Question

If the rms value of current $i=3+4\sin (\omega t+\pi /3)$ is $x$ ampere, then find $x^2$.

Answer 1

Answer: 17

$i=3+4\sin (\omega t+\pi /3)$
$i^2=9+16{\sin }^2(\omega t+\pi /3)+24\sin (\omega t+\pi /3)$
$<i^2>=9+16\left(\frac{1}{2}\right)+24[0]$
$=9+16\left(\frac{1}{2}\right)=17$
$\therefore$ Rms value $=\sqrt{17}A$