In L-C oscillator, at ... time, energy in capacitor and energy in inductor are equal.

Options

A. `T/8`
B. `T/4`
C. `T/2`
D. T

Answer

A

Explanation

When energy in capacitor and energy in inductor are equal in L-C oscillations,
`U=U_E+U_B`
`therefore U=2U_E " " (because U_E=U_B)`
`therefore q_0^2/(2C)=2(q^2/(2C))`
`therefore q^2=q_0^2/2`
`therefore q=q_0/sqrt2`
`therefore q_0 cos omega_0t=q_0/sqrt2 " "(because q=q_0 cos omega_0t)`
`therefore cosomega_0 t = 1/sqrt2`
`therefore omega_0 t=pi/4`
`therefore ((2pi)/T)t = pi/4 " " (because omega_0 =(2pi)/T)`
`therefore t=T/8`