Switches `S_(1), S_(2)` remain open and switch `S_(3)` remains closed for long time such that capacitor becomes fully charged and current in inductor coil becomes maximum, Now switches `S_(1), S_(2)` are simultaneously closed and`S_(3)` in simultaneously opened at `t=0`
Assume that battery and inductor coil are ideal

Charge (in `mu C`) on capacitor as a function of time is :

Options

A. `q = 10sqrt(2)sin[10^(4)t + (3pi)/(4)]`
B. `q = 10 sin[10^(4)t + (3pi)/(4)]`
C. `q = 10 sin[10^(2)t + (3pi)/(4)]`
D. `q = 10sqrt(2)sin[10^(2)t + (3pi)/(4)]`

Answer

A

Explanation

`(1)/(2)(Q_(0)^(2))/(C ) = (1)/(2)(Q^(2))/(C) + (1)/(2)Li rArr Q_(0) = 10sqrt(2) mu C`
`omega = (1)/(sqrt(LC)) = 10^(4)` and `Q = (Q_(0))/(sqrt(2))` [Capacitor is discharging]
`rArr q = 10sqrt(2) sin (10^(4) t + (3pi)/(4))`