Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 11 of 127
What is the mathematical expression for the root-mean-square (RMS) current of a sinusoidal alternating current wave if \( I_0 \) represents the peak current amplitude?
A
\(I_0\)
B
\(\sqrt{2}I_0\)
C
\(2I_0\)
D
\(\frac{I_0}{\sqrt{2}}\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \(\frac{I_0}{\sqrt{2}}\)
Concept:

This represents the conversion factor between peak values and effective values in sinusoidal AC waves.

Formula:

$$I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \approx 0.707 I_0$$

Solution:

The root-mean-square (RMS) value is mathematically derived as the square root of the average of the squares of the instantaneous values over one complete cycle. For any standard sinusoidal current, this yields:

$$I_{\text{rms}} = \frac{I_0}{\sqrt{2}}$$

Why other options are incorrect:

  • \( I_0 \) is the peak current.


  • \( \sqrt{2}I_0 \) would be a value higher than peak current, which is physically impossible for an RMS average.

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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