Self and Mutual Inductance

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LEVELJEE Main

The SI unit of the inductance, the henry can by written as

* Multiple Correct Options

^{2}

Two inductors $L_{1}$ (inductance $1 mH$ , internal resistance $3 Ω$ ) and $L_{2}$ (inductance $2 mH$ , internal resistance $4 Ω$ ), and a resistor $R$ (resistance $12 Ω$ ) are all connected in parallel across a $5 V$ battery. The circuit is switched on at time $t = 0$ . The ratio of the maximum to the minimum current $(I_{m a x} / I_{m i n})$ drawn from the battery is

JEE Main 2001

LEVELJEE Advanced

An inductor of inductance $L = 400 mH$ and resistors of resistances $R_{1} = 2 Ω$ and $R_{2} = 2 Ω$ are connected to a battery of emf $E = 12 V$ as shown in the figure. The internal resistance of the battery is negligible. The switch $S$ is closed at time $t = 0$ . What is the potential drop across $L$ as a function of time? After the steady state is reached, the switch is opened. What is the direction and the magnitude of current through $R_{1}$ as a function of time?

JEE Advanced 2016

LEVELJEE Advanced

A conducting loop in the shape of a right angled isosceles triangle of height 10 cm is kept such that the $9 0^{\circ}$ vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of $10 As^{- 1}$ . Which of the following statement(s) is (are) true? (2016 Adv.)

* Multiple Correct Options

(A)

There is a repulsive force between the wire and the loop.

(B)

If the loop is rotated at a constant angular speed about the wire, an additional emf of

(\frac{μ _{0}}{π})

volt is induced in the wire.

(C)

The magnitude of induced emf in the wire is

(\frac{μ _{0}}{π})

volt.

(D)

The induced current in the wire is in opposite direction to the current along the hypotenuse.

LEVELJEE Main

A uniformly wound solenoidal coil of self-inductance $1.8 \times 1 0^{- 4} H$ and resistance $6 Ω$ is broken up into two identical coils. These identical coils are then connected in parallel across a $15 V$ battery of negligible resistance. The time constant for the current in the circuit is $\dots\dots s$ and the steady state current through the battery is $\dots A$ .

LEVELJEE Main

A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L (L >> l)$ . The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to

(A)

\frac{l}{L}

(B)

\frac{l ^{2}}{L}

(C)

\frac{L}{l}

(D)

\frac{L ^{2}}{l}

LEVELJEE Main

Two different coils have self-inductances $L_{1} = 8 mH$ and $L_{2} = 2 mH$ . The current in one coil is increased at a constant rate. The current in the second coil is also increased at the same constant rate. At a certain instant of time, the power given to the two coils is the same. At that time, the current, the induced voltage and the energy stored in the first coil are $i_{1}, V_{1}$ and $W_{1}$ respectively. Corresponding values for the second coil at the same instant are $i_{2}, V_{2}$ and $W_{2}$ respectively. Then

* Multiple Correct Options

(A)

\frac{i _{1}}{i _{2}} = \frac{1}{4}

(B)

\frac{i _{1}}{i _{2}} = 4

(C)

\frac{W _{1}}{W _{2}} = \frac{1}{4}

(D)

\frac{V _{1}}{V _{2}} = 4

JEE Advanced 2012

LEVELJEE Advanced

A circular wire loop of radius $R$ is placed in the $x$ - $y$ plane centred at the origin $O$ . A square loop of side $a$ ( $a ≪ R$ ) having two turns is placed with its centre at $z = 3 R$ along the axis of the circular wire loop, as shown in figure. The plane of the square loop makes an angle of $4 5^{\circ}$ with respect to the Z-axis. If the mutual inductance between the loops is given by $\frac{μ _{0} a ^{2}}{2 ^{p /2} R}$ , then the value of $p$ is

LEVELJEE Main

A coil of inductance $8.4 mH$ and resistance $6 Ω$ is connected to a $12 V$ battery. The current in the coil is $1 A$ at approximately the time

(A)

500 s

(B)

20 s

(C)

35 ms

(D)

1 ms

LEVELJEE Main

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

(A)

maximum in situation (A).

(B)

maximum in situation (B).

(C)

maximum in situation (C).

(D)

the same in all situations.

JEE Advanced 2018

LEVELJEE Advanced

In the figure below, the switches $S_{1}$ and $S_{2}$ are closed simultaneously at $t = 0$ and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current $I$ in the middle wire reaches its maximum magnitude $I_{m a x}$ at time $t = τ$ . Which of the following statements is (are) true ?

* Multiple Correct Options

(A)

I_{m a x} = \frac{V}{2 R}

(B)

I_{m a x} = \frac{V}{4 R}

(C)

τ = \frac{L}{R} ln 2

(D)

τ = \frac{2 L}{R} ln 2

LEVELJEE Main

A solenoid has an inductance of $10 H$ and a resistance of $2 Ω$ . It is connected to a $10 V$ battery. How long will it take for the magnetic energy to reach $1/4$ of its maximum value ?

LEVELJEE Main

The network shown in figure is part of a complete circuit. If at a certain instant the current ( $I$ ) is 5A and is decreasing at a rate of $1 0^{3}$ A/s, then $V_{B} - V_{A} = ....$ V

JEE Advanced 2020

LEVELJEE Advanced

The inductors of two LR circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistances, mutual-inductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced EMF in the inductors by the time the currents reach their steady state values is________ mJ.

