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 $......A$.

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?

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

Inductance of a coil with $10^4$ turns is $10 \text{ mH}$ and it is connected to a $DC$ source of $10 \text{ V}$ with internal resistance of $10 \ \Omega$. The energy density in the inductor when the current reaches $(1/e)$ of its maximum value is $\alpha \pi \times (1/e^2) \text{ J/m}^3$. The value of $\alpha$ is . . . . . . . $(\mu_0 = 4 \pi \times 10^{-7} \text{ Tm/A})$.

Assertion : The resistance offered by an inductor in a $d.c.$ circuit is always constant.
Reason : The resistance of an inductor in a steady state is non-zero.

$A$ coil of inductance $5\,H$ is joined to a cell of $emf$ $6\,V$ through a resistance $10\,\Omega$ at time $t = 0$. The $emf$ across the coil at time $t = \ln \sqrt{2}\,s$ is:....$V$