In the `L-C` circuit shown, `C =1muF`. With capacitor charged to `100V`, switch `S` is suddenly closed at time `t = 0`. The circuit then oscillates at `10^3Hz`
(a) Calculate co and T
(b) Express `q` as a function of time
(c) Calculate ``L
(d) Calculate the average current during the first quarter-cycle.

Answer

A, D

Explanation

`a. omega=(2pi)/f,T1/f`
b. At `t=0, q=q_0=CV_0=(100muC)`
Now, `q=q_0cosomegat`
c. `omega=1/sqrt(LC)impliesL=1/(omega^2C)`
d. `|i|=|(dq)/(dt)|=q_0omegasinomegat`
Average value of current in first quarter cycle
`=(int_0^(T//4)dt)/(T//4)`