Question

An uncharged capacitor C is connected to a battery through a resistance R. Show that by the time the capacitor gets fully charged, the energy dissipated in R is the same as the energy stored in C.

Answer 1

Charge supplied by the battery,

$q=CV$

Energy supplied by the battery,

$E=qV=C{V}^2$

Energy stored in the capacitor,

$U=\frac{1}{2}C{V}^2$

$\therefore$ Energy dissipated across R in the form of heat

$=E-U$

$=\frac{1}{2}C{V}^2=U$