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
(ii) completely magnetic (i.e., stored in the inductor) ?

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 magnetic as when the electrical energy the capacitor is zero.
`q=0`
`Q=Q_(0)cos.(2pi t)/(T)=0` (from eqq(i))
`therefore cos.(2pi)/(T).t=0=(n pi)/(2)` or `t=(nT)/(4)=cos`.
It happens if `t=T//4, 3T//4,(5T)/(4)`, ......
Thus, the energy stored is completely magnetic at
`t=T//4, 3T//4, 5T//4`......