The mutual inductance of an induction coil is $5 \mathrm{H}$. In the primary coil, the current reduces from $5 \mathrm{A}$ to zero, in ${10}^{-3} \mathrm{s}$. What is the induced emf in the secondary coil?

The time constant of the given circuit, containing an inductor and few resistors, is 

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 the points $A$ and $B$. The current in the circuit, $1 \mathrm{ms}$ after the short circuit, is 

For the given circuit, calculate the current which is given by the battery:    

(i)  just after closing the key.

(ii) long time after closing the key.