An LC circuit contains a 20 mH inductor and a `50 muF` capacitor with an initial charge of 10 mC. The resistance of circuit is negligible. Let the instant the circuit is closed be t = 0.
What is the total energy stored initially ? Is it conserved during LC oscillations ?

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`
The total energy stored across the capacitor initially,
`E = (q^(2))/(2C)`
`therefore E_(i)=(Q_(i)^(2))/(2C)=((10xx10^(-3))^(2))/(2xx50xx10^(-6))=(10^(-4))/(10^(-4))1J`.
Yes, this energy is conserved during LC oscillations.