An inductor of inductance 2 mH is connected across a charged capacitor of 5 `mu` F . Let q denote the instaneous charge on the capacitor and `i` the current in the circuit . Maximum value of charge is Q = 200 `mu` C.
(a) When Q = 100 `mu` C what is the value of /di/dt / ?
(b) When Q = 200 `mu` C what is the value of `i` ?

Explanation

(a) Charge stored in the capacitor oscillates simple harmonically as
Q=`Q_(0) sin (omega tpm phi) ` and
`omega=(1)/(sqrt(LC))=(1)/(sqrt((2xx10^(-3)H)(5.0xx10^(-6)F)))=10^(4)s^(-1)`
At `t=0 , if Q = Q_(0)` , then
Q (t) = `Q_(0) cos omega t ` and if Q = `Q_(0)//(2)` then cos `omegat= 1//2`
`(di(t))/(dt)= -Q_(0)omega^(2) cos (omegat)`
`=(200xx10^(-6)C)(10^(4)s^(-1))^(2) ((1)/(2))` A/s

(b) When the energy of the capacitor is maximum the energy stored in the inductor will be zero .
i.e `(1)/(2) Li^(2)=0 implies i=0`