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Solving LC circuit with energy conservation
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[QUOTE="kuruman, post: 6810953, member: 192687"] Why do you say it didn't? The initial charge on the series combination is ##q_0=C_{eq}U=\frac{1}{2}CU##. The initial energy stored in the capacitor is ##E_0=\frac{1}{2}q_0U=\frac{1}{4}CU^2##. That energy does not change when the inductor is connected. At any time, the energy stored in the capacitor combination before breakdown is ##E_C(t)=\frac{1}{4}CU^2\cos^2\omega_0 t=E_0\cos^2\omega_0 t##. Note that it is sometimes zero and sometimes ##E_0##. When it's zero, all the energy is in the inductor; when it's ##E_0## all the energy is in the capacitors. Krotov says, that the energy of the damaged capacitor at breakdown is half of ##E_C(\tau)## whatever that value is. The balance, ##E_0-\frac{1}{2}E_C(\tau)## is the energy left in the intact capacitor and the inductor. If the breakdown occurs when ##\omega_0 \tau=\frac{2n+1}{2}\pi## (##n## = integer), all the energy is in the inductor and that is implicit in Krotov's equation for ##W##. [/QUOTE]
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Solving LC circuit with energy conservation
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