An ideal inductor is connected across a capacitor. Oscillations of energy K are set up in the circuit. The capacitor plates are slowly drawn apart such that the frequency of oscillations is quadrupled. The work done in the process is

Step-by-step solution

The energy stored in an LC circuit is K = 1 2 q^2 C = 1 2 LI^2 . The frequency of oscillation is f = 1 2 LC . Given that the frequency is quadrupled, f' = 4f . Since L is constant, 1 C' = 4 1 C , which implies C = 4 C' , or C' = C 16 . The energy stored in the capacitor is K = q^2 2C . Since the plates are drawn apart slowly, the charge q on the capacitor remains constant. The new energy K' is K' = q^2 2C' = q^2 2(C/16) = 16 ( q^2 2C ) = 16K . The work done by the external agent is equal to the change in the energy