Question

An alternating current is given by $I = I _{1} \cos \omega t +I_{2} \sin \omega t$, the root mean square current is given by

• A. $\frac{I_{1}+I_{2}}{\sqrt{2}}$
• B. $\frac{\left|I_{1}+I_{2}\right|}{2}$
• C. $\sqrt{\frac{I_{1}^{2}+I_{2}^{2}}{2}}$
• D. $\frac{\sqrt{I_{1}^2+I_{2}^{2}}}{2}$

Answer 1

Answer: (C)

The equation of alternating current (AC) is given by
$I=I_{1} \cos \omega t+I_{2} \sin \omega t$
The resultant current
$I_{0}=\sqrt{I_{1}{ }^{2}+I_{2}{ }^{2}}$
Also, $rms$ value of current is given by
$I_{ rms } =\frac{I_{0}}{\sqrt{2}}$
$\Rightarrow I_{ rms } =\sqrt{\frac{I_{1}{ }^{2}+I_{2}{ }^{2}}{2}}$