If the capacitance doubles while the voltage remains the same, what happens to the stored energy?

If the capacitance doubles while the voltage remains the same, what happens to the stored energy?

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

Answer: (A)

The stored energy in a capacitor with a fixed voltage is proportional to the capacitance, since U = (1/2) C V^2. If the capacitance doubles while the voltage stays the same, the energy becomes U' = (1/2) (2C) V^2 = 2 × [(1/2) C V^2], so the energy doubles. A larger capacitance at the same voltage means you can store more charge (Q = C V), and that extra charge translates into more electric field energy. For completeness, using U = Q^2/(2C) with V fixed gives the same result: Q doubles, and U increases by a factor of two.

The stored energy in a capacitor with a fixed voltage is proportional to the capacitance, since U = (1/2) C V^2. If the capacitance doubles while the voltage stays the same, the energy becomes U' = (1/2) (2C) V^2 = 2 × [(1/2) C V^2], so the energy doubles. A larger capacitance at the same voltage means you can store more charge (Q = C V), and that extra charge translates into more electric field energy. For completeness, using U = Q^2/(2C) with V fixed gives the same result: Q doubles, and U increases by a factor of two.