Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 30 of 127
An AC voltage of constant amplitude is applied across a capacitor. If the capacitance \(C\) is doubled, the root-mean-square current \(I_{\text{rms}}\) through the capacitor will:
A
Double
B
Halve
C
Quadruple
D
Remain the same
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: Double
Concept:

The current through a purely capacitive AC circuit is directly proportional to capacitance for a fixed voltage and frequency.

Formula / Reaction:

$$I_{\text{rms}} = \frac{V_{\text{rms}}}{X_C} = V_{\text{rms}} (2\pi f C) \implies I_{\text{rms}} \propto C$$

Solution:

  • Capacitive reactance is halved when capacitance is doubled: \(X_C' = X_C / 2\).


  • Since \(I = V / X_C\), halving the reactance doubles the current: \(I' = 2I\).


Why other options are incorrect:

  • Opt_B: Halving current would occur if capacitance were halved.


  • Opt_C: Quadrupling is an incorrect non-linear scaling.


  • Opt_D: Current changes proportionally with capacitance.

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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