What is the energy stored in a charged capacitor?

What is the energy stored in a charged capacitor?

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

Answer: (A)

Energy stored in a capacitor is the work required to assemble the charges against the electric field between the plates. If the capacitor carries charge Q, the voltage is V = Q/C. The small amount of work to add a bit of charge dq is V dq, so the total energy is U = ∫ from 0 to Q of V(q) dq = ∫0^Q (q/C) dq = Q^2/(2C). Substituting Q = CV gives U = (1/2) C V^2. This shows the same energy can be written in multiple equivalent forms, such as (1/2) C V^2, or (1/2) QV, or Q^2/(2C). In the given context, the standard form in terms of C and V is (1/2) C V^2, which is why that option is correct.

Energy stored in a capacitor is the work required to assemble the charges against the electric field between the plates. If the capacitor carries charge Q, the voltage is V = Q/C. The small amount of work to add a bit of charge dq is V dq, so the total energy is U = ∫ from 0 to Q of V(q) dq = ∫0^Q (q/C) dq = Q^2/(2C). Substituting Q = CV gives U = (1/2) C V^2.

This shows the same energy can be written in multiple equivalent forms, such as (1/2) C V^2, or (1/2) QV, or Q^2/(2C). In the given context, the standard form in terms of C and V is (1/2) C V^2, which is why that option is correct.