A capacitor of capacitance C is connected to a battery of emf ϵ at t = 0 through a resistance R. Find the maximum rate at which energy is stored in the capacitor. When does the rate has this maximum value?

Formula/Consepts Used:

Energy stored by capacitor:

For a capacitor of capacitance C , with charge Q, and potential difference V across it, the energy stored is given by:

Charging a capacitor:

A capacitor of capacitance C is connected in series with a resistor of resistance R, a switch, and battery of emf ϵ . It is uncharged at first. The switch is closed at t = 0, then at time any time t the charge stored on the capacitor is given by

Energy stored in the capacitor is

For maxima,

Taking the natural logarithm on both sides,

(Note that and

Now, the maximum rate is