The energy stored in a capacitor is given by which formula?

• A. E = 1/2 C V^2.
• B. E = CV.
• C. E = QV.
• D. E = 2 C V^2.

Answer: (A)

When a capacitor is charged, the voltage across it rises as more charge is moved onto the plates, so the work done to charge it is not simply QV. The correct way to find the energy is to integrate the incremental work dW = V dq, with V = q/C. This gives W = ∫0^Q (q/C) dq = Q^2/(2C). Replacing Q with CV yields W = (1/2) C V^2, which is the energy stored. It can also be written as E = QV/2, since Q = CV. The other expressions don’t fit because they either assume a linear, not halved, relationship with the final voltage or charge, or double the correct amount of energy (for example, E = CV would be too large by a factor of 2, and E = QV would equal CV^2, which is twice the actual energy).