An AC current is given by $i=i_1 \cos \omega t+i_2 \sin \omega t$. The rms current is given by:

$\frac{1}{\sqrt{2}}\left(i_1+i_2\right)$ $\frac{1}{\sqrt{2}}\left(i_1+i_2\right)^2$ $\frac{1}{\sqrt{2}}\left(i_1^2+i_2^2\right)^{\frac{1}{2}}$ $\frac{1}{2}\left(i_1^2+i_2^2\right)^{\frac{1}{2}}$

$\frac{1}{\sqrt{2}}\left(i_1^2+i_2^2\right)^{\frac{1}{2}}$

The correct answer is Option (3) → $\frac{1}{\sqrt{2}}\left(i_1^2+i_2^2\right)^{\frac{1}{2}}$