Question

The sum of the electrical and magnetic energies in an L-C circuit is 0.800 J. At a certain instant the energy is exactly half electrical and half magnetic, the capacitor charge is 5.30 mC, and the current is 8.00 A. Find (a) the capacitance, (b) the inductance, and (c) the angular frequency of oscillation.

Answer 1

Part A. given that at a certain instant the energy is exactly half electrical and half magnetic, So

electrical energy stored in capacitor is given by:

Ue = Q^2/(2*C)

C = Capacitance = ?

C = Q^2/(2*Ue)

Ue = energy stored in capacitor = 0.800/2 = 0.400 J

So,

C = (5.30*10^-3)^2/(2*0.400)

C = 35.1*10^-6 F = 35.1 F

Part B.

Magnetic energy stored in inductor is given by:

Um = (1/2)*L*I^2

L = Inductance = ?

L = 2*Um/I^2

Um = energy stored in inductor = 0.800/2 = 0.400 J

So,

L = 2*0.400/8.00^2

L = 0.0125 H = 12.5*10^-3 H = 12.5 mH

Part C.

angular frequency of oscillation in LC circuit is given by:

w = 1/sqrt (L*C)

w = 1/sqrt (12.5*10^-3*35.1*10^-6)

w = angular frequency = 1509.7 rad/sec

w = 1510 rad/sec = 1.51*10^3 rad/sec

Let me know if you've any query.