Physics Alternating Current PMDC Conceptual Practice
PMDC Verified Question 10 of 127
The instantaneous current in an AC circuit is given by the equation:

$$I = \sqrt{2} \sin(\omega t + \phi)\text{ Amperes}$$

What is the root-mean-square (RMS) value of this current?
A
2 A
B
1 A
C
\(\sqrt{2}\text{ A}\)
D
\(\frac{1}{\sqrt{2}}\text{ A}\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: 1 A
Concept:

The RMS value of a sinusoidal current wave is calculated directly from its peak value.

Formula:

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

Solution:

Given current equation: \( I = \sqrt{2} \sin(\omega t + \phi) \).

Comparing this with the standard format \( I = I_0 \sin(\omega t + \phi) \), the peak current amplitude is:

$$I_0 = \sqrt{2}\text{ A}$$

Calculate the RMS current value:

$$I_{\text{rms}} = \frac{\sqrt{2}}{\sqrt{2}} = 1\text{ A}$$

Why other options are incorrect:

  • \( \sqrt{2}\text{ A} \) is the peak current value, not the RMS value.


  • Other values like \( 2\text{ A} \) or \( \frac{1}{\sqrt{2}}\text{ A} \) are mathematically incorrect.

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