$A$ resistor of $20 \, \Omega$ and an inductor of $5 \, H$ are connected in series with a $5 \, V$ battery. What is the rate of change of current at $t = 0.25 \, s$?

An $LR$ circuit with a battery is connected at $t = 0$. Which of the following quantities is not zero just after the circuit is closed?

$A$ 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 inductance coil has a time constant of $4 \, sec$. If it is cut into two equal parts and connected in parallel,then the new time constant of the circuit is.....$sec$.

The figure shows a circuit that contains three resistors with resistance $R = 2.0 \, \Omega$, two inductors with inductance $L = 2.0 \, mH$, and an ideal battery with $emf$ $E = 9 \, V$. The current $i$ just after the switch $S$ is closed will be .... $A$.

Three identical resistors with resistance $R = 12\,\Omega$ and two identical inductors with self-inductance $L = 5\,mH$ are connected to an ideal battery with an emf of $12\,V$ as shown in the figure. The current through the battery long after the switch has been closed will be $......A$.