I find it difficult to understand as to why current behaves differently in an RL and an RC circuit. At time $t=0$, in an RC circuit the current is maximum, whereas in an RL circuit its $0$. Why is it so? The current should rise from $0$ to some value in both the circuits, so where am I going wrong?
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> Why is it so?
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Well, it isn't actually *always* so. It will depend on the actual circuit configuration and whether the switch opens or closes when $t=0$.

But first, here are a couple of *crucial* results to *always* keep in mind when solving these type of switched circuits:

* the current through an inductor must be continuous
* the voltage across a capacitor must be continuous

In this context, this means that the current through the inductor the instant *after* the switch changes position must be the same as the current through the inductor *before* the switch changes position.

Similarly, the voltage across the capacitor the instant *after* the switch changes position must be the same as the voltage across the capacitor *before* the switch changes position.

So, for example, if we have a resistor $R$, inductor $L$, and switch in series with a voltage source $V$ and the switch is *closed* at $t=0$, it is indeed true that the inductor current is initially zero and asymptotically approaches a constant value

$$i\_L(0-) = i\_L(0+) = 0$$
$$i\_L(t) \rightarrow \frac{V}{R}\,,\quad t\rightarrow \infty $$

This must be the case since the inductor current is zero before the switch is closed and so, must be zero the instant after the switch is closed.

If the inductor is replaced with a capacitor, the voltage across the capacitor $C$ is initially zero and so, must be zero the instant after the switch is closed.

This means that the entire voltage $V$ is across the resistor and so, the series current must 'jump' from zero to $\frac{V}{R}$ at $t=0$ and then decay asymptotically to zero.

$$v\_C(0-) =v\_C(0+) = 0 \Rightarrow i\_C(0+) = \frac{V}{R}$$

$$i\_C(t) \rightarrow 0\,,\quad t \rightarrow \infty $$
1. Charge on the capacitor does not change instantaneously or suddenly if there if a resistance in the path(series) of the capacitor.
2. When an uncharged capacitor is connected with battery then its charge is zero initally hence potential difference across it is zero. At this time the capacitor can be treated as a conducting wire.
3. The current will become zero finally(that means in steady state)in the branch which contains capacitor.