Self-Inductance & Energy

The current flowing through an inductor of self-inductance L is continuously increasing at constant rate. The variation of induced e.m.f. (e) versus time $t$ is shown graphically by

Two coils A and B have 180 and 360 turns respectively. The current of 1A flows through both the coils. Due to current of 1A in coil A, flux per turn of $0.8 \times 10^{-3}$ Wb is linked with coil A. Due to current of 1A in coil B, flux per turn of $1 \times 10^{-3}$ Wb is linked with coil B. The self inductance of coil A is $L_A$ and the self inductance of coil B is $L_B$. The ratio $L_A$ to $L_B$ is

A graph of magnetic flux ($\Phi$) versus current (I) is shown for four inductors A, B, C, D. The smallest value of self inductance is for inductor.

The current flowing through the inductor of self inductance 'L' is continuously increasing at constant rate. The variation of induced e.m.f. (e) versus $\frac{dI}{dt}$ is shown graphically by figure

The inductance of a coil is proportional to

What is the self inductance of a solenoid of length $10\pi$ cm, area of cross-section $10^{-3}$ m${}^{2}$ and total number of turns $10^{3}$? ($\mu_0 = 4\pi \times 10^{-7}$ SI unit)

A coil of wire of radius $r$ has $600$ turns and a self-inductance of $108$ mH. The self inductance of a coil with same radius and $500$ turns is

The self inductance of an air-core inductor (solenoid) is $0.03$ mH. By introducing an iron core into inductor the self-inductance increases to $30$ mH. The relative permeability of the core used is

Consider a long solenoid of length $l$ and radius $r$. If $n$ is the number of turns per unit length and $\mu_0$ is the permeability of free space, the inductance of the solenoid is:

The magnetic energy stored in an inductor of inductance $4$ H carrying a current of $1.5$ A is

If current of 4 A produces magnetic flux of $3 \times 10^{-3}$ Wb through a coil of 400 turns, the energy stored in the coil will be

The magnetic potential energy stored in a certain inductor is $49$ mJ when the current in the inductor is $70$ mA. The inductance of the inductor is

An air cored coil has a self inductance of $0.1$ H. A soft iron core of relative permeability $1000$ is $\text{th}$

introduced inside cored coil and number of turns reduced to $\left(\frac{1}{10}\right)$. The value of self inductance now becomes

A solenoid is connected to a battery so that a steady current flows through it. If an iron core is inserted into the solenoid, then the current in the coil

Two solenoids A and B of equal number of turns have their lengths and radii in the same ratio $1 : 3$. The ratio of the self-inductance of solenoid A to that of B will be

A 30 cm long solenoid has 10 turns per cm and area of $5\text{ cm}^{2}$. The current through the solenoid coil varies from 2 A to 4 A in 3.14 s. The e.m.f. induced in the coil is $\alpha \times 10^{-5}\text{ V}$. The value $\alpha$ is ______.

The self induced e.m.f. of a coil is $25$ V. When the current in it is changed at uniform rate from $10$ A to $25$ A in $1$ s, the change in the energy of the inductance is

Two different coils have self-inductance $3L$ and $L$. The current in both the coils is increased at the same constant rate. At certain instant of time, the power given to the two coils is same. At that time there was current and voltage induced in the two coils. At the same instant, the ratio of energy stored in the first coil to that in the second coil is

Two coils have self inductance $L_1$ and $L_2$. The current through them is increasing at constant rate. If the power dissipated in both the coils is same, then the ratio of energy stored in the coil having inductance $L_1$ to that in $L_2$ is

Inductance of a coil with $10^{4}$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of $10\ \Omega$. The energy density in the inductor when the current reaches $\left(\frac{1}{e}\right)$ of its maximum value is $\alpha \pi \times \frac{1}{e^2}\text{ J/m}^{3}$. The value of $\alpha$ is

______.

$\left(\mu_0 = 4\pi \times 10^{-7}\text{ Tm/A}\right).$

The plot of magnetic flux ' $\phi$ ' linked with the coil versus current ' I ' is as shown in figure for two inductors $L_1$ and $L_2$. The self inductance of

When a current in the conducting coil is changed from 5 A in one direction to 5 A in opposite direction in 0.5 second, an average induced e.m.f in the coil is 2 V. The selfinductance of the coil is

A graph of magnetic flux $(\phi)$ versus current $(I)$ is shown for four inductors $P, Q, R, S$. The largest value of self-inductance is for inductor

The current flowing through an inductor of selfinductance L is continuously increasing at constant rate. The variation of induced e.m.f. (e) verses $dI/dt$ is shown graphically by figure

Regarding self-inductance:

