A fully charged capacitor C with initial charge Q 0 is connected to an ideal inductor of self-inductance L at t = 0 . The time at which energy is stored equally between the electric and the magnetic fields is

Question

A fully charged capacitor C with initial charge Q 0 is connected to an ideal inductor of self-inductance L at t = 0 . The time at which energy is stored equally between the electric and the magnetic fields is, π 4 L C, 2 π L C, L C, π L C

MARKS App · Accepted Answer

The charge on the capacitor at any instant of time is Q = Q 0 cos ω t ⇒ i = d Q d t = - ω Q 0 sin ω t 1 2 L i 2 = Q 2 2 C ⇒ 1 2 L ω Q 0 sin ω t 2 = Q 0 cos ω t 2 2 C ω = 1 L C ⇒ tan ω t = 1 ω t = tan - 1 1 = π 4 t = π 4 ω = π 4 L C

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