Question

A capacitor of capacitance $C$ and an inductor of inductance $L$ are connected to a DC battery as shown at $t = 0$, the switch is closed. Choose correct option(s).

• A. Polarity of charge on capacitor never reverses with time.
• B. Maximum charge on capacitor is $2CV$.
• C. Maximum current in the circuit is $V\sqrt{\frac{C}{L}}$.
• D. Maximum current in the circuit is $2V\sqrt{\frac{C}{L}}$.

Answer 1

Answer: (A), (B), (C)

A, B, C

Answer 2

The circuit equation is $V - L \frac{di}{dt} - \frac{q}{C} = 0$. With initial conditions $q(0)=0$ and $i(0)=0$, the charge is $q(t) = CV(1 - \cos(\omega t))$ and current is $i(t) = V\sqrt{\frac{C}{L}} \sin(\omega t)$, where $\omega = \frac{1}{\sqrt{LC}}$.

• A: $q(t) \ge 0$, so polarity never reverses.
• B: $q_{max} = CV(1 - (-1)) = 2CV$.
• C: $i_{max} = V\sqrt{\frac{C}{L}} |\sin(\omega t)|_{max} = V\sqrt{\frac{C}{L}}$.