Question

An alternating current having peak value 14.14 A is used to heat a metal wire. The value of the direct current \(i\) required to produce the same heating effect in the same wire is

• A. 0.707 A
• B. 28.28 A
• C. 7.07 A
• D. 10 A
• E. 14 A
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Hint:

The RMS value of an AC is crucial for calculating equivalent heating effects, power ratings, and other practical aspects of electrical circuits.

Answer 1

The Correct Option is D

Step 1: The heating effect of a current is given by \(I_{rms}^2 R\), where \(I_{rms}\) is the root mean square current. 
Step 2: For an AC current with a peak value \(I_p = 14.14 A\), \(I_{rms} = \frac{I_p}{\sqrt{2}} = \frac{14.14}{\sqrt{2}} = 10 A\). 
Step 3: To achieve the same heating effect with DC, the DC current must equal the RMS value of the AC current. 
Step 4: Therefore, the direct current required is 10 A.