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 sqrt(LC)`
B. `(pi)/(4) sqrt(L C)`
C. `2pi sqrt(L C)`
D. `sqrt(L C) 5`

Answer

B

Explanation

Charge on the capacitor at any time `'t'`
`q = q_(0) cos omega t`
At time when energy stored equally in electric and magnetic field, at this time
Energy of a capacitor `= (1)/(2)` Total energy
`(1)/(2) (q^(2))/(C ) = (1)/(2)((1)/(2)(q_(0)^(2))/( C)) rArr q = (q_(0))/(sqrt(2))`
From equation (i)
`(q_(0))/(sqrt(2)) = q_(0) cos omega t`
`cos omega t = (1)/(sqrt(2)) rArr omega t = cos^(-1) ((1)/(sqrt(2))) = (pi)/(4)`
`t = (pi)/(4 omega) = (pi)/(4) sqrt(LC)(because omega = (1)/(sqrt(LC)))`