A. The self-inductance of the coil depends on its geometry.

B. Self-inductance does not depend on the permeability of the medium.

C. Self-induced e.m.f. opposes any change in the current in a circuit.

D. Self-inductance is electromagnetic analogue of mass in mechanics.

E. Work needs to be done against self-induced e.m.f. in establishing the current. Choose the correct answer from the options given below:

A coil of wire of radius ' $r$ ' has 600 turns and a self-inductance of 108 mH. The self-inductance of a coil with same radius and 500 turns is

The self-inductance of a circuit is numerically equal to

A coil is wound on a core of rectangular cross-section. If all the linear dimensions of core are increased by a factor 3 and number of turns per unit length of coil remains same, the self- inductance increases by a factor

To manufacture a solenoid of length ' $l$ ' and inductance ' $L$ ', the length of the thin wire required is (Diameter of the solenoid is very less than length, $\mu_0 =$ permeability of free space)

Two inductors of 80 mH each are joined in parallel. The current passing through the combination is 2.1 A. The energy stored in this combination of inductors is

Two circuits A and B are connected to identical d.c. sources each of e.m.f. 10 volt. Self-inductances of circuits A and B are respectively $L_A = 10\text{ H}$ and $L_B = 10\text{ mH}$. The total resistance of each circuit is $40\ \Omega$. The ratio of energy consumed in circuit A and circuit B to build up the current to steady value is

When three inductors of same inductance ' $L$ ' are connected in series and ' I ' is the current passing through the circuit. The energy stored in the circuit is

A solenoid having area A and length ' $l$ ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is:

A graph of magnetic flux $(\phi)$ versus current (I) is shown for 4 different inductors $P, Q, R, S$. Minimum value of inductance is for inductor

A current of 0.5 A is passed through winding of a long solenoid having 400 turns. The magnetic flux linked with each turn is $3 \times 10^{-3}\text{ Wb}$. The self inductance of the solenoid is

A graph of magnetic flux $(\phi)$ versus current ( 1) is shown for four inductors A, B, C, D. Smaller value of self inductance is for inductor

In a coil, the current changes from $-2\text{ A}$ to $+2\text{ A}$ in $0.2\text{ s}$ and induces an emf of $0.1\text{ V}$. The self inductance of the coil is:

When the number of turns in a coil are made 3 times without any change in the length of the coil, its self inductance becomes

If number of turns per unit length in a solenoid is tripled, the self inductance of solenoid will

When the number of turns in a coil is doubled without any change in the length of the coil, its self- inductance

If current of 4 A produces magnetic flux of $3 \times 10^{-3}\text{ Wb}$ through a coil of 400 turns, the energy stored in the coil will be

The current in LR circuit if reduced to half What will be the energy stored in it?

The magnetic energy stored in an inductor of inductance $5\ \mu\text{H}$ carrying a current of 2 A is

The current in an inductor is given by $I = (3t + 8)$ where $t$ is in second. The magnitude of induced emf produced in the inductor is $12\text{ mV}$. The self-inductance of the inductor _________ $\text{mH}$.

A coil is wound on a core of rectangular crosssection. If all the linear dimensions of the core are increased by a factor 2 and number of turns per unit length of coil remains same, the self inductance increases by a factor of (Assume, permeability is same)

An air cored coil has a self inductance 0.1 H. A soft iron core of relative permeability 1000 is introduced and the number of turns is reduced $\left(\frac{1}{10}\right)$th. The value of self inductance is

Two solenoids of equal number of turns have their lengths as well as radii in the same ratio $1 : 3$. The ratio of their self inductance will be

A closely wound coil of 100 turns and of cross-section $1\text{ cm}^{2}$ has coefficient of self inductance 1 mH. The magnetic induction at the centre of the core of a coil when a current of 2 A flows in it, will be (in $\text{Wb/m}^{2}$)

An air cored coil has self inductance of 0.1 H. A soft iron core of relative permeability 1000 is introduced and the number of turns is reduced to $\left(\frac{1}{10}\right)$th. The value of self inductance is now

Let us consider two solenoids $A$ and $B$, made from same magnetic material of relative permeability $\mu_r$ and equal area of cross-section. Length of $A$ is twice that of $B$ and the number of turns per unit length in $A$ is half that of $B$. The ratio of self inductances of the two solenoids, $L_A : L_B$ is

A long solenoid has 1500 turns. When a current of $3.5\text{ A}$ flows through it, the magnetic flux linked with each turn of solenoid is $2.8 \times 10^{-3}$ weber. The self-inductance of solenoid is

SI units of self inductance is

When a current of $1\text{ A}$ is passed through a coil of 100 turns, the flux associated with it is $2.5 \times 10^{-5}\text{ Wb/}$ turn. The self inductance of the coil in millihenry is

A graph of magnetic flux $(\phi)$ versus current (I) is plotted for four inductors A, B, C, D. Larger value of self inductance is for inductor

