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Question:

Calculate the energy stored in the inductor at t 1.40 ms.?

A 20.0 uF capacitor is charged by a 170.0 V power supply, then disconnected from the power and connected in series with a 0.270 mH inductor.

Answer:

The natural (radian) frequency of oscillation is: ω 1/sqrt(L*C) 1/sqrt(270*10^-6 * 20*10^-6) 13.61*10^3 radian/sec At the start of the transient, the inductor current is zero, and all of the energy is stored as electric field energy in the capacitor. The current in the inductor will be sinusoidal with zero crossings at every N*π where N 0, 1, 2, 3 The angle of the sinusoidal inductor current at 1.40ms is: θ ω*t 13.61*10^3 * 1.4*10^-3 19.05 radians Divide this by 2*π to find out how many complete periods are included in the 19.05 radians: N 19.05/(2*π) 3.03 This is probably close enough to 3 complete periods of the inductor current to conclude that for practical purposes, all of the energy has been returned to the capacitor, and only a very small amount of energy (within the significant figures of the component values given) would be in the inductor. I'd answer: approximately zero

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