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An uncharged capacitor is connected to a...

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.

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Let capacitance of a capacitor = C
emf of the battery = V
`:.` Charge given to the capacitor, q = CV
Energy supplied by battery = work done by battery = qV
Energy stored in the capacitor
`= (1)/(2) CV^(2) = (1)/(2) qV`
So, half energy is lost as beat while charging the capacitor.
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