Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 44 of 127
What is the mathematical expression for the capacitive reactance \(X_C\) of a capacitor of capacitance \(C\) connected to an AC source of frequency \(f\)?
A
\(X_C = \frac{1}{2\pi f C}\)
B
\(X_C = 2\pi f C\)
C
\(X_C = \frac{2\pi f}{C}\)
D
\(X_C = \frac{C}{2\pi f}\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \(X_C = \frac{1}{2\pi f C}\)
Concept:

Capacitive reactance \(X_C\) is the effective opposition offered by a capacitor to alternating current, measured in ohms (\(\Omega\)).

Formula / Reaction:

$$X_C = \frac{V_0}{I_0} = \frac{1}{\omega C} = \frac{1}{2\pi f C}$$

Solution:

  • Using \(q = C v = C V_0 \sin(\omega t)\), the current is \(i = \frac{dq}{dt} = \omega C V_0 \cos(\omega t)\).


  • The peak current amplitude is \(I_0 = \omega C V_0\).


  • Reactance \(X_C = \frac{V_0}{I_0} = \frac{1}{\omega C} = \frac{1}{2\pi f C}\).


Why other options are incorrect:

  • Opt_B: \(2\pi f C\) is capacitive susceptance \(B_C = 1/X_C\), not reactance.


  • Opt_C: Inverts the placement of capacitance.


  • Opt_D: Inverts the placement of 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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