In an `L-C` circuit, `L=3.3H` and `C=840pF`. At `t=0` charge on the capacitor is `105muC` and maximum. Compute the following quantities at `t=2.0ms`.
a. The energy stored in the capacitor.
b. The total energy in the circuit,
c. The energy stored in the inductor.

Options

A. `6.0J` , `1.56J` , `0.56`
B. `6.0J` , `6.56J` , `1.56`
C. `4.0J` , `6.56J` , `0.56`
D. `6.0J` , `6.56J` , `0.56`

Answer

D

Explanation

Given `L=3.3H,C=840xx10^-12F` and `q_0=105xx10^-6C`
The angular frequency of `L-C` oscillations is
`omega=1/sqrt(LC)=1/sqrt(3.3xx840xx10^-12)`
`=1.9xx10^4rad//s`
Charge stored in the capacitor at time `t` would be
`q=q_0cosomegat`
a. At `t=2xx10^-3s`,
`q=(105xx10^-6)cos[1.9xx10^4][2xx10^-3]`
`=100.3xx10^-6C`
`:.` Energy stored in the capacitor,
`U_C=1/2 q^2/C`
`=((100.3xx10^-6)^2)/(2xx840xx10^-12)` ltbgt. `=6.0J`
b. Total energy in thhe circuit,
`U=1/2q_0^2/C=((105xx10^-6)^2)/(2xx840xx10^-12)`
`=6.56J`
c. Energy stored in inductor in the given time
=total energy in circuit-energy stored in capacitor
`=(6.56-6.0)J`
`=0.56J`