Question

An alternating current is given by $i=I_{1}sin\omega t+I_{2}cos\omega t$ Then, the rms current is given by

• A. $\frac{I_1+I_2}{\sqrt{2}}$
• B. $\sqrt{\frac{I_1+I_2}{2}}$
• C. $\sqrt{\frac{I_1^2+I_2^2}{\sqrt{2}}}$
• D. none of the above

Answer 1

The correct option is D none of the above

$i=I_1\sin \omega t+I_2\cos \omega t$

putting

$I_1=I\cos \varphi$

$I_2=I\sin \varphi$

where

$I=\sqrt{I_1^2+I_2^2}$

we get

$i=I(\cos \varphi \sin \omega t+\sin \varphi \cos \omega t)$

$i=I\sin (\omega t+\varphi )$

Now its a normal current equation for this

$i_{rms}=\frac{I}{\sqrt{2}}=\frac{\sqrt{I_1^2+I_2^2}}{\sqrt{2}}$.