The self induction (L) produced by solenoid of length '$l$' having '$N$' number of turns and cross sectional area '$A$' is given by the formula ($\phi =$ magnetic flux, $\mu_0 =$ permeability of vacuum)

The self inductance '$L$' of a solenoid of length '$l$' and area of cross-section '$A$', with a fixed number of turns '$N$' increases as

Self inductance of solenoid is

$12\text{ V}$ battery connected to a coil of resistance $6\ \Omega$ through a switch, drives a constant current in the circuit. The switch is opened in $1\text{ ms}$. The emf induced across the coil is $20\text{ V}$. The inductance of the coil is:

Inductance per unit length near the middle of a long solenoid is $(\mu_0 =$ permeability of free space, $n =$ number of turns per unit length, $d =$ the diameter of the solenoid)

To manufacture a solenoid of length $1\text{ m}$ and inductance $1\text{ mH}$, the length of thin wire required is (cross - sectional diameter of a solenoid is considerably less than the length)

Two inductors of $60\text{ mH}$ each are joined in parallel. The current passing through this combination is $2.2\text{ A}$. The energy stored in this combination of inductors in joule is

A graph of magnetic flux $(\phi)$ versus current (I) is drawn for four inductors A, B, C, D. Larger value of self inductance is for inductor.

A 10 $\Omega$, 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after switch is opened current becomes zero in 100 $\mu$s. The average e.m.f. induced in the coil is ____________ V.

Self inductance of a solenoid cannot be increased by

The current in a coil of self inductance 2.0 H is increasing according to I = 2 sin(t2) A. The amount of energy spent during the period when current changes from 0 to 2 A is ____________ J.

A current 'I' produces a magnetic flux '$\phi$' per turn in a coil of '$n$' turns. Self inductance of the coil is '$L$'. The relation between them is

The self inductance of solenoid of length $31.4\text{ cm}$, area of cross section $10^{-3}\text{ m}^{2}$ having total number of turns 500 will be nearly [$\mu_0 = 4\pi \times 10^{-7}$ SI unit]

A circular coil of radius '$R$' has '$N$' turns of a wire. The coefficient of self induction of the coil will be ( $\mu_0 =$ permeability of free space)

. If the current of '$I$' A gives rise to a magnetic flux '$\phi$' through a coil having '$N$' turns then mangetic energy stored in the medium surrounding the coil is

The magnetic potential energy stored in a certain inductor is $25\text{ mJ}$, when the current in the inductor is $50\text{ mA}$. This inductor is of inductance

A coil of inductance 2 H having negligible resistance is connected to a source of supply whose voltage is given by V = 3t volt. (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.

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

The length of solenoid is $I$ whose windings are made of material of density $D$ and resistivity $\rho$. The winding resistance is $R$. The inductance of solenoid is [$m =$ mass of winding wire, $\mu_0 =$ permeability of free space]

The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to:

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of 3, keeping the number of turns of the coil per unit length of the frame the same, then the self inductance of the coil:

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 -

A long solenoid has 1000 turns. When a current of 4 A flows through it, the magnetic flux linked with each turn of the solenoid is 4 $\times 10^{-3}$ Wb. The self-inductance of the solenoid is

When current in a coil changes from 5 A to 2 A in 0.1 s, an average voltage of 50 V is produced. The self - inductance of the coil is:

A current of 2.5 A flows through a coil of inductance 5 H. The magnetic flux linked with the coil is

The current $i$ in a coil varies with time as shown in the figure. The variation of induced emf with time would be

A long solenoid has 500 turns. When a current of 2 ampere is passed through it, the resulting magnetic flux linked with each turn of the solenoid is 4 $\times$ 10$-$3 Wb. The self-inductance of the solenoid is

When the current changes from $+2\text{ A}$ to $-2\text{ A}$ in $0.05$ second, an $e.m.f.$ of $8\text{ V}$ is inducted in a coil. The coefficient of self- induction of the coil is

For a coil having L = 2 mH, current flow through it is $I = t^2 e^{-t}$ then, the time at which emf become zero

The current $I$ in an A.C. circuit with inductance coil varies with time according to the graph given below.

Which one of the following graphs gives the variation of voltage with time?

What is the self-inductance of a coil which produces 5 V when the current changes from 3 ampere to 2 ampere in one millisecond?

If $N$ is the number of turns in a coil, the value of self inductance varies as

If the number of turns per unit length of a coil of solenoid is doubled, the self-inductance of the solenoid will

A 100 millihenry coil carries a current of 1 A. Energy stored in its magnetic field is

The current in self inductance $L = 40\text{ mH}$ is to be increased uniformly from 1 amp to 11 amp in 4 milliseconds. The e.m.f. induced in inductor during process is

An inductor may store energy in

Energy in a current carrying coil is stored in the form of