State the energy stored in a capacitor in terms of C and V.

State the energy stored in a capacitor in terms of C and V.

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

Answer: (B)

The energy stored in a capacitor comes from the work needed to move charge onto the plates against the electric field. This energy can be found by integrating the voltage times the incremental charge: U = ∫ V dQ. For a capacitor, V = Q/C, so building up charge from zero to Q gives U = ∫_0^Q (Q'/C) dQ' = Q^2/(2C). Substituting Q = C V yields U = (1/2) C V^2. This form is the one asked for, expressed purely in terms of C and V. The other equivalent expressions, U = Q^2/(2C) and U = (1/2) QV, are the same amount of energy written with Q instead of V.

The energy stored in a capacitor comes from the work needed to move charge onto the plates against the electric field. This energy can be found by integrating the voltage times the incremental charge: U = ∫ V dQ. For a capacitor, V = Q/C, so building up charge from zero to Q gives U = ∫_0^Q (Q'/C) dQ' = Q^2/(2C). Substituting Q = C V yields U = (1/2) C V^2. This form is the one asked for, expressed purely in terms of C and V. The other equivalent expressions, U = Q^2/(2C) and U = (1/2) QV, are the same amount of energy written with Q instead of V.