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The charge of the capacitor in an L-C oscillatory circuit, when the energies associated with the inductor and the capacitor are equal, is ______ [Q₀ is the initial charge on the capacitor].

Asked in GUJCET 2023 · Energy exchange and damping in LC

• (1) (Q₀)/2
• (2) Q₀
• (3) (Q₀)/(√3)
• (4) (Q₀)/(√2)

Step-by-step solution

Why the other options are wrong

• (1) Halves the charge instead of the energy. The capacitor's energy goes as q², so q = (Q₀)/2 leaves only a quarter of the energy in the capacitor and three-quarters in the inductor.
• (2) With q = Q₀ all the energy is in the capacitor and none in the inductor: the current is zero at that instant.
• (3) q = (Q₀)/(√3) leaves one-third of the energy in the capacitor and two-thirds in the inductor: magnetic energy twice the electric, not equal to it.

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