A capacitor of capacitance C is charged to a voltage V. If the voltage is halved

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Question: A capacitor of capacitance C is charged to a voltage V. If the voltage is halved, what is the new energy stored in the capacitor?

Options:

Correct Answer: U/4

Solution:

The energy stored in a capacitor is given by U = 1/2 CV². If the voltage is halved, the new energy becomes U\' = 1/2 C(V/2)² = U/4.

A capacitor of capacitance C is charged to a voltage V. If the voltage is halved, what is the new energy stored in the capacitor?

A capacitor of capacitance C is charged to a voltage V. If the voltage is halved, what is the new energy stored in the capacitor?

Correct Answer: U/4

Step 1: Understand that the energy stored in a capacitor is calculated using the formula U = 1/2 CV².
Step 2: Identify the initial voltage V and the capacitance C of the capacitor.
Step 3: Calculate the initial energy stored using the formula: U = 1/2 C(V)².
Step 4: Recognize that if the voltage is halved, the new voltage becomes V/2.
Step 5: Substitute the new voltage into the energy formula: U' = 1/2 C(V/2)².
Step 6: Simplify the equation: U' = 1/2 C(V²/4) = (1/4)(1/2 CV²).
Step 7: Conclude that the new energy U' is one-fourth of the original energy U, so U' = U/4.

Capacitance and Energy Storage – Understanding how the energy stored in a capacitor is related to its capacitance and the square of the voltage.
Voltage and Energy Relationship – Recognizing that energy is proportional to the square of the voltage applied across the capacitor.