If the potential difference across a capacitor is doubled, what happens to the s

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Question: If the potential difference across a capacitor is doubled, what happens to the stored energy?

Options:

Correct Answer: It quadruples

Solution:

Energy stored in a capacitor is given by U = 1/2 C V^2. If V is doubled, U becomes 1/2 C (2V)^2 = 2CV^2, which is quadrupled.

If the potential difference across a capacitor is doubled, what happens to the stored energy?

If the potential difference across a capacitor is doubled, what happens to the stored energy?

Step 1: Understand that the energy stored in a capacitor is calculated using the formula U = 1/2 C V^2, where U is the energy, C is the capacitance, and V is the voltage (potential difference).
Step 2: Identify what happens when the voltage (V) is doubled. If V becomes 2V, we need to substitute this into the energy formula.
Step 3: Substitute 2V into the formula: U = 1/2 C (2V)^2.
Step 4: Calculate (2V)^2, which equals 4V^2.
Step 5: Now substitute this back into the energy formula: U = 1/2 C (4V^2).
Step 6: Simplify the equation: U = 2 (1/2 C V^2).
Step 7: Notice that 2 (1/2 C V^2) means the energy has doubled, so the stored energy is now 4 times the original energy.

Capacitor Energy Storage – The energy stored in a capacitor is proportional to the square of the voltage across it, as described by the formula U = 1/2 C V^2.