What is the energy stored in a capacitor when voltage V is across it and the capacitance is C?

• A. W_C = 1/2 C V^2
• B. W_C = C V^2
• C. W_C = 1/2 L V^2
• D. W_C = 2 C V^2

Answer: (A)

When a capacitor stores energy, that energy comes from the work done to move charge onto the plates as the capacitor charges. The incremental work is V dq, and the total energy is W = ∫0^Q V dq. Since the voltage across a capacitor is V = q/C, substitute and integrate: W = ∫0^Q (q/C) dq = Q^2/(2C). With Q = CV, this becomes W = (1/2) C V^2. So the energy stored is one-half times the capacitance times the voltage squared.

The other forms don’t fit: using an inductance with voltage would describe energy in an inductor, not a capacitor; dropping the 1/2 factor gives the wrong magnitude; and forms like 2 C V^2 or C V^2 without the 1/2 don’t match the actual charging work calculation.