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

Resultant Current $I$ is given as,

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

$I_{rms}=\frac{1}{\sqrt{2}}=\sqrt{\frac{I_1^2+I_2^2}{2}}$