Question

An alternating current is given by the equation $i = i _{1} \sin \omega t + i _{2}$ cos $\omega t$ The rms current will be

• A. $\frac{1}{\sqrt{2}}\left(i_{1}^{2}+i_{2}^{2}\right)^{\frac{1}{2}}$
• B. $\frac{1}{\sqrt{2}}\left( i _{1}+ i _{2}\right)^{2}$
• C. $\frac{1}{2}\left(i_{1}^{2}+i_{2}^{2}\right)^{\frac{1}{2}}$
• D. $\frac{1}{\sqrt{2}}\left( i _{1}+ i _{2}\right)$

Answer 1

Answer: (A)

$i = i _{1} \sin \omega t + i _{2} \sin (\omega t +90)$
$i =\sqrt{ i _{1}^{2}+ i _{2}^{2}} \sin (\omega t +\phi)$
$i _{ rms }=\frac{ i _{0}}{\sqrt{2}}=\frac{\sqrt{ i _{1}^{2}+ i _{2}^{2}}}{\sqrt{2}}$