An LC circuit contains a 20 mH inductor and a `50 mu F` 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 the oscillalions?
(b) What is the natural frequency of the circuit?
(c ) At what time is the energy stored? (i) Completely electrical ? (ii) Completely magnetic ?
(d) At what time 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 ?

Explanation

Given Inductance `L = 20 mH = 20xx10^(-3)H`
Capacitance of capacitor
`C=50 mu f=50xx10^(-6)F`
Initial charge on the capacitor,
`Q_(i)=10mc =10xx10^(3)C`
As a resistor is inserted in the circuit, all of the energy loss during heating. Energy loss = 1 J. The oscillations becomes damped and becomes disappear after sometime as the total energy loss in the form of heat.