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

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

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

Answer: (A)

Energy stored in a capacitor comes from the work needed to move charge onto the plates as the voltage rises. The incremental work is dU = V dQ. For a capacitor with constant capacitance, Q = C V, so dQ = C dV. Substituting gives dU = C V dV, and integrating from 0 to the final voltage V yields U = ∫0^V C V' dV' = (1/2) C V^2. This also matches the form U = (1/2) Q V since Q = C V, but expressed in terms of C and V the correct expression is (1/2) C V^2. The other forms either miss the 1/2 factor or have the wrong dependence, so they don’t describe the energy correctly.

Energy stored in a capacitor comes from the work needed to move charge onto the plates as the voltage rises. The incremental work is dU = V dQ. For a capacitor with constant capacitance, Q = C V, so dQ = C dV. Substituting gives dU = C V dV, and integrating from 0 to the final voltage V yields U = ∫0^V C V' dV' = (1/2) C V^2. This also matches the form U = (1/2) Q V since Q = C V, but expressed in terms of C and V the correct expression is (1/2) C V^2. The other forms either miss the 1/2 factor or have the wrong dependence, so they don’t describe the energy correctly.