q5 A 225muF capacitor is charged by a 1380V power supply the

q5

A 22.5-muF capacitor is charged by a 138.0-V power supply, then disconnected from the connected in series with a 0.255-mH inductor. Calculate the oscillation frequency of the circuit. Calculate the energy stored in the capacitor at time t = 0ms ( the moment of connection with the inductor). Calculate the energy stored in the inductor at t = 1.30ms.

Solution

Here ,

a)

Oscillation frequency = 1/(2pi * sqrt(L * C))

Oscillation frequency = 1/(2pi * sqrt(22.5 *10^-6 * 0.255 *10^-3))

Oscillation frequency = 2101.6 Hz = 2.101 kHz

the Oscillation frequency is 2.101 kHz

b)

energy stored in capacitor =0.5 * C * V^2

energy stored in capacitor = 0.5 * 22.5 *10^-6 * 138^2

energy stored in capacitor =0.214 J

the energy stored in capacitor is 0.214 J

c)

now , for the energy stored in inductor at t = 1.3 ms

Volatge across the capacitor ,

V = 138 * cos(2*pi * 2101 * 1.3 *10^-3)

V = 16.8 V

energy stored in inductor = 0.214 - 0.5 * 22.5 *10^-6 * 16.8^2

energy stored in capacitor = 0.211 J

the energy stored in capacitor is 0.211 J