Question

An LC circuit contains a 20 mH inductor and a 50 µF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0.
(a) What is the total energy stored initially? Is it conserved during LC oscillations?
(b) What is the natural frequency of the circuit?
(c) At what time is the energy stored
(d) completely electrical (i.e., stored in the capacitor)?
(e) completely magnetic (i.e., stored in the inductor)?
(f) At what times is the total energy shared equally between the inductor and the capacitor?
(e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat?

Answer 1

L = 20mH = 20 × 10³ H
C = 50 µF = 50 x 10^-6 F
charge on the capacitor initially,

(d) The total energy is shared equally between the inductor and the capacitor, when the energy stored in capacitor becomes equal to one half of the total energy. If q is charge on the capacitor at that instant, then

(e) When resistance is introduced, whole of the energy will be dissipated in the form of heat. The introduction of resistance produces damped oscillations.