Which expression gives the energy stored in a capacitor in terms of capacitance C and voltage V?

• A. U = (1/2) C V^2
• B. U = (1/2) Q V
• C. U = Q V
• D. U = Q^2 / (2 C)

Answer: (A)

When a capacitor is charged, energy is stored in the electric field created between its plates, and that energy comes from the work done to move charges onto the plates. For a small amount of charge dq being added, the incremental work is dU = V dq, since the voltage across the capacitor is the potential difference the charge experiences. With constant capacitance, the voltage relates to charge by V = q/C, so dU = (q/C) dq. Integrating from zero to the final charge Q gives U = ∫(q/C) dq = Q^2/(2C). Replacing Q with CV to express everything in terms of C and V yields U = (C V)^2/(2C) = (1/2) C V^2. This form shows the energy depends on both the capacitance and the square of the voltage. The other expressions, like (1/2) Q V or Q^2/(2C), are equivalent only when you use Q = C V; they’re not written purely in terms of C and V.