The time constant of an $LR$ circuit represents the time in which the current in the circuit

The figure shows three circuits with identical batteries,inductors,and resistors. Rank the circuits according to the currents through the battery just after the switch is closed,greatest first.

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.)

$A$ coil of inductance $1\, H$ and resistance $10\, \Omega$ is connected to a battery of $emf$ $50\, V$ and negligible internal resistance at time $t = 0.$ The ratio of the rate at which magnetic energy is stored in the coil to the rate at which energy is supplied by the battery at $t = 0.1\, s$ is:

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 . . . . . . . $(\mu_0 = 4 \pi \times 10^{-7} \text{ Tm/A})$.

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