Self and Mutual inductance

A choke coil is preferred to a rheostat in AC circuit as,

Consider a conducting wire of length $L$ bent in the form of a circle of radius $R$ and another conductor of length $a\left(a<<R\right)$ is bent in the form of a square. The two loops are then placed in same plane such that the square loop is exactly at the centre of the circular loop. What will be the mutual inductance between the two loops?

A system consists of two coaxial circular current-carrying rings as shown in the figure. Their self inductances are $L_1$ and $L_2$, respectively, and $M$ is the coefficient of mutual induction. They carry current in the indicated directions. The magnetic energy of the system is,

An AC of $50 \mathrm{Hz}$ and $1 \mathrm{A}$ peak value flows in a transformer whose mutual inductance is $1.5 \mathrm{H}$. The induced emf in the secondary is,

Three inductances $L_1=0.75 \mathrm{H}$, $L_2=L_3=0.5 \mathrm{H}$ are connected as shown below. Assuming no coupling, the resultant inductance will be

When the current $i$ in a certain inductor coil is $5.0 \mathrm{A}$ and is increasing at the rate of $10.0 \mathrm{A} {\mathrm{s}}^{-1}$, the potential difference across the coil is $140 \mathrm{V}$. When the current is $5.0 \mathrm{A}$ and decreasing at the rate of $10.0 \mathrm{A} {\mathrm{s}}^{-1}$, the potential difference is $60 \mathrm{V}$. The self inductance of the coil is -

The energy stored in an electromagnet is $400 \mathrm{mJ}$ when a current $2 \mathrm{A}$ flows in the coils. The self-inductance of the coil is 

Find the self-inductance of a coil in which an emf of $10 \mathrm{V}$ is induced when the current in the circuit changes uniformly from $1 \mathrm{A}$ to $0.5 \mathrm{A}$ in $0.2 \mathrm{s}$.

Two coils $A$ and $B$ have mutual inductance $2\times {10}^{-2} \mathrm{H}$ .If the current in the primary is $i=5\sin \left(10\pi t\right)$ then the maximum value of e.m.f. induced in coil $B$ is 

Two coils of self inductance $100 \mathrm{mH}$ and $400 \mathrm{mH}$ are placed very close to each other. Find the maximum mutual inductance between the two when $4 \mathrm{A}$ current passes through them

Two coils are at fixed locations. When coil $1$ has no current and the current in coil $2$ increases at the rate $15.0 \mathrm{A} {\mathrm{s}}^{-1}$ the e.m.f. in coil $1$ in $25.0 \mathrm{mV}$, when coil $2$ has no current and coil $1$ has a current of $3.6 \mathrm{A}$, flux linkage in coil $2$ is

The number of turns, cross-sectional area and length for four solenoids are given in the following table.

The solenoid with maximum self inductance is:

A wire of fixed length is wound on a solenoid of length $l$ and radius $r$. Its self inductance is found to be $L$. Now if same wire is wound on a solenoid of length $\frac{l}{2}$and radius $\frac{r}{2}$, then the self inductance will be:

A small, circular loop of wire is placed inside a long solenoid carrying a current. The plane of the loop contains the axis of the solenoid. If the current in the solenoid is varied, the current induced in the loop is

A wire of fixed length is wound in such a way that it forms a solenoid of length $l$ and radius $r$. Its self inductance is found to be $L$. Now, if the same wire is wound in such a way that it forms a solenoid of length $\frac{l}{2}$ and radius $\frac{r}{2}$, then the self inductance will be 

A solenoid of inductance $\mathrm{L}$ and resistance $\mathrm{R}$ has a soft iron core. It is connected to a battery of E.M.F $\mathrm{E}$ as shown in the figure and allowed to attain its steady state.


At an instant, the iron core is suddenly pulled out and because of it, inductance decreases to $\frac{\mathrm{L}}{3}$.
The work done by an external agent in pulling out the iron core is

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

The number of turns of primary and secondary coils of a transformer is $5$ and $10$ respectively and mutual inductance of the transformer is $25 \mathrm{H}$. Now, the number of turns in primary and secondary are made $10$ and $5$ respectively. Mutual inductance of the transformer will be