Question

If the total charge stored in the LC circuit is $Q_0$, then for $t\ge 0$

• A. the charge on the capacitor is $Q=Q_0\cos (\frac{\pi }{2}+\frac{t}{\sqrt{LC}})$
• B. the charge on the capacitor is $Q=Q_0\cos (\frac{\pi }{2}-\frac{t}{\sqrt{LC}})$
• C. the charge on the capacitor is $Q=-LC\frac{d^{2}Q}{d{t}^2}$
• D. the charge on the capacitor is $Q=-\frac{1d^{2}Q}{\sqrt{LC}d{t}^2}$

Answer 1

Answer: (C)

the charge on the capacitor is $Q=-LC\frac{d^{2}Q}{d{t}^2}$

If the charge at any instant on capacitor is Q and current through inductor is I, then as per KVL,

$\frac{Q}{C}+L\frac{dI}{dt}=0$

Since $I=\frac{dQ}{dT}$

Substituting above, we get $Q=-LC\frac{d^{2}Q}{d{t}^2}$.