times 10^{-2}{/tex} T acts at right angles to a coil of area {tex}100 cm^{2}{/tex}, with 50 turns. The average e.m.f induced in the coil is 0.1 V when it is removed from the field in t sec. The value of t is

A

10{tex} s {/tex}

0.1{tex} \mathrm { s } {/tex}

C

0.01{tex} \mathrm { s } {/tex}

D

1{tex} \mathrm { s } {/tex}

Explanation

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Q 15. The magnetic flux through a circuit of resistance R changes by an amount {tex}\Delta \phi{/tex} in a time {tex}\Delta t{/tex}. Then the total quantity of electric charges Q that passes any point in the circuit during the time {tex}\Delta t{/tex} is represented by

A

{tex} Q = R \cdot \frac { \Delta \phi } { \Delta t } {/tex}

B

{tex} Q = \frac { 1 } { R } \cdot \frac { \Delta \phi } { \Delta t } {/tex}

{tex} Q = \frac { \Delta \phi } { R } {/tex}

D

{tex} Q = \frac { \Delta \phi } { \Delta t } {/tex}

Explanation

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Q 16. Fig shown below represents an area A = 0.5 {tex}m^{2}{/tex} situated in auniform magnetic field B = 2.0 {tex}weber/m^{2}{/tex} and making an angle of {tex}60^{\circ}{/tex} with respect to magnetic field.

The value of the magnetic flux through the area would be equal to

A

2.0 weber

B

{tex} \sqrt { 3 } {/tex} weber

C

{tex} \sqrt { 3 } / 2 {/tex} weber

0.5 weber

Explanation

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Q 17. As a result of change in the magnetic flux linked to the closed loop shown in the fig, an e.m.f. V volt is induced in the loop. The work done (joule) in taking a charge Q coulomb once along the loop is

{tex} \mathrm { QV } {/tex}

B

2{tex} \mathrm { QV } {/tex}

C

{tex} \mathrm { QV } / 2 {/tex}

D

Zero

Explanation

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Q 18. Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon

A

the rates at which currents are changing in the two coils

relative position and orientation of the two coils

C

the materials of the wires of the coils

D

the currents in the two coils

Explanation

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon. Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon relative position and orientation of the two coils.

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Q 19. The Self-induced emf of a coil is 25 volts, When the current in it is changed at uniform rate from 10 A to 25 A in 1s, the change in the energy of the inductance is :

437.5 J

B

740 J

C

637.5 J

D

540 J

Explanation

Energy stored in the magnetic field of the inductor -

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Q 20. A conducting wire frame is placed in a magnetic field which is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced current in wires AB and CD are

{tex} \mathrm { B } {/tex} to {tex} \mathrm { A } {/tex} and {tex} \mathrm { D } {/tex} to {tex} \mathrm { C } {/tex}

B

{tex} A {/tex} to {tex} B {/tex} and {tex} C {/tex} to {tex} D {/tex}

C

{tex} A {/tex} to {tex} B {/tex} and {tex} D {/tex} to {tex} C {/tex}

D

{tex} \mathrm { B } {/tex} to {tex} \mathrm { A } {/tex} and {tex} \mathrm { C } {/tex} to {tex} \mathrm { D } {/tex}

Explanation

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Q 21. Two different wire loops are concentric and lie in the same plane. The current in the outer loop (I) is clockwise and increases with time. The induced current in the inner loop

A

is clockwise

B

is zero

is counter clockwise

D

has a direction that depends on the ratio of the loop radii.

Explanation

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Q 22. When current in a coil changes from {tex} \mathrm { 5A } {/tex} to {tex} \mathrm { 2A } {/tex} in {tex} \mathrm { 0.1s } {/tex} , average voltage of {tex} \mathrm {50 V } {/tex} is produced. The self-inductance of the coil is :

A

{tex} 6\mathrm { H } {/tex}

B

{tex}0.67 \mathrm { H } {/tex}

C

{tex}3 \mathrm { H } {/tex}

{tex}1.67 \mathrm { H } {/tex}

Explanation

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Q 23. In a series resonant LCR circuit, the voltage across {tex} R {/tex} is 100 volts and {tex} R = 1 \mathrm { k } \Omega {/tex} with {tex} \mathrm { C } = 2 \mu \mathrm { F } {/tex} . The resonant frequency {tex} \omega {/tex} is {tex} \mathrm {200 rad } / \mathrm { s } {/tex} . At resonance, the voltage across {tex} L {/tex} is

A

{tex} 2.5 \times 10 ^ { - 2 } \mathrm { V } {/tex}

B

{tex} \mathrm { 40V } {/tex}

{tex} \mathrm {250 V } {/tex}

D

{tex} 4 \times 10 ^ { - 3 } \mathrm { V } {/tex}

Explanation

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Q 24. For the circuit shown in the fig., the current through the inductor is 0.9 A while the current through the condenser is 0.4 A. Then

A

current drawn from generator {tex} I = 1.13 \mathrm { A } {/tex}

B

{tex} \omega = 1 / ( 1.5 \mathrm { LC } ) {/tex}

{tex} I = 0.5 \mathrm { A } {/tex}

D

{tex} I = 0.6 \mathrm { A } {/tex}

Explanation

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Q 25. A capacitor has capacity {tex} \mathrm { C } {/tex} and reactance {tex} \mathrm { X } {/tex} . If capacitance and frequency become double, then reactance will be

A

4{tex} X {/tex}

B

{tex} \mathrm { X } / 2 {/tex}

{tex} \mathrm { X } / 4 {/tex}

D

2{tex} X {/tex}