A capacitor with capacitance C is charged to voltage V. Which expression represents the energy stored?

• A. QV
• B. 1/2 C V^2
• C. C^2 V
• D. V^2/(2C)

Answer: (B)

The energy stored in a charged capacitor comes from the work done to move charge onto the plates. As you add a small amount of charge dq, you have to do work dW = V dq at the current voltage V. Since the voltage during charging is V = q/C, the total energy is E = ∫ from 0 to Q of (q/C) dq = Q^2/(2C). Substituting Q = C V gives E = (1/2) C V^2.

So the correct expression is the one that shows energy scaling with the square of the voltage and with the capacitance, (1/2) C V^2. The other forms don’t match this relationship or units; for example, QV represents the work done by the source, not the energy stored, and the remaining forms do not align with the integral result.