Question

In the given figure, if $i_1=3\sin \omega t$ and $i_2=4\cos \omega t$, then $i_3$ is $5\sin \left(\omega t+{\varphi }^{\circ }\right)$. Find $\varphi$.

Answer 1

Answer: 53

$i_3=i_1+i_2$
$=5\left(\frac{3}{5}\sin \omega t+\frac{4}{5}\cos \omega t\right)$
$=5\left(\sin \omega t\cdot \cos 53^{\circ }+\cos \omega t\cdot \sin 53^{\circ }\right)$
$=5\sin \left(\omega t+53^{\circ }\right)$