Energy stored in a capacitor:

The energy stored in a capacitor with capacitance C , charge is given by:

where V is the potential difference across the capacitor.

Power supplied by the battery:

If a battery of emf ϵ gives a current I, then the power supplied by the battery is given by:

Kirchhoff’s loop rule:

The sum of potential differences around a closed loop is zero.

Potential Difference (V) across a resistor of resistance R when current I passes through it is given by Ohm’s law:

(a)

By Kirchhoff’s loop rule,

As ϵ is constant,

At t = 0, there is no charge on the capacitor. Hence . So, V_r is maximum at t = 0.

(b) Initially, current flows through the circuit treating capacitor as short-circuit. But as charge accumulates on the capacitor the current reduces with time. It is maximum at t =0.

Using Kirchhoff’s loop rule,

I is max at t = 0 and

(c)

Using Kirchhoff’s loop rule,

As R and ϵ are constant

Current is minimum at equilibrium when capacitor acts as an open switch and current is zero. Hence,

(d)

The energy stored by the capacitor is given by:

As C is constant,

We know from (c) that the maximum potential difference across the capacitor is ϵ. Hence,

(e)

Power delivered by the battery is given by:

As ϵ is a constant,

Using the result from (b), we get

(f)

The resistor converts energy into heat:

As R is constant,

Now, using the result from (b),