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In an LC oscillating circuit, at a certain instant the charge on the capacitor is Q and the current through the inductor is I. At this instant the energy stored in the capacitor equals the energy stored in the inductor. What is the time period of the electrical oscillations?
- 2*pi*Q / I
- 2*pi*sqrt(I / Q)
- pi*Q / I
- pi*sqrt(Q / I)
Correct answer: 2*pi*Q / I
Solution
When energy in capacitor = energy in inductor, each is half the total energy, which gives Q = Q0/sqrt(2) and I = Q0*omega/sqrt(2). Therefore Q/I = 1/omega, and T = 2*pi/omega = 2*pi*Q/I.
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