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  4. If the rms value of current i=3+4 sin (ω t+π / 3) is x ampere, then find x2.

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

Alternating Current

Solution:

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