In the given circuit the capacitor (C) may be charged through resistance R by a battery V by closing switch `(S_1)`. Also when `(S_1)` is opend and `(S_2)` is closed the capacitor is connected in series with inductor (L).

Given taht the total charge stored in the LC circuit is `(Q_0)`. for `Tge0, the charge on the capacitor is

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/sqrt(LC))`
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

`L(di)/(dt)-Q/C=0,-L(d^(2)Q)/(dt^(2))-Q/C=0, Q=-LC(d^(2)Q)/(dt^(2))`