A `1.00 mH` inductor and a `1.00muF` capacitor are connected in series. The current in the circuit is described by `i = 20 t`, where t, is in second and `i` is in ampere. The capacitor initially has no charge. Determine
(a) the voltage across the inductor as a function of time,
(b) the voltage across the capacitor as a function of time,
(c) the time when the energy stored in the capacitor first exceeds that in the inductor.

Answer

B, C

Explanation

a. `V_L=L (di)/(dt)(1xx10^-3)d/(dt)(20T)=0.02V`
`=20mV`
b. `q=int_0^i i dt = int_0^t(20t)dt=10t^2`
`V=q/C=(10t^2)/(10^-6)=(10^+7t^2)V`
`q^2/(2c)gt1/2Li^2`
or `((10t^2)^2)/(2x10^-6)gt1/2xx10^-3xx(20t)^2`
or `tgt63.2xx1^-6s`s
or `tgt63.2mus`