An uncharged capacitor is connected to a battery. Show that half the energy supplied by the battery is lost as heat while charging the capacitor.

Explanation

Suppose the capacitance of the capacitor is C and the emf of the battery is V. The charge given to the capacitor is Q = CV. The work done by the battery is W = QV. The battery supplies this energy. The battery supplies this energy. The energy stored in the capacitor is `
` U = (1)/(2)CV^2 = (1)/(2) QV`
`. The remaining energy `
`QV - (1)/(2) QV = (1)/(2) QV`
` is lost as heat. thus, half energy supplied by the battery is lost as heat.