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

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

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

Answer: (C)

The energy stored in a capacitor can be written as U = (1/2) C V^2. To express it in terms of charge Q and capacitance C, use the relation V = Q/C. Substituting gives U = (1/2) C (Q/C)^2 = Q^2/(2C). So the energy in terms of Q and C is U = Q^2/(2C). This also matches the form U = (1/2) QV since V = Q/C, which yields U = (1/2) Q (Q/C) = Q^2/(2C). The other expressions do not fit: U = QV would overcount the energy by a factor of 2, and U = C Q^2 has incorrect units for energy.

The energy stored in a capacitor can be written as U = (1/2) C V^2. To express it in terms of charge Q and capacitance C, use the relation V = Q/C. Substituting gives U = (1/2) C (Q/C)^2 = Q^2/(2C). So the energy in terms of Q and C is U = Q^2/(2C). This also matches the form U = (1/2) QV since V = Q/C, which yields U = (1/2) Q (Q/C) = Q^2/(2C). The other expressions do not fit: U = QV would overcount the energy by a factor of 2, and U = C Q^2 has incorrect units for energy.