The energy stored in a capacitor with charge Q and capacitance C is:

The energy stored in a capacitor with charge Q and capacitance C is:

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

Answer: (C)

The energy stored in a capacitor is the work required to assemble the charge on the plates. As you add a small amount of charge dq, the voltage across the plates is V = q/C, so the incremental work is dW = V dq = (q/C) dq. Integrating from zero to the final charge Q gives U = ∫0^Q (q/C) dq = Q^2/(2C). This shows energy depends on the charge and the capacitance as U = Q^2/(2C). You can also write it as (1/2) QV or (1/2) C V^2 by using V = Q/C, and all forms are equivalent.

The energy stored in a capacitor is the work required to assemble the charge on the plates. As you add a small amount of charge dq, the voltage across the plates is V = q/C, so the incremental work is dW = V dq = (q/C) dq. Integrating from zero to the final charge Q gives U = ∫0^Q (q/C) dq = Q^2/(2C). This shows energy depends on the charge and the capacitance as U = Q^2/(2C). You can also write it as (1/2) QV or (1/2) C V^2 by using V = Q/C, and all forms are equivalent.