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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[@Floris' answer](https://physics.stackexchange.com/a/143737/44176) being good, i'll give another view on the matter.

A **capacitor is equivalent to an open circuit** (since simply put, a capacitor is an element consisting of two plates which do not actually touch but through another medium, the *dielectric*, the circuit is **not connected** at that point where the capacitor is located), whereas an **inductor is equivalent to a short circuit** (since simply put, an inductor is an element which is a wire folded around a magnetic material, the circuit is **connected** at that point)

**For Direct current (DC):**

In DC how would these behave (as a first approximation)? 

The capacitor would be an open circuit while the inductor would be a closed circuit.

Now a capacitor (and an inductor) **are not immediately open or closed circuits**, for example the capacitor needs to be charged first, then it acts as an open circuit. Similarly the inductor needs to overcome any magnetic effects before acting as a closed circuit.

**For Alternating current (AC):**

So lets assume a frequency of operation where the capacitor does not have time to charge completely, then it will **not act as an open circuit** but maybe close to it (depending on frequency of operation)

Similarly an inductor will not act as closed circuit (depending on frequency of operation), but close to it.

The above provide basic explanation (and mnemonic rules) to infer the behaviour of capacitors/inductors in AC circuits

The images are from different sites (just for illustration), represent the resistor voltage in RC and RL circuits:

**RC in series (Resistor voltage in time):**

![RC Resistor voltage in time](https://i.stack.imgur.com/yyK3e.jpg)

**RL in series (Resistor voltage in time):**

![RL Resistor voltage in time](https://i.stack.imgur.com/Tq8kG.gif)
Circuits with inductors are sensitive to changes in the signal - think of them as differentiators. Circuits with capacitors are responding to the integral of the signal over time.

When you first turn on a circuit, the current wants to make a step change - which the capacitor doesn't care about, but the inductor resists vigorously. Thus the current will flow through the capacitor without any problem (there is no built up charge so no potential resisting the current flow), but the inductor will not permit the instantaneous change in current (back emf given by $-L\frac{dI}{dt}$).

So current in the capacitor starts big, then drops off; in the inductor, it starts small, then builds up (at some point the current in the inductor is only limited by the series resistance; while current through the capacitor goes to zero once enough charge is built up to get a potential equal to the applied potential).