JEE Advanced 2026

LEVELJEE Advanced

Consider a circuit consisting of a capacitor of capacitance $C$ and a coil with $N$ turns per unit length, cross sectional area $S$ and length $d$ , where $d^{2} ≫ S$ . There is another coil of length $d /2$ , cross sectional area $S /2$ and $2 N$ turns per unit length completely inside the larger coil, as shown in the figure. The ends of this smaller coil are connected with each other by an insulated conducting wire. The self-inductance of the larger coil is $L$ . Neglecting edge effects and all the Ohmic resistances, the resonant frequency of the circuit is:

(A)

\frac{4}{15 L C}

(B)

\frac{6}{5 L C}

(C)

\frac{2}{3 L C}

(D)

\frac{2}{3 L C}

JEE Main 2021

LEVELJEE Main

The time taken for the magnetic energy to reach $25%$ of its maximum value, when a solenoid of resistance $R$ , inductance $L$ is connected to a battery, is

(A)

\frac{L}{R} ln 5

(B)

infinite

(C)

\frac{L}{R} ln 2

(D)

\frac{L}{R} ln 10

JEE Main 2019

LEVELJEE Advanced

Consider the $L - R$ circuit shown in the figure. If the switch $S$ is closed at $t = 0$ , then the amount of charge that passes through the battery between $t = 0$ and $t = \frac{L}{R}$ is

(A)

\frac{2.7 E L}{R ^{2}}

(B)

\frac{E L}{2.7 R ^{2}}

(C)

\frac{7.3 E L}{R ^{2}}

(D)

\frac{E L}{7.3 R ^{2}}

JEE Main 2020

LEVELJEE Main

An emf of $20 V$ is applied at time $t = 0$ to a circuit containing in series $10 mH$ inductor and $5Ω$ resistor. The ratio of the currents at time $t = \infty$ and at $t = 40 s$ is close to (Take, $e^{2} = 7.389$ )

A $20 H$ inductor coil is connected to a $10 ohm$ resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is

(A)

\frac{2}{l n 2}

(B)

\frac{1}{2} ln 2

(C)

2 ln 2

(D)

ln 2

JEE Main 2020

LEVELJEE Main

In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be …… .

JEE Main 2021

LEVELJEE Main

An inductor coil stores 64 J of magnetic field energy and dissipates energy at the rate of 640 W when a current of 8A is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit in seconds.

Consider an electrical circuit containing a two way switch $S$ . Initially $S$ is open and then $T_{1}$ is connected to $T_{2}$ . As the current in $R = 6Ω$ attains a maximum value of steady state level, $T_{1}$ is disconnected from $T_{2}$ and immediately connected to $T_{3}$ . Potential drop across $r = 3Ω$ resistor immediately after $T_{1}$ is connected to $T_{3}$ is ……… V. (Round off to the nearest integer)

JEE Main 2019

LEVELJEE Main

A coil of self inductance $10 mH$ and resistance $0.1 Ω$ is connected through a switch to a battery of internal resistance $0.9 Ω$ . After the switch is closed, the time taken for the current to attain $80%$ of the saturation value is [Take, $ln 5 = 1.6$ ]

(A)

0.002 s

(B)

0.324 s

(C)

0.103 s

(D)

0.016 s

JEE Main 2021

LEVELJEE Advanced

A small square loop of side $a$ and one turn is placed inside a larger square loop of side $b$ and one turn ( $b ≫ a$ ). The two loops are coplanar with their centres coinciding. If a current $I$ is passed in the square loop of side $b$ , then the coefficient of mutual inductance between the two loops is

(A)

\frac{μ _{0}}{4 π} 82 \frac{a ^{2}}{b}

(B)

\frac{μ _{0}}{4 π} \frac{8 2}{a}

(C)

\frac{μ _{0}}{4 π} 82 \frac{b ^{2}}{a}

(D)

\frac{μ _{0}}{4 π} \frac{8 2}{b}

JEE Main 2021

LEVELJEE Main

A coil of inductance $2 H$ having negligible resistance is connected to a source of supply whose voltage is given by $V = 3 t V$ (where, $t$ is in second). If the voltage is applied when $t = 0$ , then the energy stored in the coil after $4 s$ is ............ J.

The SI unit of the inductance, the henry can by written as

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A coil of inductance 8.4 mH and resistance 6 Ω is connected to a 12 V battery. The current in the coil is 1 A at approximately the time

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

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The network shown in figure is part of a complete circuit. If at a certain instant the current (I) is 5A and is decreasing at a rate of 103 A/s, then VB​−VA​=.... V

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Consider the L−R circuit shown in the figure. If the switch S is closed at t=0, then the amount of charge that passes through the battery between t=0 and t=RL​ is

In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be …… .

An inductor coil stores 64 J of magnetic field energy and dissipates energy at the rate of 640 W when a current of 8A is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit in seconds.

A coil of inductance $8.4 mH$ and resistance $6 Ω$ is connected to a $12 V$ battery. The current in the coil is $1 A$ at approximately the time

The network shown in figure is part of a complete circuit. If at a certain instant the current ( $I$ ) is 5A and is decreasing at a rate of $1 0^{3}$ A/s, then $V_{B} - V_{A} = ....$ V

The time taken for the magnetic energy to reach $25%$ of its maximum value, when a solenoid of resistance $R$ , inductance $L$ is connected to a battery, is

Consider the $L - R$ circuit shown in the figure. If the switch $S$ is closed at $t = 0$ , then the amount of charge that passes through the battery between $t = 0$ and $t = \frac{L}{R}$ is