Physics - EMI/AC Question with Solution | TestHub

$\mathrm{i}=\left({\mathrm{i}}_1\right)\cos \mathrm{\omega t}+\left({\mathrm{i}}_2\right)\sin \mathrm{\omega t}$

${\left({\mathrm{i}}^2\right)}_{\mathrm{mean}}={\mathrm{i}}_1^2 \overline{{\cos }^2\mathrm{\omega t}}+{\mathrm{i}}_2^2 \overline{{\sin }^2\mathrm{\omega t}}+{\mathrm{i}}_1{\mathrm{i}}_2 \overline{\cos \mathrm{\omega t} \mathrm{sin\; \omega t}}$

${\mathrm{i}}_1^2\times \frac{1}{2}\times {\mathrm{i}}_2^2\times \frac{1}{2}+2{\mathrm{i}}_1{\mathrm{i}}_2\times 0$

${\mathrm{i}}_{\mathrm{rms}}=\sqrt{{\left({\mathrm{i}}^2\right)}_{\mathrm{mean}}}=\sqrt{\frac{{\mathrm{i}}_1^2+{\mathrm{i}}_2^2}{2}}$