Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 2 of 127
A capacitor and an inductor are connected to an AC supply. If we double the frequency of the AC supply, then the effect on capacitive reactance \( X_C \) and inductive reactance \( X_L \) will be:
A
Both \( X_C \) and \( X_L \) are doubled
B
Both \( X_C \) and \( X_L \) are halved
C
\( X_L \) is doubled and \( X_C \) reduces to half
D
\( X_C \) is doubled and \( X_L \) reduces to half
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \( X_L \) is doubled and \( X_C \) reduces to half
Concept:

Reactance measures the frequency-dependent opposition of inductors and capacitors to alternating current.

Formula:

$$X_L = 2\pi f L$$

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

Solution:

If the new frequency is \( f' = 2f \):

  • For the Inductor:
    $$X_L' = 2\pi (2f) L = 2(2\pi f L) = 2 X_L$$
    Thus, \( X_L \) is doubled.


  • For the Capacitor:
    $$X_C' = \frac{1}{2\pi (2f) C} = \frac{1}{2} \left(\frac{1}{2\pi f C}\right) = \frac{X_C}{2}$$
    Thus, \( X_C \) reduces to half.


Why other options are incorrect:

  • Because \( X_L \) is directly proportional to frequency and \( X_C \) is inversely proportional, they cannot change in the same direction (e.g., both doubling or both halving).

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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