Question

A capacitor of unknown capacitance \( C \) is connected across a battery of \( V \) volt. The charge stored in it becomes \( Q \) coulomb. When potential across the capacitor is reduced by \( V' \) volt, the charge stored in it becomes \( Q' \) coulomb. The capacitance \( C \) is

• A. \( \frac{Q - Q'}{\sqrt{V'}} \)
• B. \( \frac{V'}{Q - Q'} \)
• C. \( \frac{Q + Q'}{V'} \)
• D. \( \frac{Q - Q'}{V'} \)

Hint:

Capacitance is directly proportional to the charge stored and inversely proportional to the potential across the capacitor.

Answer 1

The Correct Option is D

Step 1: Understanding the capacitor's equation.
The capacitance of a capacitor is given by: \[ C = \frac{Q}{V} \] Where \( Q \) is the charge stored and \( V \) is the potential across the capacitor. The change in charge is proportional to the change in voltage, thus: \[ C = \frac{Q - Q'}{V - V'} \] Therefore, the capacitance is given by \( \frac{Q - Q'}{V'} \), and the correct answer is (D).