Find the current in the $4 \Omega$ resistance shown in the figure in the following cases:
$(a)$ Just after the closing of the key.
$(b)$ $A$ long time after the closing of the key.

Two $L-R$ circuits are shown in the figure. Based on the given current-time graph,select the correct relation between the inductances $L_1$ and $L_2$.

In an $LR$ circuit,the current increases to one-fourth of its maximum value in $4 \, sec$. What is the time constant of the circuit?

Find $V_A - V_B$ in steady state. (in $, V$)

$A$ blackbox $(BB)$ which may contain a combination of electrical circuit elements (resistor, capacitor or inductor) is connected with other external circuit elements as shown in figure $(A)$. After the switch $S$ is closed at time $t=0$, the current $I$ as a function of time $t$ is shown in figure $(B)$. From this, we can infer that the blackbox contains:

In the circuits $(a)$ and $(b)$,switches $S_1$ and $S_2$ are closed at $t = 0$ and are kept closed for a long time. The variations of current in the two circuits for $t \ge 0$ are roughly shown by which figure? (Figures are schematic and not drawn to scale.)