For the given circuit,the current through the battery of $6\,V$ just after closing the switch $S$ will be $.......A$.

The resistance and inductance of a series $RL$ circuit are $5 \, \Omega$ and $20 \, H$ respectively. At the instant of closing the switch,the current is increasing at the rate of $4 \, A/s$. The supply voltage is ... $V$.

$A$ 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 $...\,s$.

In the circuit shown,the key $(K)$ is closed at $t = 0$. Find the current through the key at the instant $t = 10^{-3} \ln 2 \, s$.

The total heat produced in resistor $R$ in an $RL$ circuit when the current in the inductor decreases from $I_0$ to $0$ is

In the figure below,the switches $S_1$ and $S_2$ are closed simultaneously at $t=0$ and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) $V$ and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current $I$ in the middle wire reaches its maximum magnitude $I_{\max}$ at time $t=T$. Which of the following statements is (are) true?
$(A)$ $I_{\max}=\frac{V}{2R}$
$(B)$ $I_{\max}=\frac{V}{4R}$
$(C)$ $T=\frac{L}{R} \ln 2$
$(D)$ $T=\frac{2L}{R} \ln 2$