Physics Electrostatics ETEA 2023
PMDC Verified Question 49 of 131
Q.166 If both the plate area and the plate separation of a parallel-plate capacitor are doubled, the capacitance is:
A
Doubled
B
Halved
C
Unchanged
D
Tripled
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: Unchanged
1. Concept:

Capacitance geometry relies on a ratio. Altering the top and bottom of that ratio identically results in perfect mathematical cancellation.

2. Formula:

$$ C = \frac{\epsilon_0 A}{d} $$

3. Solution:

  • The original capacitance is \( C = \frac{\epsilon_0 A}{d} \).


  • The area is doubled: \( A' = 2A \).


  • The separation is doubled: \( d' = 2d \).


  • Substitute: \( C' = \frac{\epsilon_0 (2A)}{2d} \).


  • The '2' in the numerator perfectly cancels the '2' in the denominator, leaving \( C' = C \), meaning the net capacitance remains entirely unchanged.


4. Why other options are incorrect:

Capacitance would double if only Area was doubled. It would halve if only Separation was doubled. Modifying both identically nullifies the change.

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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