$A$ coil of self-inductance $50\,H$ is connected to the terminals of a battery of $e.m.f.$ $2\,V$ through a resistance of $10\,\Omega$,and a steady current is flowing through the circuit. If the battery is now disconnected,the time in which the current will decay to $1/e$ of its steady value is $...\,s$.

An ideal coil of $10 \, H$ is joined in series with a resistance of $5 \, \Omega$ and a battery of $5 \, V$. $2 \, s$ after joining, the current flowing in the circuit in amperes will be:

Consider an electrical circuit containing a two-way switch $S$. Initially,$S$ is open and then $T_{1}$ is connected to $T_{2}$. As the current in $R = 6 \, \Omega$ attains a maximum value of steady-state level,$T_{1}$ is disconnected from $T_{2}$ and immediately connected to $T_{3}$. The potential drop across the $r = 3 \, \Omega$ resistor immediately after $T_{1}$ is connected to $T_{3}$ is $.... \, V$. (Round off to the nearest integer)

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 $t = 0.25 \ s$?

Consider the $LR$ circuit shown in the figure. If the switch $S$ is closed at $t = 0$, then the amount of charge that passes through the battery between $t = 0$ and $t = \frac{L}{R}$ is

The resistance $R$ is the same as that of the coil that makes $L$. Which of the following statements gives the correct description of the happenings when the switch $S$ is closed?