Question

The peak value of an alternating current is 10 A. Its root mean square value will be?

• A. 5 A
• B. 7.07 A
• C. 10 A
• D. 14.14 A

Hint:

RMS value = Peak value / \(\sqrt{2}\) for sinusoidal AC.

Answer 1

The Correct Option is B

Step 1: Formula for Root Mean Square (RMS) value.
The relationship between the peak value (\(I_0\)) and the root mean square (RMS) value (\(I_{\text{rms}}\)) for alternating current is given by: \[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \] where \(I_0 = 10 \, \text{A}\) is the peak current.
Step 2: Calculate the RMS value.
Substitute the peak value into the formula: \[ I_{\text{rms}} = \frac{10}{\sqrt{2}} \approx 7.07 \, \text{A} \]
Step 3: Analyze options.
- (A) 5 A: Incorrect. This is not the RMS value.
- (B) 7.07 A: Correct. This is the RMS value for a peak value of 10 A.
- (C) 10 A: Incorrect. The peak value is given, not the RMS value.
- (D) 14.14 A: Incorrect. This is the value for the peak value itself.
Step 4: Conclusion.
The RMS value of the current is 7.07 A.