Question

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.
At what time is the energy stored
(i) Completely electrical (i.e., stored in the capacitor) ?

Answer 1

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`
Let at any instant the energy stored is completely electrical the charge on the capacitor `Q = Q_(0) cos omega t`
`Q=Q_(0)cos.(2 pi)/(T).t` ....(1)
Q is maximum as it is equal to `Q_(0)`, only if
`cos.(2pi)/(T)t = pm 1 = cosn pi` or t
`= (nT)/(2)`, where n = 1, 2, 3 ....
`t=0, T//2, T, 3T//2`, ....
Thus, the energy stored is completely electrical at `t = 0,T//2, T, 3//2` ....