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

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

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

The given AC circuit is expressed as -

$i=i_1\cos(ωt)+i_2\sin(ωt)$

Also,

$i_{rms}=\sqrt{<i^2>}$

$=\sqrt{\frac{A^2}{2}+\frac{B^2}{2}}$

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