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. `pisqrt(LC)`

Answer

A

Explanation

(a) Energy stored in magnetic field `=1/2 Li^(2)`
Energy stored in electric field `=1/2 (q^2)/(C)`
`:. 1/2 (Li^(2))=1/2(q^2)/(C)` Also `q=(q_0) cos (omega)t and (omega)=(1)/(sqrt(LC))`
on solving `t=(pi)/(4)sqrt(LC)`.