If the total charge stored in the `LC` circuit is `Q_(0)`, then for `tgt= 0`

Options

A. The charge on the capacitor is Q = `Q_(0)cos ((pi)/(2) + (t)/(sqrt LC))`
B. The charge on the capacitor is Q = `Q_(0) cos((pi)/(2) - (t)/(sqrtLC))`
C. The charge on the capacitor is Q = `= - LC (d^(2)Q)/(dt^(2))`
D. The charge on the capacitor is Q = `(1)/(sqrt LC)(d^(2)Q)/(dt^(2))`

Answer

C

Explanation

If Q is the instantaneous charge on the capacitor, then
`(Q^(2))/(2C) + (1)/(2) Li^(2) = (Q_(0)^(2))/(2C)` or `(d)/(dt)[(Q^(2))/(2C) + (1)/(2)Li^(2)] = 0`
or `(2Q)/(2C)(dQ)/(dt) + (L)/(2) xx 2i xx (di)/(dt) = 0 therefore Q = - LC (d^(2)Q)/(dt^(2))`