Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 28 of 127
If the frequency of an alternating current supply is doubled, the capacitive reactance \(X_C\) of a connected capacitor will:
A
Double
B
Halve
C
Quadruple
D
Remain constant
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: Halve
Concept:

Capacitive reactance is inversely proportional to the frequency of the alternating current source.

Formula / Reaction:

$$X_C = \frac{1}{2\pi f C} \implies X_C \propto \frac{1}{f}$$

Solution:

  • Let initial reactance be \(X_C = \frac{1}{2\pi f C}\).


  • When frequency is doubled (\(f' = 2f\)):


  • \(X_C' = \frac{1}{2\pi (2f) C} = \frac{1}{2} \left(\frac{1}{2\pi f C}\right) = \frac{X_C}{2}\).


  • Thus, capacitive reactance is reduced to half its initial value.


Why other options are incorrect:

  • Opt_A: Inductive reactance \(X_L\) doubles, but \(X_C\) is halved.


  • Opt_C: Quadrupling would require an inverse-square dependence, which is not the case.


  • Opt_D: Reactance changes inversely with frequency.

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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