Question

The RMS value of AC is:

• A. \( 0.707 \times \text{Peak value} \)
• B. \( 1.414 \times \text{Peak value} \)
• C. \( 0.5 \times \text{Peak value} \)
• D. \( 1 \times \text{Peak value} \)

Hint:

The RMS value of AC is always \( 0.707 \) times the peak value for a sinusoidal wave.

Answer 1

The Correct Option is A

Step 1: Meaning of RMS value
The RMS value of an AC quantity represents its effective value in terms of power dissipation in a resistor, equivalent to a DC current.

Step 2: Sinusoidal AC relation
For a sine wave current:
\( I = I_0 \sin \omega t \) The RMS value is obtained by averaging the square over one complete cycle:
\( I_{\text{RMS}} = \frac{I_0}{\sqrt{2}} \)

Step 3: Final expression
\[ I_{\text{RMS}} = 0.707 \, I_0 \]

Final Answer:
Thus, RMS value equals \(0.707 \times\) peak value of AC.