An `L-C` circuit consists of an inductor with `L = 0.0900 H` and a capacitor of `C = 4 xx 10^-4 F`. The initial charge on the capacitor is `5.00 muC`, and the initial current in the inductor is zero.
(a) What is the maximum voltage across the capacitor?
(b) What is the maximum current in the inductor?
(c) What is the maximum energy stored in the inductor?
(d) When the current in the inductor has half its maximum value, what is the charge on the capacitor and what is the energy stored in the inductor?

Answer

A

Explanation

`a. 1/2 q_i^2/C+1/2LI_i^2=1/2CV_0^2`
`:. V_0=q_i/C` (as `I_(i) = 0)`
b. `1/2CV_0^2=1/2LI_0^2`
`:. I_0=sqrt((C)/(L)) V_0`
`c.U_(max)=1/2LI_0^2`
`d. U_L=1/2L(I_0/2)^2`
`U_C=1/2q^2/C=U_(max)-U_L`