Question

An alternating current is given by $I=I_1\cos \omega t+I_2\sin \omega t$. The RMS value of current is given by?

• A. $\frac{I_1+I_2}{\sqrt{2}}$
• B. $\frac{{(I_1+I_2)}^2}{2}$
• C. $\sqrt{\frac{I_1^2+I_2^2}{2}}$
• D. $\frac{\sqrt{I_1^2+I_2^2}}{2}$

Answer 1

The correct option is C $\sqrt{\frac{I_1^2+I_2^2}{2}}$

$I=I_{1}cos\omega t+I_{2}sin\omega t$

$I=\sqrt{I_1^2+I_2^2+I_1{I}_{2}cos90\circ }$

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

$I_{rms}=\frac{I}{\sqrt{2}}$

$I_{rms}=\frac{\sqrt{{I_1}^2+I_2^2}}{\sqrt{2}}$

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