Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 23 of 127
What is the angular frequency (\(\omega\)) of an alternating current operating at a frequency of \(50\text{ Hz}\)?
A
\(100\pi\text{ rad/s}\)
B
\(50\pi\text{ rad/s}\)
C
\(25\pi\text{ rad/s}\)
D
\(200\pi\text{ rad/s}\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \(100\pi\text{ rad/s}\)
Concept:

Angular frequency \(\omega\) is the rate of change of phase angle per unit time and is related to linear frequency \(f\) by \(\omega = 2\pi f\).

Formula / Reaction:

$$\omega = 2\pi f$$

Solution:

  • Given \(f = 50\text{ Hz}\):


  • \(\omega = 2\pi(50) = 100\pi\text{ rad/s} \approx 314.16\text{ rad/s}\).


Why other options are incorrect:

  • Opt_B: \(50\pi\text{ rad/s}\) omits the factor of 2.


  • Opt_C: \(25\pi\text{ rad/s}\) divides frequency by 2 instead of multiplying.


  • Opt_D: \(200\pi\text{ rad/s}\) corresponds to a frequency of \(100\text{ Hz}\).

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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