Which expression correctly gives the energy stored in a capacitor when the capacitance is C and the voltage across it is V?

Which expression correctly gives the energy stored in a capacitor when the capacitance is C and the voltage across it is V?

• A. W = 0.5 C V^2
• B. W = C V
• C. W = Q V
• D. W = C V^2

Answer: (A)

Energy stored in a capacitor comes from the work done to charge it. The work is W = ∫0^Q V dq. Since the voltage across a capacitor is V = q/C, this becomes W = ∫0^Q (q/C) dq = Q^2/(2C). Using Q = C V, that gives W = (1/2) C V^2. This matches the expression 0.5 C V^2. You can also write it as (1/2) QV, which is the same because Q = CV. The other forms either miss the 1/2 factor or don’t have the correct units for energy.

Energy stored in a capacitor comes from the work done to charge it. The work is W = ∫0^Q V dq. Since the voltage across a capacitor is V = q/C, this becomes W = ∫0^Q (q/C) dq = Q^2/(2C). Using Q = C V, that gives W = (1/2) C V^2. This matches the expression 0.5 C V^2. You can also write it as (1/2) QV, which is the same because Q = CV. The other forms either miss the 1/2 factor or don’t have the correct units for energy.