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Electromagnetic Induction and Alternating Currents

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Q 1. Two identical circular loops of metal wire are lying on a table without touching each other. Loop-A carries a current which increases with time. In response, the loop-B

remains stationary

is attracted by the loop{tex} \operatorname - \mathrm { A } {/tex}

is repelled by the loop {tex} \operatorname - \mathrm { A } {/tex}

rotates about its {tex}\mathrm {CM} {/tex}, with {tex}\mathrm {CM} {/tex} fixed

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Q 2. A coil of inductance {tex} 8.4 \mathrm { mH } {/tex} and resistance {tex} 6 \Omega {/tex} is connected to a {tex} 12 \mathrm { V } {/tex} battery. The current in the coil is {tex} 1.0 \mathrm { A } {/tex} at approximately the time

{tex} 500 \mathrm { s } {/tex}

{tex} 25 \mathrm { s } {/tex}

{tex} 35 \mathrm { ms } {/tex}

{tex} 1 \mathrm { ms } {/tex}

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Q 3. A coil of wire having inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time {tex} t = 0 , {/tex} so that a time-dependent current {tex} I _ { 1 } ( t ) {/tex} starts flowing through the coil. If {tex} I _ { 2 } ( t ) {/tex} is the current induced in the ring, and {tex} B ( t ) {/tex} is the magnetic field at the axis of the coil due to {tex} I _ { 1 } ( t ) , {/tex} then as a function of time {tex} ( t > 0 ) , {/tex} the product {tex} I _ { 2 } ( t ) B ( t ) {/tex}

increases with time

decreases with time

does not vary with time

passes through a maximum

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Q 4. A metallic square loop {tex} A B C D {/tex} is moving in its own plane with velocity {tex} v {/tex} in a uniform magnetic field perpendicular to its plane as shown in the figure. An electric field is induced

in {tex} \mathrm {A D} , {/tex} but not in {tex} \mathrm {B C} {/tex}

in {tex} B C , {/tex} but not in {tex} A D {/tex}

neither in {tex} A D {/tex} nor in {tex} B C {/tex}

in both {tex} A D {/tex} and {tex} B C {/tex}

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Q 5. An infinitely long cylinder is kept parallel to an uniform magnetic field {tex} B {/tex} directed along positive z-axis. The direction of induced current as seen from the z-axis will be

zero

anticlockwise of the +ve z axis

clockwise of the +ve z axis

along the magnetic field

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Q 6. The circuit given in Fig has a resistanceless choke coil {tex} L {/tex} and a resistance {tex} R . {/tex} The voltage across {tex} R {/tex} and {tex} L {/tex} are given in Fig. The virtual of the applied voltage is

{tex} 100 \mathrm { V } {/tex}

{tex} 200 \mathrm { V } {/tex}

{tex} 300 \mathrm { V } {/tex}

{tex} 400 \mathrm { V } {/tex}

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Q 7. A coil has an inductance of {tex} 0.7 \mathrm { H } {/tex} and is series with a resistance of {tex} 220 \Omega {/tex}. When an alternating emf of {tex} 220 \mathrm { V } {/tex} at {tex} 50 \mathrm { cps } {/tex} is applied to it, then the wattles component of the current in the circuit is (take {tex} 0.7 \pi = {/tex} {tex} 2.2 ) {/tex}

{tex} 5 \mathrm { A } {/tex}

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

{tex} 0.7 \mathrm { A } {/tex}

{tex} 7 \mathrm { A } {/tex}

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Q 8. A transmitter transmits at a wavelength of {tex} 300 \mathrm { m } {/tex}. A condenser of capacitance {tex} 2.4 \mu \mathrm { F } {/tex} is being used. The value of the inductance for the resonant circuit is approximately

{tex} 10 ^ { - 4 } \mathrm { H } {/tex}

{tex} 10 ^ { - 6 } \mathrm { H } {/tex}

{tex} 10 ^ { - 8 } \mathrm { H } {/tex}

{tex} 10 ^ { - 10 } \mathrm { H } {/tex}

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Q 9. For the circuit shown in Fig, current in inductance is {tex} 0.8 \mathrm { A } {/tex} while that in capacitance is {tex} 0.6 \mathrm { A } {/tex}. What is the current drawn from the source?

{tex} 0.1 \mathrm { A } {/tex}

{tex} 0.3 \mathrm { A } {/tex}

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

{tex} 0.2 \mathrm { A } {/tex}

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Q 10. In the circuit shown in fig, switch {tex} S {/tex} is closed at time {tex} t = 0 . {/tex} The charge that passes through the battery in one time constant is

{tex} \frac { e R ^ { 2 } E } { L } {/tex}

{tex} E \left( \frac { L } { R } \right) {/tex}

{tex} \frac { E L } { e R ^ { 2 } } {/tex}

{tex} \frac { e L } { E R } {/tex}

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Q 11. A rectangular loop of slides {tex} 10 \mathrm { cm } {/tex} and {tex} 5 \mathrm { cm } {/tex} with cut is stationary between the pole pieces of an electromagnet. The magnetic field of the magnet is normal to the loop. The current feeding the electromagnet is reduced so that the field decreases from its initial value of {tex}0.3\mathrm T {/tex} at the rate of {tex}0.02 \mathrm { T s} ^ { - 1 } {/tex}. If the cut is joined and the loop has a resistance of {tex} 2.0 \Omega , {/tex} the power dissipated by the loop as heat is

{tex} 5 \mathrm {n W} {/tex}

{tex} 4 \mathrm {n W }{/tex}

{tex} 3 \mathrm { n W} {/tex}

{tex} 2 \mathrm { nW } {/tex}

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Q 12. A metallic square loop {tex} A B C D {/tex} is moving in its own plane with velocity {tex} v {/tex} in a uniform magnetic field perpendicular to its plane as shown in the figure. An electric filed is induced

{tex} \ln A D , {/tex} but not in {tex} B C {/tex}

{tex} \ln B C , {/tex} but not in {tex} A D {/tex}

Neither in {tex} A D {/tex} nor in {tex} B C {/tex}

In both {tex} A D {/tex} and {tex} B C {/tex}

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Q 13. {tex}AB{/tex} is a resistanceless conducting rod which forms a diameter of a conducting ring of radius {tex} r {/tex} rotating in a uniform magnetic field {tex} B {/tex} as shown in figure. The resistors {tex} R _ { 1 } {/tex} and {tex} R _ { 2 } {/tex} do not rotate. Then the current through the resistor {tex} R _ { 1 } {/tex} is

{tex} \frac { B \omega r ^ { 2 } } { 2 R _ { 1 } } {/tex}

{tex} \frac { B \omega r ^ { 2 } } { 2 R _ { 2 } } {/tex}

{tex} \frac { B \omega r ^ { 2 } } { 2 R _ { 1 } R _ { 2 } } \left( R _ { 1 } + R _ { 2 } \right) {/tex}

{tex} \frac { B \omega r ^ { 2 } } { 2 \left( R _ { 1 } + R _ { 2 } \right) } {/tex}

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Q 14. The wire is found to vibrate in the third harmonic. The maximum emf induced is

{tex} \frac { 4 ( A B ) \omega } { k } {/tex}

{tex} \frac { 3 ( A B ) \omega } { k } {/tex}

{tex} \frac { 2 ( A B ) \omega } { k } {/tex}

{tex} \frac { ( A B ) \omega } { k } {/tex}

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