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

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Multiple Choice

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

Explanation:
The amount of energy stored in a capacitor depends on the voltage as E = (1/2) C V^2. If the voltage is doubled while the capacitance stays the same, plug in 2V: E' = (1/2) C (2V)^2 = 4 × (1/2) C V^2. So the stored energy becomes four times larger. This quadratic relationship means energy scales with the square of the voltage, not linearly.

The amount of energy stored in a capacitor depends on the voltage as E = (1/2) C V^2. If the voltage is doubled while the capacitance stays the same, plug in 2V: E' = (1/2) C (2V)^2 = 4 × (1/2) C V^2. So the stored energy becomes four times larger. This quadratic relationship means energy scales with the square of the voltage, not linearly.

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