An LC circuit is shown in the figure below. The 49 pF capacitor is initially cha

Question

An LC circuit is shown in the figure below. The 49 pF capacitor is initially charged by the 6 V battery when S is at position a. Then S is thrown to position b so that the capacitor is shorted across the 13 mH inductor. What is the maximum value for the oscillating current assuming no resistance in the circuit? Answer in units of A. What is the natural angular frequency of the circuit? Answer in units of rad/s. What is the maximum energy stored in the magnetic field of the inductor? Answer in units of J.

Explanation / Answer

a)

i(t) = V0*sqrt(C/L)sin(wt)

where w^2 = 1/LC

I(max) = V0*sqrt(C/L)

I(max) = 6*sqrt[(49 x -12 / 13 x 10^-3)

I(max) = 0.360 mA.

b)

Resonant frequency = w = 1/sqrt(LC)

w = 1 / sqrt(13 x 10^-3 x 49 x 10^-12)

w = 1.25 x 10^6 rad/s

c)

Max energy in inductor must be = max energy in capacitor since this is a lossless circuit. Since there are times when

i = 0, answer must be

1/2 CV^2 = (49 x 10^-12 x 36) = 8.82 x 10^-10 J

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