A capacitor of capacity `2 muF` is charged to a potential difference of `12 V`. It is then connected across an inductor of inductance `6 mu H`. What is the current (in `A`) in the circuit at a time when the potential difference across the capacitor is `6.0 V`?

Options

A. 0.6A
B. 1.2A
C. 2.2A
D. 3.2A

Answer

A

Explanation

In the case of oscillatory discharge of a capacitor through an inductor
`q = q_0 cos omega t ` where `omega = (1)/(sqrt(LC))`
For a capacitor , q = CV
` therefore cos omega t = (q)/(q_0) = (V)/(V_0) = 6/12 = 1/2, omega t = cos^(-1) (1/2) = pi/3 rad `
`omega = (1)/(sqrt(LC)) = (1)/(sqrt((0.6 xx 10^(-3) )(2 xx 10^(-6))) ) = (10^5)/(sqrt12) rad s^(-1)`
`I = (dq)/(dt) = -q_0 omega sin omega t `
`|I| = CV_0 omega sin omega t `
`|I| = (2 xx 10^(-6))(12) xx (10^5)/(sqrt12) xx (sqrt3)/(2) = 0.6 A`