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(LC)`
C. `2 pi sqrt(LC)`
D. `sqrt(LC)`

Answer

B

Explanation

As `q = q_(0) cos omega t and i = i_(0) sin omega t`
For equal energy `I_(0) sin omega t = (I_(0))/(sqrt(2))`
`:. omega t = (pi)/(2)`
or `(2 pi)/( T) xx t = (pi)/( 4) rArr t = (T)/( 8) = (2 pi sqrt(LC))/(8) rArr t = (pi sqrt(LC))/(4)`