Question

An alternating current is given by $i=i_{1}cos\omega t+i_{2}sin\omega t$ . The value of rms current is

• A. $\frac{i_1+i_2}{\sqrt{2}}$
• B. $\frac{|i_1+i_2|}{\sqrt{2}}$
• C. $\sqrt{\frac{i_1^2+i_2^2}{2}}$
• D. $\sqrt{\frac{i_1^2+i_2^2}{\sqrt{2}}}$

Answer 1

Answer: (C)

$i=\left(i_1\right)cos\omega t+\left(i_2\right)sin\omega t$
${\left(i^2\right)}_{\text{mean }}=i_1^2\overline{{\cos }^2\omega t}+i_2^2\overline{{\sin }^2\omega t}+i_1{i}_2\overline{\cos \omega t\sin \omega t}$
$i_1^2\times \frac{1}{2}\times i_2^2\times \frac{1}{2}+2i_1{i}_2\times 0$
$i_{rms}=\sqrt{{\left(i^2\right)}_{mean}}=\sqrt{\frac{i_1^2+i_2^2}{2}}$