Question

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be ______.

Options

• 1/2

• 1

• 2

• 1/4

Answer 1

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be 1/2.

Explanation:

Energy in capacitor = `1/2`CV²

Work done by battery = QV = CV²

where C = Capacitance of capacitor

V = Potential difference,

e = emf of battery 

Required ratio = `(1/2"CV"^2)/("CV"^2) = 1/2` (∵ V = e)