Question

The energy stored in a capacitor \( C \) when a voltage \( V \) exists across it is:

• A. \( \dfrac{1}{2}CV^2 \)
• B. \( \dfrac{1}{2}VC^2 \)
• C. \( \dfrac{1}{2}CV \)
• D. \( \dfrac{1}{2}(CV)^2 \)

Hint:

Memorize the energy formula for capacitors: \( U = \frac{1}{2}CV^2 \). It’s a standard result used in many electrostatics problems.

Answer 1

The Correct Option is A

The energy stored in a capacitor \(C\) when a voltage \(V\) exists across it is calculated using the fundamental formula for capacitive energy storage:

\(E = \dfrac{1}{2}CV^2\)

Where:

• \(E\): Energy stored in the capacitor (joules)
• \(C\): Capacitance of the capacitor (farads)
• \(V\): Voltage across the capacitor (volts)

This equation derives from the integration of the voltage-charge relationship for a capacitor, and it represents the amount of energy stored as electrical potential energy.

From the given options, the correct expression for the energy stored in a capacitor is clearly provided by:

\( \dfrac{1}{2}CV^2 \)