For a capacitor with fixed capacitance C, if the charge on the plates is doubled, what happens to the stored energy?

For a capacitor with fixed capacitance C, if the charge on the plates is doubled, what happens to the stored energy?

• A. It doubles
• B. It quadruples
• C. It remains the same
• D. It halves

Answer: (B)

The stored energy in a capacitor with fixed capacitance is proportional to the square of the charge: U = Q^2/(2C) (or equivalently U = (1/2) C V^2). If you double the charge, the voltage also doubles since V = Q/C. Because energy depends on the square of the voltage, doubling the voltage makes the energy increase by a factor of four. So the new energy is four times the original: U' = 4U.

The stored energy in a capacitor with fixed capacitance is proportional to the square of the charge: U = Q^2/(2C) (or equivalently U = (1/2) C V^2). If you double the charge, the voltage also doubles since V = Q/C. Because energy depends on the square of the voltage, doubling the voltage makes the energy increase by a factor of four. So the new energy is four times the original: U' = 4U.