Question

If a capacitor is charged by connecting it to a battery, then the ratio of work done by the battery and the energy stored in the capacitor is

• A. \(3:2\)
• B. \(1:2\)
• C. \(1:1\)
• D. \(2:1\)

Hint:

While charging a capacitor, \[ \boxed{ W_{\text{battery}}=CV^2, \qquad U=\frac12CV^2. } \] Half of the work done by the battery is stored in the capacitor and the remaining half is dissipated as heat.

Answer 1

The Correct Option is D

Step 1: Find the work done by the battery. When a capacitor of capacitance \(C\) is charged to a potential difference \(V\), \[ Q=CV. \] The work done by the battery is \[ W=QV=CV^2. \]

Step 2: Find the energy stored in the capacitor. The energy stored in the capacitor is \[ U = \frac12CV^2. \]

Step 3: Find the required ratio. Therefore, \[ W:U = CV^2:\frac12CV^2 = 2:1. \] Hence, \[ \boxed{2:1}. \] Thus, \[ \boxed{(D)} \] is the correct answer.