In the following electrical network at `t = lt 0` Fig key is placed on (1) till the capacitor got fully charged. Key is placed on (2) at `t = 0`. Time when the energy in both the same for the time is

Options

A. `(pi)/(4) sqrt(LC)`
B. `(3pi)/(4) sqrt(LC)`
C. `(pi)/(3) sqrt(LC)`
D. `(2pi)/(3) sqrt(LC)`

Answer

A

Explanation

When energy on both is same, means energy on capacitor is half of its maximum energy.
`(q^(2))/(2C) = (1)/(2) (Q^(2))/(2C) rArr q = (Q)/(sqrt(2))`
`rArr Q cos omega t = (Q)/(sqrt(2)) rArr cos omega t = (1)/(sqrt(2))`
`rArr omegat = (pi)/(4) rArr t = (pi)/(4 omega) = (pi)/(4) sqrt(LC)`