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. `Q=Q_(0)cos((pi)/(2)+(t)/(sqrt(LC)))`
B. `Q=Q_(0)cos((pi)/(2)-(t)/(sqrt(LC)))`
C. `Q=-LC(d^(2)Q)/(dt^(2))`
D. `Q=-(1)/(sqrt(LC))(d^(2)Q)/(dt^(2))`

Answer

C

Explanation

(c) Apply Kirchhofff's law in the circuit
`Q/C-L(dI)/(dt)=0impliesQ/C=L(dI)/(dt)`
`implies Q=LC(d)/(dt)(-(dQ)/(dt))=-LC(d^(2)Q)/(dt^2)`.