Physics Electrostatics NUMS 2022
PMDC Verified Question 84 of 131
Q.144 Energy stored in a capacitor is given by:
A
\( E = \frac{1}{2} CV^2 \)
B
\( E = 2CV^2 \)
C
\( E = CV^2 \)
D
\( E = CV \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \( E = \frac{1}{2} CV^2 \)
1. Concept:

The electrical potential energy is calculated by integrating the voltage across the capacitor as charge progressively builds up from zero to its maximum.

2. Formula:

$$ dU = V \cdot dQ \implies \int_0^Q \frac{q}{C} dq $$

3. Solution:

  • Integrating \( q/C \) yields \( \frac{Q^2}{2C} \).


  • Substituting \( Q = CV \) into that result gives the standard formula: \( E = \frac{1}{2} C V^2 \).


4. Why other options are incorrect:

Option C is missing the integral's \( 1/2 \) coefficient, representing a capacitor charging instantly at full voltage rather than ramping up. Option D evaluates strictly to Charge (\( Q \)), not Energy.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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