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  4. The average value of current i=I m sin ω t from t=(π/2 ω) to t=(3 π/2 ω) is how many times of I m ?

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Q. 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 $I_{ m } ?$

Alternating Current

Solution:

$< i >=\frac{\int\limits_{\pi / 2 \omega}^{3 \pi / 2 \omega} I_{ m } \sin \omega t d t}{\frac{3 \pi}{2 \omega}-\frac{\pi}{2 \omega}}$
$=\frac{I_{m}\left(-\frac{\cos \omega t}{\omega}\right)_{\pi / 2 \omega}^{3 \pi / 2 \omega}}{\frac{\pi}{\omega}}=0$