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A capacitor is fully charged by connecting it to a battery (key position 1). At t = 0 the key is switched to position 2, connecting the capacitor to an inductor. At what earliest time does the energy stored in the capacitor equal the energy stored in the inductor?

1. pi * sqrt(LC) / 4
2. pi * sqrt(LC) / 2
3. 5 * pi * sqrt(LC) / 4
4. 5 * pi * sqrt(LC) / 2

Correct answer: pi * sqrt(LC) / 4

Solution

After the switch, the charge oscillates as q = q₀ cos(omega*t) with omega = 1/sqrt(LC). The capacitor energy E_C = E₀ cos²(omega*t) and inductor energy E_L = E₀ sin²(omega*t). Setting E_C = E_L gives cos²(omega*t) = sin²(omega*t), so omega*t = pi/4, yielding t = pi*sqrt(LC)/4.

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