A fully charged capacitor C with initial charge `q_(0)` is connected to a coil of self inductance L at t=0. The time at which the energy is stored equally between the electric and the magnetic fields is

Options

A. `(pi)/(4) sqrt(LC)`
B. `2 pi sqrt(LC)`
C. `sqrt(LC)`
D. `pi sqrt(LC)`

Answer

1

Explanation

As initially charge is maximum
`q = q_(0) cos omega t`
`implies i = (dq)/(dt) = - omega q_(0) sin omega t`
Given `(1)/(2) Li^(2) = (q^(2))/(2C)`
`implies (1)/(2) (omega q_(0) sin omega t)^(2) = ((q_(0) cos omega t)^(2))/(2C)`
But, `omega = (1)/(sqrt(LC)) implies tan omega t = 1`
`omega t = (pi)/(4) implies t = (pi)/(4 omega) = (pi)/(4) sqrt(LC)`