Self and Mutual Induction

The SI unit of coefficient of mutual induction is

The S.I. unit of self-inductance of a coil is 

The circuit arrangement given below shows that when A.C. passes through the coil $A$, the current starts flowing in coil $B$.

Mention the underlying principle involved.

A coil has an inductance of $2 \mathrm{H}$ and resistance of $4 \mathrm{\Omega }$. A $10 \mathrm{V}$ is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be _____ $\times {10}^{-2} \mathrm{J}$

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

The magnitude of induced e.m.f. in a coil of inductance $1 \mathrm{mH}$ in which a current is changing from$0.1 \mathrm{A}$to $2.1 \mathrm{A}$ in $0.01$ sec is

The mutual inductance of the system of two coils is $5 \mathrm{mH}$. The current in the first coil varies according to the equation $I=I_0\sin \omega t$ where $I_0=10 \mathrm{A}$ and $\omega =100\pi \mathrm{rad} {\mathrm{s}}^{-1}$. The value of maximum induced emf in the second coil is _____ .

An emf induced in a secondary coil is $20000 \mathrm{V}$ when the current breaks in the primary. The mutual inductance is$5 \mathrm{H}$and the current reaches to zero in ${10}^{-4} \mathrm{s}$ in primary. Calculate the maximum current in the primary before the break.

If the difference between the equivalent inductance in the following figures is $nL$ then find the value of $n$. Given coupling coefficient is $C=\sqrt{2} (\mathrm{Where} \mathrm{coupling} \mathrm{coefficient} \mathrm{is} \mathrm{defined} \mathrm{as} C=\frac{\sqrt{L_1{L}_2}}{M})$

In a uniform and constant magnetic field of induction $B$, two long conducting wires $ab$ and $cd$ are kept parallel to each other at distance $l$ with their plane perpendicular to $B$. The ends $a$ and $c$ are connected together by an ideal inductor of inductance $L$. A conducting slider wire $PQ$ is imparted a speed $v_0$, at time $t=0$. The situation is shown in the figure. AT time $t=\frac{\pi \sqrt{mL}}{4Bl}$, the value of current $I$ through the wire $PQ$ is (ignore any resistance, electrical as well as mechanical)

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In the figure shown, $V_{ab}$ at $t=1 \mathrm{s}$ is

The effective inductance between $A$ and $B$ is KL. Determine K?

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A mutual inductor consists of two coils $X$ and $Y$ as shown in figure in which one-quarter of the magnetic flux produced by $X$ links with $Y$, giving a mutual inductance $M$. What will be the mutual inductance when $Y$ is used as the primary?

Two coils are fixed in space at some distance from each other such that there is a flux linkage between them. When coil $1$ has no current and the current in the coil $2$ increases at the rate $15.0$ $\mathrm{A} {\mathrm{s}}^{-1}$, the emf in the coil $1$ is $25.0 \mathrm{mV}$. When coil $2$ has a current of $3.6 \mathrm{A}$, the flux linkage in coil $2$ (in $\mathrm{mWb}$) is 

If $0.1\mathrm{ J}$ of energy is stored for the flow of current of $0.2 \mathrm{A}$ in an inductor, then its inductance value is

Two coils are fixed in space at some distance from each other such that there is a flux linkage between them. When coil $1$ has no current and the current in the coil $2$ increases at the rate $15.0$ $\mathrm{A} {\mathrm{s}}^{-1}$, the emf in the coil $1$ is $25.0 \mathrm{mV}$. When coil $2$ has a current of $3.6 \mathrm{A}$, the flux linkage in coil $2$ (in $\mathrm{mWb}$) is 

When induced emf in inductor coil is $50\%$ of its maximum value, then stored energy in inductor coil in the given circuit will be (in $\mathrm{\mu J}$):

A condenser of capacity $6 \mathrm{\mu F}$ is fully charged using a $6 \mathrm{V}$ battery. The battery is removed and a resistance less $0.2 \mathrm{mH}$ inductor is connected across the condenser. If the current which is flowing through the inductor (in $\mathrm{A}$) when ${\frac{1}{3}}^{rd}$ of the total energy is in the magnetic field of the inductor is $I$, what is the value of $10I$?

Calculate the self-inductance of a long solenoid having $500$ turns, if the flux linked with each turn of the solenoid is $4 \times {10}^{–3} \mathrm{Wb}$ when the current of $2 \mathrm{A}$ passes through it.