If the charge on a capacitor is doubled, what happens to the energy stored in it?

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Q: If the charge on a capacitor is doubled, what happens to the energy stored in it?

Solution: The energy stored in a capacitor is given by U = 1/2 * C * V^2. If the charge is doubled, the energy stored quadruples.

Steps: 10

Step 1: Understand that a capacitor stores energy based on its charge and voltage.
Step 2: Know the formula for energy stored in a capacitor: U = 1/2 * C * V^2, where U is energy, C is capacitance, and V is voltage.
Step 3: Recognize that charge (Q) on a capacitor is related to voltage (V) by the formula Q = C * V.
Step 4: If the charge (Q) is doubled, then Q' = 2Q.
Step 5: Since Q = C * V, if Q is doubled, the new voltage (V') will also change. We can express the new voltage as V' = Q' / C = (2Q) / C = 2V.
Step 6: Substitute the new voltage (V') into the energy formula: U' = 1/2 * C * (2V)^2.
Step 7: Calculate (2V)^2, which equals 4V^2.
Step 8: Now substitute this back into the energy formula: U' = 1/2 * C * 4V^2.
Step 9: Simplify the equation: U' = 2 * (1/2 * C * V^2) = 2U.
Step 10: Conclude that if the charge is doubled, the energy stored in the capacitor quadruples.