Question

An alternating current having a peak value of $14A$ is used to heat a metal wire. To produce the same heating effect, a constant current $I$ can be used, where $I$ is

• A. $14A$
• B. About $20A$
• C. $7A$
• D. About $10A$

Answer 1

The correct option is D

About $10A$

Step 1: Given

Peak Value of current: $I_p=14A$

Step 2: Formula Used

$I_{rms}=\frac{I_p}{\sqrt{2}}$

Step 3: Calculate the root mean square, since the rms of AC is equal to constant current

$$\begin{gathered} I_{rms}=\frac{I_p}{\sqrt{2}} \\ =\frac{14A}{\sqrt{2}} \\ =9.9A \\ \approx 10A \end{gathered}$$

Hence, Option(D) is correct. the constant current will be around $10A$.