Mutual Induction

Is a transformer used to convert alternating current into direct current?

Correct the following sentence$:$

The dimension of mutual inductance is $\left[\mathrm{M} {\mathrm{L}}^2 {\mathrm{T}}^3 {\mathrm{A}}^{-1}\right]$.

The magnetic flux linked with a large circular coil, of radius $R$, is $0.5\times {10}^{-3} \mathrm{Wb}$ when a current of $0.5 \mathrm{A}$, flows through a small neighbouring coil of radius $r$, calculate the coefficient of mutual inductance for the given pair of coils $($in $\mathrm{mH})$.

The current in a coil changes at $0.02 \mathrm{A} {\mathrm{s}}^{-1}$. Find the mutual inductance between this coil and nearby coil in which an emf of $0.4 \mathrm{mV}$ is induced.

A solenoid of length $12 \mathrm{cm}$ and radius $2 \mathrm{cm}$ has $2000$ turns and it is placed inside another solenoid of the same length and same number of turns but of radius $4 \mathrm{cm}$. Find the mutual inductance between the solenoids.

The current in the primary of an induction coil of mutual inductance $5 \mathrm{H}$ is suddenly switched off so that an emf of $30000 \mathrm{V}$ is induced in the secondary. Find the current in the primary before break if it is uniformly reduced to zero in ${10}^{-4} \mathrm{s}$.

A long solenoid having $220 \mathrm{turns} \mathrm{per} \mathrm{cm}$ , carries a current of $1.5 \mathrm{A}$, its diameter being $3.2 \mathrm{cm}$. Another close$‐$packed coil $C$ of $130 \mathrm{turns}$ and diameter $2.1 \mathrm{cm}$ lies co$‐$axially at the centre of the solenoid. Find the emf induced $($in $\mathrm{mV})$ in $C$ when the current in the solenoid is reduced to zero at a steady rate in $25 \mathrm{ms}$.

(Answer to the nearest integer)

Two identical coils, one of radius $r$ and the other of radius $R$ are placed co-axially with their centres coinciding. For $R>>r$, obtain an expression for the mutual inductance of the arrangement.

How does the mutual conductance of a pair of coils change when the number of turns in each coil is decreased. Justify your answer.

How does the mutual conductance of a pair of coils change when the distance between the coils is increased. Justify your answer.

What happens to $M$ if the number of turns in the secondary coil is increased without affecting the primary circuit.

Explain the factors on which the coefficient of mutual induction depends.

Explain what is mutual induction.

Write the dimension of mutual inductance.

Define coefficient of mutual induction.

Mutual inductance between two circuits does not depend on