Which formula gives the energy stored in a capacitor?

Which formula gives the energy stored in a capacitor?

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

Answer: (D)

Energy stored in a capacitor comes from the electric field between its plates and depends on how much charge is on the plates and the voltage across them. For a capacitor with capacitance C and voltage V, the energy stored is E = (1/2) C V^2. This result comes from charging: the incremental work to move a small amount of charge dQ through the instantaneous voltage V = Q/C is dW = V dQ = (Q/C) dQ. Integrating from zero to the final charge Q gives E = ∫0^Q (Q'/C) dQ' = Q^2/(2C). Using Q = C V, this becomes E = (1/2) C V^2, also equal to E = (1/2) QV or E = Q^2/(2C). The 1/2 factor reflects that the voltage rises from 0 to V during charging, so the average voltage during the process is V/2.

Energy stored in a capacitor comes from the electric field between its plates and depends on how much charge is on the plates and the voltage across them. For a capacitor with capacitance C and voltage V, the energy stored is E = (1/2) C V^2. This result comes from charging: the incremental work to move a small amount of charge dQ through the instantaneous voltage V = Q/C is dW = V dQ = (Q/C) dQ. Integrating from zero to the final charge Q gives E = ∫0^Q (Q'/C) dQ' = Q^2/(2C). Using Q = C V, this becomes E = (1/2) C V^2, also equal to E = (1/2) QV or E = Q^2/(2C). The 1/2 factor reflects that the voltage rises from 0 to V during charging, so the average voltage during the process is V/2.