Question

An alternating current having peak value $15\sqrt{2}\text{A}$ is used to heat a metal wire. To produce the same heating effect, a constant current $i$ can be used. The value of $i\left(\text{in A}\right)$ is (integer only)

Answer 1

Given :

For $AC$, $i_{peak}=15\sqrt{2}\text{A}$

The root mean square value of current is

$i_{rms}=\frac{i_{peak}}{\sqrt{2}}$

$\Rightarrow i_{rms}=\frac{15\sqrt{2}}{\sqrt{2}}=15\text{A}$

A $DC$ current $i$ will produce the same heating effect as $AC$ current, when the $DC$ current $i$ is equal to the root mean square value of $AC$ current.

$\therefore i=i_{rms}$

$\Rightarrow i=15\text{A}$