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

Answer

A

Explanation

During discharging of capacitor C through inductance L, let at any instant, charge in capacitor be Q.
`thereforeQ=Q_0sinomegat`
Maximum energy stored in capacitor-`1/2Q_0^2/C`
Let at an instant t, the energy be stored equally between electric and magnetic field. Then energy stored in electric field at instant t is
`1/2Q^2/C=1/2[1/2Q_0^2/C]`or,`Q^2=Q_0^2/2`
or,`Q=Q_0/sqrt2`or,`sinomegat=Q_0/sqrt2`
or,`omegat=pi/4`or,`t=pi/(4omega)=(pisqrt(LC))/4[becauseomega1/sqrt(LC)]`