If the potential difference across a capacitor is halved, what happens to the en

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Question: If the potential difference across a capacitor is halved, what happens to the energy stored in the capacitor? (2019)

Options:

Correct Answer: Halved

Exam Year: 2019

Solution:

The energy stored in a capacitor is given by U = 1/2 CV^2. If V is halved, the energy becomes U\' = 1/2 C(V/2)^2 = 1/8 CV^2, which is halved.

If the potential difference across a capacitor is halved, what happens to the energy stored in the capacitor? (2019)

If the potential difference across a capacitor is halved, what happens to the energy stored in the capacitor? (2019)

Step 1: Understand the formula for energy stored in a capacitor, which is U = 1/2 CV^2, where U is energy, C is capacitance, and V is voltage (potential difference).
Step 2: Identify that if the potential difference V is halved, we can express this as V' = V/2.
Step 3: Substitute V' into the energy formula: U' = 1/2 C(V/2)^2.
Step 4: Simplify the equation: U' = 1/2 C(V^2/4) = (1/2 C V^2) / 4.
Step 5: Recognize that 1/2 C V^2 is the original energy U, so U' = U / 4.
Step 6: Conclude that when the potential difference is halved, the energy stored in the capacitor becomes one-fourth of the original energy.

Capacitor Energy Storage – Understanding the relationship between voltage, capacitance, and energy stored in a capacitor, specifically the formula U = 1/2 CV^2.
Effect of Voltage Change – Analyzing how changes in voltage affect the energy stored in a capacitor, particularly when voltage is halved.