Physics Alternating Current ETEA 2015
PMDC Verified Question 104 of 127
An A.C current varies with time (t) sec as \(i = 4 \sin (200\pi t)\), the r.m.s value of current in ampere is:
A
2 A
B
\(4 \sqrt{2}\text{ A}\)
C
\(\frac{2}{\sqrt{2}}\text{ A}\)
D
\(2 \sqrt{2}\text{ A}\)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \(2 \sqrt{2}\text{ A}\)
Concept:

The root mean square (RMS) current of a sinusoidal wave is related to the peak current by \(I_{\text{rms}} = \frac{I_0}{\sqrt{2}}\).

Formula / Reaction:

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

Solution:

  • From the equation \(i = 4 \sin(200\pi t)\), peak current \(I_0 = 4\text{ A}\).


  • \(I_{\text{rms}} = \frac{4}{\sqrt{2}} = \frac{2 \times 2}{\sqrt{2}} = 2\sqrt{2}\text{ A}\).


Why other options are incorrect:

  • Opt_A: \(2\text{ A}\) incorrectly divides \(I_0\) by \(2\) instead of \(\sqrt{2}\).


  • Opt_B: Multiplies \(I_0\) by \(\sqrt{2}\) instead of dividing.


  • Opt_C: While \(4/\sqrt{2}\) is mathematically equivalent to \(2\sqrt{2}\), the simplified textbook form \(2\sqrt{2}\) is the standard final answer.

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