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A fully charged capacitor C (initial charge q0) is connected at t = 0 to an ideal inductor L. At what time is the stored energy shared equally between the capacitor's electric field and the inductor's magnetic field?
- (pi/4)*sqrt(LC)
- pi*sqrt(LC)
- sqrt(LC)
- 2*pi*sqrt(LC)
Correct answer: (pi/4)*sqrt(LC)
Solution
In an LC circuit the charge is q(t) = q0 cos(omega t), omega = 1/sqrt(LC). Electric energy is proportional to q². Equal sharing means q² = q0²/2, so cos(omega t) = 1/sqrt(2), giving omega t = pi/4 and t = (pi/4) sqrt(LC).
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