An inductor coil carries a steady-state current of $2.0 \ A$ when connected across an ideal battery of $emf$ $4.0 \ V$. If its inductance is $1.0 \ H$,find the time constant of the circuit in $sec$.

In the circuit shown,the final current through the $30\, \Omega$ resistance when the circuit is completed is ......... $A$.

In series with a $20 \ \Omega$ resistor,a $5 \ H$ inductor is placed. To this combination,an $e.m.f.$ of $5 \ V$ is applied. What will be the rate of increase of current at $t = 0.25 \ s$?

Find the current in the sliding rod $AB$ (resistance $= R$) for the arrangement shown in the figure. $\vec{B}$ is constant and is directed out of the paper. The parallel wires have no resistance. $v$ is constant. The switch $S$ is closed at time $t = 0$.

Find the time constant of the following circuit.

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