A 18.0 ? ? F capacitor is placed across a 22.5 ? V battery for a few seconds and

Question

A 18.0??F capacitor is placed across a 22.5?V battery for a few seconds and is then connected across a 12.0?mH inductor that has no appreciable resistance.

After connecting the capacitor and inductor together, find the maximum current in the circuit.

When the current is a maximum, what is the charge on the capacitor?

How long after connecting the capacitor and inductor together does it take for the capacitor to be completely discharged for the first time?

How long after connecting the capacitor and inductor together does it take for the capacitor to be completely discharged for the second time?

Explanation / Answer

Try an energy balance since resistance is negligible.

(1/2) C v^2 = (1/2) L (imax)^2
solve for imax

When the current is max, the capacitor has discharged and so Q = 0.

The frequency of oscillation would be given by w^2 L C = 1
w = 1/sqrt(LC)
f = 1/(2 pi sqrt(LC) )
T = 2 pi sqrt(LC) would be the period of the oscillation.

The first discharge is reached in (1/4) T
The next one would be 1/2 cycle later or (3/4) T

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