Concepts/Formula used:

Current when capacitor is charging:

A capacitor of capacitance C is being charged using a batteru of emf ϵ through a resistance R . A switch S is also connected in series with the capacitor. The switch is initially open. The capacitor is uncharged at first. At t=0, the switch is closed. The current through the circuit at anytime t>0 is given by:

Where I₀ is the initial current.

Note that is known as time constant

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:

Now, at anytime t > 0,

Now, power is maximum when the current is maximum i.e. when t = 0

We wish to find time t such that

The time in 0.69 times the time constant.