If the voltage across a capacitor is doubled while the capacitance remains the same, by what factor does the stored energy increase?

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Study for the UCF PHY2054 General Physics Exam. Use flashcards and multiple-choice questions complete with hints and explanations. Boost your understanding and get exam-ready!

Multiple Choice

If the voltage across a capacitor is doubled while the capacitance remains the same, by what factor does the stored energy increase?

Explanation:
Energy stored in a capacitor with fixed capacitance scales with the square of the voltage: U = (1/2) C V^2. If the voltage doubles, U' = (1/2) C (2V)^2 = 4 × (1/2) C V^2 = 4U. So the stored energy increases by a factor of 4. This comes from the voltage squared dependence; capacitance being constant means the only change is V, and squaring the voltage gives the fourfold increase.

Energy stored in a capacitor with fixed capacitance scales with the square of the voltage: U = (1/2) C V^2. If the voltage doubles, U' = (1/2) C (2V)^2 = 4 × (1/2) C V^2 = 4U. So the stored energy increases by a factor of 4. This comes from the voltage squared dependence; capacitance being constant means the only change is V, and squaring the voltage gives the fourfold increase.

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