An `LC` circuit contains a `20 mH` inductor asn a `50 mu F` capacitor with initial change of `10 mC`. The resistance of the circuit is negligible. Let the instant the circuit is closed be `t = 0`.

Options

A. Energy stored in the circuit in completely electrical at `t = (n pi)/(2000)`
B. Energy stored in the circuitin completely magnetic at `t = ((2n + 1)pi)/(2000)`
C. Energy stored in the circuit in shared equally between the inductor and capacitor at `t = ((2n + 1)pi)/(4000)`
D. Energy stored in the circuit is shared euqally between the inductor and capacitor at `t = (n pi)/(2000)`

Answer

1,2,3

Explanation

Instantaneous electrical energy
`U_(E) = (q_(0)^(2) cos^(2) omega t)/(2C)`
At `omega t = 0, pi, 2 pi, 3 pi`….. The energy is completely electrical.
`t = (2 pi)/(2 pi f) = (n)/(2 f) = (n pi)/(1000)` sec , `n = 1, 2, 3, 4`
or `t = 0, T//2, 3T//2`....
Instantaneous magnetic energy
`U_(B) = (1)/(2) Lq_(0)^(2) omega^(2) sin^(2) omega t` or `U_(B) = (q_(0)^(2))/(2C) sin^(2) omega t`
So, at `omega t = pi//2, 3 pi//2, 5pi //2`
The energy is completely magnetic
`t = ((2n + 1) pi)/(2(2pi f)) = ((2n + 1))/(4f) = ((2n + 1))/(2000) sec`
Where `n = 0,1,2,3,4`......
or `t = T//4, 3T//4, 5T//4`.......
Timings for energy shared equally between inductor and capacitor.
`U_(B) = U_(E)`
`(q_(0)^(2))/(2C ) sin^(2) omega t = (q_(0)^(2))/(2C) cos^(2) omega t`
`tan^(2) omega t = 1` or `tan omega t = tan pi//4`
`t = (pi)/(4 omega), (3 pi)/(4 omega),(5 pi)/(4 omega)`,............or `t = (T)/(8), (3T)/(8), (5T)/(8)`............