# JEE Advanced > Electromagnetic Induction and Alternating Currents

Explore popular questions from Electromagnetic Induction and Alternating Currents for JEE Advanced. This collection covers Electromagnetic Induction and Alternating Currents previous year JEE Advanced questions hand picked by experienced teachers.

Physics
Chemistry
Mathematics
Q 1.

Correct4

Incorrect-1

A thin circular ring of area {tex} A {/tex} is held perpendicular to a uniform magnetic field of induction {tex} B{/tex} . 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}\mathrm { \frac { B R } { A }} {/tex}

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

C

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

D

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

##### Explanation

Q 2.

Correct4

Incorrect-1

A thin semi-circular conducting ring of radius {tex} \mathrm { R } {/tex} is falling with its plane vertical in horizontal magnetic induction {tex} \vec { B } {/tex}. At the position {tex} M N Q {/tex} the speed of the ring is {tex} v , {/tex} and the potential difference developed across the ring is

A

zero

B

{tex} B v \pi R ^ { 2 } / 2 {/tex} and {tex} M {/tex} is at higher potential

C

{tex} \pi R B v {/tex} and {tex} Q {/tex} is at higher potential

{tex} 2 R B v {/tex} and {tex} Q {/tex} is at higher potential.

##### Explanation

Q 3.

Correct4

Incorrect-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

A

remains stationary

B

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

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

D

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

##### Explanation

Q 4.

Correct4

Incorrect-1

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

A

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

B

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

C

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

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

##### Explanation

Q 5.

Correct4

Incorrect-1

A uniform but time-varying magnetic field {tex} \mathrm {B}(t) {/tex}exists in a circular region of radius {tex}a{/tex} and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point {tex}\mathrm {P} {/tex} at a distance {tex}\mathrm {r} {/tex} from the centre of the circular region

A

is zero

decreases as {tex} 1 / r {/tex}

C

increases as {tex} r {/tex}

D

decreases as {tex} 1 / r ^ { 2 } {/tex}

##### Explanation

Q 6.

Correct4

Incorrect-1

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}

A

increases with time

decreases with time

C

does not vary with time

D

passes through a maximum

##### Explanation

Q 7.

Correct4

Incorrect-1

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

A

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

B

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

C

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

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

##### Explanation

Q 8.

Correct4

Incorrect-1

Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be

maximum in situation(a)

B

maximum in situation (b)

C

maximum in situation (c)

D

the same in all situations

##### Explanation

Q 9.

Correct4

Incorrect-1

As shown in the figure, {tex} P {/tex} and {tex} Q {/tex} are two coaxial conducting loops separated by some distance. When the switch {tex} S {/tex} is closed, a clockwise current {tex} I _ { P } {/tex} flows in {tex} P ( \text { as seen by } E ) {/tex} and an induced current {tex} I _ { Q 1 } {/tex} flows in {tex} Q {/tex}. The switch remains closed for a long time. When {tex} S {/tex} is opened, a current {tex} I _ { Q 2 } {/tex} flows in {tex} Q . {/tex} Then the direction {tex} I Q _ { 1 } {/tex} and {tex} I Q _ { 2 } {/tex} (as seen by {tex} E {/tex} ) are

A

respectively clockwise and anti-clockwise

B

both clockwise

C

both anti-clockwise

respectively anti-clockwise and clockwise

##### Explanation

Q 10.

Correct4

Incorrect-1

A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be

A

halved

the same

C

doubled

D

##### Explanation

Q 11.

Correct4

Incorrect-1

When an {tex} A C {/tex} source of emf {tex} e = E _ { 0 } \sin ( 100 t ) {/tex} is connected across a circuit, the phase difference between the emf {tex} e {/tex} and the current in the circuit is observed to be {tex} \pi / 4 , {/tex} as shown in the diagram. If the circuit consists possibly only of {tex} R - C {/tex} or {tex} R - L {/tex} or {tex} L - C {/tex} in series, find the relationship between the two elements

{tex} R = 1 k \Omega , C = 10 \mu F {/tex}

B

{tex} R = 1 k \Omega , C = 1 \mu F {/tex}

C

{tex} R = 1 k \Omega , L = 10 H {/tex}

D

{tex} R = 1 k \Omega , L = 1 H {/tex}

##### Explanation

Q 12.

Correct4

Incorrect-1

A small bar magnet is being slowly inserted with constant velocity inside a solenoid as shown in figure. Which graph best represents the relationship between emf induced with time

A

B

D

##### Explanation

Q 13.

Correct4

Incorrect-1

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

B

anticlockwise of the +ve z axis

C

clockwise of the +ve z axis

D

along the magnetic field

##### Explanation

Q 14.

Correct4

Incorrect-1

Find the time constant (in {tex} \mu \mathrm { s } ) {/tex} for the given {tex} R C {/tex} circuits in the given order respectively

{tex} R _ { 1 } = 1 \Omega , R _ { 2 } = 2 \Omega , C _ { 1 } = 4 \mu F , C _ { 2 } = 2 \mu F {/tex}

A

{tex} 18,4 , \frac { 8 } { 9 } {/tex}

{tex} 18 , \frac { 8 } { 9 } , 4 {/tex}

C

{tex} 4,18 , \frac { 8 } { 9 } {/tex}

D

{tex} 4 , \frac { 8 } { 9 } , 18 {/tex}

##### Explanation

Q 15.

