$A$ coil of inductance $40 \, H$ is connected in series with a resistance of $8 \, \Omega$ and the combination is joined to the terminals of a $2 \, V$ battery. The time constant of the circuit is ...... $s$.

An inductor of inductance $L = 400 \ mH$ and resistors of resistance $R_1 = 2 \ \Omega$ and $R_2 = 2 \ \Omega$ are connected to a battery of emf $E = 12 \ V$ as shown in the figure. The internal resistance of the battery is negligible. The switch $S$ is closed at $t = 0$. The potential drop across $L$ as a function of time is:

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 .... $A$.

An $L-R$ circuit has a cell of $e.m.f.$ $E$,which is switched on at time $t = 0$. The current in the circuit after a long time will be

In a decaying $L-R$ circuit,the time after which energy stored in the inductor reduces to one-fourth of its initial value is

The ratio of time constants during growth and decay of current in the circuit is