Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 18 of 127
Which of the following mathematical relationships between peak voltage \( V_0 \) and RMS voltage \( V_{\text{rms}} \) in a sinusoidal AC circuit is correct?
A
\( V_0 = 10.10 \times V_{\text{rms}} \)
B
\( V_0 = 1.414 \times V_{\text{rms}} \)
C
\( V_0 = 10.70 \times V_{\text{rms}} \)
D
\( V_0 = 0.707 \times V_{\text{rms}} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( V_0 = 1.414 \times V_{\text{rms}} \)
Concept:

RMS (root-mean-square) voltage represents the effective value of a sinusoidal alternating voltage wave.

Formula:

$$V_{\text{rms}} = \frac{V_0}{\sqrt{2}} \implies V_0 = \sqrt{2} \times V_{\text{rms}}$$

Solution:

The mathematical value of the square root of 2 is:

$$\sqrt{2} \approx 1.414$$

Substitute this value into the equation:

$$V_0 = 1.414 \times V_{\text{rms}}$$

Why other options are incorrect:

  • \( 0.707 \times V_{\text{rms}} \) represents an incorrect inversion, as \( 0.707 = \frac{1}{1.414} \), which means \( V_{\text{rms}} = 0.707 \times V_0 \).


  • Other values are mathematically incorrect.

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