Correct4

Incorrect-1

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. {tex} I _ { 1 } {/tex} and {tex} I _ { 2 } {/tex} are the currents in the segments {tex} a b {/tex} and {tex} c d . {/tex} Then,

A

{tex} I _ { 1 } > I _ { 2 } {/tex}

B

{tex} I _ { 1 } < I _ { 2 } {/tex}

C

{tex} I _ { 1 } {/tex} is in the direction {tex} b a {/tex} and {tex} I _ { 2 } {/tex} is in the direction {tex} c d {/tex}

{tex} I _ { 1 } {/tex} is in the direction {tex} a b {/tex} and {tex} I _ { 2 } {/tex} is in the direction {tex} d c {/tex}

##### Explanation

Q 16.

Correct4

Incorrect-1

An AC voltage source of variable angular frequency {tex} \omega {/tex} and fixed amplitude {tex} V _ { 0 } {/tex} is connected in series with a capacitance {tex} C {/tex} and an electric bulb of resistance {tex} R {/tex} (inductance zero). When {tex} \omega {/tex} is increased

A

the bulb glows dimmer

the bulb glows brighter

C

total impedance of the circuit is unchanged

D

total impedance of the circuit increases

##### Explanation

Q 17.

Correct4

Incorrect-1

An inductive coil has resistance of {tex} 100 \Omega {/tex}. When an ac signal of frequency {tex} 1000 \mathrm { Hz } {/tex} is fed to the coil, the applied voltage leads the current by {tex} 45 ^ { \circ } . {/tex} What is the inductance of the coil?

A

{tex} 2 \mathrm { mH } {/tex}

B

{tex} 3.3 \mathrm { mH } {/tex}

{tex} 16 \mathrm { mH } {/tex}

D

{tex} \sqrt { 5 } \mathrm { mH } {/tex}

##### Explanation

Q 18.

Correct4

Incorrect-1

Fig shows a source of alternating voltage connected to a capacitor and a resistor. Which of the following phasor diagrams correctly describes the phase relationship between {tex} I _ { c } , {/tex} the current between the source and the capacitor, and {tex} I _ { R } {/tex}, the current in the resistor?

B

C

D

##### Explanation

Q 19.

Correct4

Incorrect-1

Determine the rms value of a semi-circular current wave which has a maximum value of {tex} a {/tex}

A

{tex} ( 1 / \sqrt { 2 } ) a {/tex}

B

{tex} \sqrt { ( 3 / 2 ) } a {/tex}

{tex} \sqrt { ( 2 / 3 ) } a {/tex}

D

{tex} ( 1 / \sqrt { 3 } ) a {/tex}

##### Explanation

Q 20.

Correct4

Incorrect-1

The value of current in two series {tex} L C R {/tex} circuits at resonance is same. Then

A

Both circuits must be having same value of capacitance and inductance

B

In both circuits ratio of {tex} L {/tex} and {tex} C {/tex} will be same

For both the circuits {tex} X _ { L } / X _ { C } {/tex} must be same at that frequency

D

Both circuits must have same impedance at all frequencies

##### Explanation

Q 21.

Correct4

Incorrect-1

An LCR circuit contains resistance of {tex} 100 \Omega {/tex} and a supply of {tex} 200 \mathrm { V } {/tex} at {tex}300{/tex} rad angular frequency. If only capacitance is taken out from the circuit and the rest of the circuit is joined, current lags behind the voltage by {tex} 60 ^ { \circ } . {/tex} If, on the other hand, only inductor is taken out the current leads by {tex} 60 ^ { \circ } {/tex} with the applied voltage. The current flowing in the circuit is

A

{tex} 1 \mathrm { A } {/tex}

B

{tex} 1.5 \mathrm { A } {/tex}

{tex} 2 \mathrm { A } {/tex}

D

{tex} 2.5 \mathrm { A } {/tex}

##### Explanation

Q 22.

Correct4

Incorrect-1

Which voltmeter will give zero reading at resonance?

A

{tex} \mathrm V _ { 1 } {/tex}

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

C

{tex} \mathrm V _ { 3 } {/tex}

D

None

##### Explanation

Q 23.

Correct4

Incorrect-1

In the series {tex} L C R {/tex} circuit, the voltmeter and ammeter readings are:

{tex}\mathrm { V = 100 \mathrm { V } , I = 2 \mathrm { A }} {/tex}

B

{tex} \mathrm {V = 100 \mathrm { V } , I = 5 \mathrm { A }} {/tex}

C

{tex}\mathrm { V = 1000 \mathrm { V } , I = 2 \mathrm { A } }{/tex}

D

{tex}\mathrm { V = 300 \mathrm { V } , I = 1 \mathrm { A }} {/tex}

##### Explanation

Q 24.

Correct4

Incorrect-1

A capacitor of capacitance {tex} 1 \mu F {/tex} is charged to a potential of {tex} 1 \mathrm { V } {/tex}. It is connected in parallel to an inductor of inductance {tex} 10 ^ { - 3 } \mathrm { H } {/tex}. The maximum current that will flow in the circuit has the value.

{tex} \sqrt { 1000 } \mathrm { mA } {/tex}

B

{tex} 1 \mathrm { mA } {/tex}

C

{tex} 1 \mu \mathrm { A } {/tex}

D

{tex} 1000 \mathrm { mA } {/tex}

##### Explanation

Q 25.

Correct4

Incorrect-1

A resistor and a capacitor are connected to an ac supply of {tex} 200 \mathrm { V } , 50 \mathrm { Hz } {/tex} in series. The current in the circuit is {tex} 2 \mathrm { A } {/tex}. If the power consumed in the circuit is {tex} 100 \mathrm { W } {/tex} then the resistance in the circuit is

A

{tex} 100 \Omega {/tex}

{tex} 25 \Omega {/tex}

C

{tex} \sqrt { 125 \times 75 } \Omega {/tex}

D

{tex} 400 \Omega {/tex}