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 field is

Options

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

Answer

B

Explanation

In `LC` oscillation energy is transferred `C` to `L` or `L` to `C` maximum energy in `L` is `=1/2LI_(max)^(2)`
Maximum energy in `C` is =`(q_(max)^(2))/(2C)`
Equal energy will be when `1/2LI^(2)=1/2 1/2 LI_(max)^(2) rArrI=1/sqrt2I_(max)sin omegat=1/sqrt2I_(max)rArr omegat=pi/4`
or `(2pi)/T t=pi/4` or `t=T/8 rArr t=1/8 2pisqrt(LC) =pi/4sqrt(LC)`