Current in the primary coil of a mutual inductor is $2 \mathrm{A}$ and is increasing at the rate of $3 \mathrm{A} {\mathrm{s}}^{-1}$. If the mutual inductance is $4 \mathrm{H}$, find flux and emf in the secondary coil.

Find mutual inductance of

(a)          (b) 

(c)    (d) 

An inductor $(L=100 \mathrm{mH}),$ a resistor $(R=100 \mathrm{\Omega })$ and a battery $(E=100 \mathrm{V})$ are initially connected in series as shown in the figure. After a long time, the battery is disconnected after short-circuiting points $A$ and $B$. The current in the circuit,$1 \mathrm{ms}$ after the short circuit is: 

Find time constant for following circuits.

 (a) (b) 

(c)  (d)

Switch was in position $1$ for a long time. It is suddenly switch to position $2$. Find voltage drop across inductor immediately after the switch is toggled.

Key is closed at time $t=0$. $i=i_1$ at $t=0$ and $i=i_2$ at time $t=\infty$. $\frac{i_1}{i_2}$ equals

Switch is in position $A$ for a long time. It is suddenly switched to the side $B$. Mass of rod is $m$ and length is I. Maximum speed of rod will be .....

Find current $\left(i\right)$ at time $t=0$ and time $t=\infty$ in the following circuits.

(a)  (b) 

(c)  (d) 

As a result of change in the magnetic flux linked to the closed loop shown in the figure, an emf $V$ volt is induced in the loop. The work done (joules) in taking a charge $Q$ coulomb once along the loop is