Question

In the circuit shown, the symbols have their usual meanings. The cell has emf $E$. $X$ is initially joined to $Y$ for a long time. Then, $X$ is joined to $Z$. The maximum charge on $C$ at any later time will be

• A. $\frac{E}{R \sqrt {LC}}$
• B. $\frac{E R}{2 \sqrt {LC}}$
• C. $\frac{E \sqrt {LC}}{2R}$
• D. $\frac{E \sqrt {LC}}{R}$

Answer 1

Answer: (D)

Current in inductor $=\frac{E}{R}$
$\therefore $ its energy $=\frac{1}{2} \frac{L E^{2}}{R^{2}}$
Same energy is later stored in capacitor
$\frac{Q^{2}}{2 C}=\frac{1}{2} \frac{L E^{2}}{R^{2}} $
$\Rightarrow Q=\frac{\sqrt{L C}}{E} \frac{E}{R}$