Question

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

• A. $\frac{i_{1} + i_{2}}{\sqrt{2}}$
• B. $\frac{\left|i_{1} + i_{2}\right|}{\sqrt{2}}$
• 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)

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