Question

The average value of current $i=I_m\sin \omega t$ from $t=\frac{\pi }{2\omega }$ to $t=\frac{3\pi }{2\omega }$ is how many times of $I_m?$

Answer 1

Answer: 0

$<i>=\frac{\underset{\pi /2\omega }{\overset{3\pi /2\omega }{\int }}{I}_m\sin \omega tdt}{\frac{3\pi }{2\omega }-\frac{\pi }{2\omega }}$
$=\frac{I_m{\left(-\frac{\cos \omega t}{\omega }\right)}_{\pi /2\omega }^{3\pi /2\omega }}{\frac{\pi }{\omega }}=0$