The energy stored in a capacitor of capacitance C charged to voltage V is?

The energy stored in a capacitor of capacitance C charged to voltage V is?

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

Answer: (B)

Energy stored in a capacitor comes from the work done to move charge onto the plates, which builds up the voltage as you charge it. The voltage across the plates is V = Q/C, so as you add a tiny amount of charge dq, the work required is dW = V dq. But V at that moment depends on how much charge you already have, V = q/C. To find the total energy, integrate from empty to full charge: U = ∫0^Q (q/C) dq = Q^2/(2C). Using Q = C V, this becomes U = (1/2) C V^2. Another way to see it is U = (1/2) QV, since the average voltage during charging is V/2. The factor 1/2 arises because the voltage increases from 0 to V as the capacitor charges.

Energy stored in a capacitor comes from the work done to move charge onto the plates, which builds up the voltage as you charge it. The voltage across the plates is V = Q/C, so as you add a tiny amount of charge dq, the work required is dW = V dq. But V at that moment depends on how much charge you already have, V = q/C. To find the total energy, integrate from empty to full charge: U = ∫0^Q (q/C) dq = Q^2/(2C). Using Q = C V, this becomes U = (1/2) C V^2. Another way to see it is U = (1/2) QV, since the average voltage during charging is V/2. The factor 1/2 arises because the voltage increases from 0 to V as the capacitor charges.