In the given circuits (a) and (b), switches $$S_1$$ and $$S_2$$ are closed at $$t = 0$$ and kept close for a long time. The variation of currents in the two circuits for $$t \geq 0$$ are shown in the options. (Figures are schematic and not drawn to scale.)

1. Analysis of Circuit (a): RC Series Circuit

In an RC circuit, when the switch $$S_1$$ is closed at $$t=0$$:

The current decays exponentially according to the equation: $$i_a(t) = \frac{E}{R} e^{-\frac{t}{RC}}$$

Curve must start at $$i = \frac{E}{R}$$ and approach $$0$$ as $$t$$ increases.

2. Analysis of Circuit (b): RL Series Circuit

In an RL circuit, when the switch $$S_2$$ is closed at $$t=0$$:

The current grows exponentially towards its steady-state value according to the equation: $$i_b(t) = \frac{E}{R} \left(1 - e^{-\frac{Rt}{L}}\right)$$

Curve must start at $$i = 0$$ and approach $$\frac{E}{R}$$ as $$t$$ increases.

Option (B) correctly depicts curve (a) as a decaying exponential starting from $$\frac{E}{R}$$ and curve (b) as a rising exponential approaching the steady-state value $$\frac{E}{R}$$