In a L-C oscillator circuit at any instant of time current is I and charge on capacitor is Q then the total energy of the system will be ………

Options

A. `Q^2/(2C)`
B. `Q/(2C^2)`
C. `Q_0^2/(2C)`
D. `Q_0^2/(2C^2)`

Answer

C

Explanation

`U=Q^2/(2C)+1/2LI^2`
`=(Q_0^2cos^2omega_0t)/(2C)+1/2LQ_0^2omega_0^2 sin^2 omega_0t`
`=1/2Q_0^2[(cos^2 omega_0t)/C+Lomega_0^2 sin^2 omega_0t]`
`=Q_0^2/2[(cos^2omega_0t)/C+1/C sin^2omega_0t] [because omega_0^2 =1/(LC)]`
`=Q^2/2[cos^2 omega_0^t +sin^2omega_0t]`
`=Q^2/(2C)`