Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 47 of 127
An alternating voltage source is described by \(V(t) = 141.4 \sin(314 t)\text{ volts}\). What are the root-mean-square voltage \(V_{\text{rms}}\) and frequency \(f\) of this source?
A
\(141.4\text{ V}, 100\text{ Hz}\)
B
\(141.4\text{ V}, 50\text{ Hz}\)
C
\(100\text{ V}, 50\text{ Hz}\)
D
\(100\text{ V}, 314\text{ Hz}\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \(100\text{ V}, 50\text{ Hz}\)
Concept:

Compare the given voltage equation directly to the standard sinusoidal equation \(V(t) = V_0 \sin(2\pi f t)\).

Formula / Reaction:

$$V_{\text{rms}} = \frac{V_0}{\sqrt{2}}, \quad f = \frac{\omega}{2\pi}$$

Solution:

  • Peak voltage: \(V_0 = 141.4\text{ V}\).


  • \(V_{\text{rms}} = \frac{141.4}{1.414} = 100\text{ V}\).


  • Angular frequency: \(\omega = 314\text{ rad/s}\).


  • \(f = \frac{314}{2\pi} = \frac{314}{6.283} = 50\text{ Hz}\).


Why other options are incorrect:

  • Opt_A, Opt_B: Incorrectly use the peak voltage \(141.4\text{ V}\) as the RMS value.


  • Opt_D: Confuses angular frequency \(\omega = 314\text{ rad/s}\) with linear frequency in \(\text{Hz}\).

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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