MHT-CET Physics Electrostatics PYQ - Capacitor Stored Energy

13) A capacitor of capacitance \( C \) has a charge \( Q \) and stores energy \( W \). If the charge is increased to \( 3Q \), then the stored energy becomes:

A. \( \frac{W}{3} \)

B. \( \frac{W}{6} \)

C. \( 3W \)

D. \( 9W \)

Solution:

The energy stored in a capacitor is given by: \[ W = \frac{Q^2}{2C}. \]

Initially, the stored energy is: \[ W = \frac{Q^2}{2C}. \]

If the charge is increased to \(3Q\), then the energy becomes: \[ W' = \frac{(3Q)^2}{2C} = \frac{9Q^2}{2C}. \]

Comparing with the original energy, \[ W' = 9 \times \frac{Q^2}{2C} = 9W. \]

Thus, the stored energy increases to \( 9W \), so the correct answer is option D.