The dimensions of the "time constant" $\frac{L}{R}$ during the growth and decay of current in an inductive circuit are the same as those of:

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.

In the given figure,an inductor of $L = 4 \, H$ and a resistor of $R = 25 \, \Omega$ are connected in series with a battery of emf $E$ volt. $\frac{E^a}{2b} \, J/s$ represents the maximum rate at which energy is stored in the magnetic field of the inductor. The numerical value of $\frac{b}{a}$ is ............

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

Regarding the given circuit,the correct statement is:

When the switch $S$ is closed at time $t = 0$,what will be the nature of the graphs for the induced $emf$ $e$ across the inductor $L$ and the current $i$ in the circuit?