A 20 uF capacitor is initially charged by a 12 V battery by keeping the switch c

Question

A 20 uF capacitor is initially charged by a 12 V battery by keeping the switch connected between the points a and b for a long time (see the adjacent figure). Then, at t=0, the switch is thrown from b to d so that points a and d are now connected and we have an oscillating LC circuit. Here L=0.25 H.

a. Find the maximum charge on the capacitor.

b. Find the maximum current in the inductor.

c. Compute the energy stored in the capacitor at t=1.5 ms.

d. Compute the energy stored in the inductor at t=1.5 ms.

Explanation / Answer

a. maximum charge = CV = 12 *20*10^-6 = 240uC

b. initial energy = 0.5CV^2 = 0.5Li^2

    thus i = 0.107A

c. w = 1/root(LC) = 447.21rad/s

   q =q0cos(wt)

   at t= 1.5ms

   q = 188uC

energy stored in capacitor = q^2/2C = 883 uJ

d. energy stored in inductor = initial energy - 883 = 1440-883 = 557 uJ

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