Let a capacitor be charged qm (at t = 0) and connected to an inductor as shown in the figure. The charge oscillates from one plate of capacitor to another plate through the inductor. This results in electric oscillations called LC oscillation.
The moment the circuit is completed, the charge on the capacitor starts decreasing, giving rise to current in the circuit. As q decreases , energy stored in the capacitor decreases and the energy transferred from capacitor to inductor.
Once the capacitor is fully discharged, magnetic field begin to decrease produces an opposing emf. Now capacitor is begin to but in opposite direction( acc to Lenz’* law). Charge oscillates simple harmonically with natural frequency ω0 = 1/√LC
Charge varies sinusoidally with time as q = qm cos(ωot). And current varies sinusoidally with time as i = ωoqmsinωt = im sinωt.
At time t = 0, electrical energy stored in the capacitor,
and magnetic energy in the inductor UB = 0
Similarly, when ܷUB = 1/2 Lim2 then UE = 0
∴ Total energy of the LC circuit at any instant of time,
