Question:
An alternating current is given by the equation $\mathrm{i}=\mathrm{i}_{1} \sin \omega \mathrm{t}+\mathrm{i}_{2} \cos \omega \mathrm{t}$. The rms current will be
Correct Option: 1
Solution:
$\mathrm{i}=\mathrm{i}_{1} \sin \omega \mathrm{t}+\mathrm{i}_{2} \sin (\omega \mathrm{t}+90)$
$\mathrm{i}=\sqrt{\mathrm{i}_{1}^{2}+\mathrm{i}_{2}^{2}} \sin (\omega \mathrm{t}+\phi)$
$\mathrm{i}_{\mathrm{rms}}=\frac{\mathrm{i}_{0}}{\sqrt{2}}=\frac{\sqrt{\mathrm{i}_{1}^{2}+\mathrm{i}_{2}^{2}}}{\sqrt{2}}$
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