Question

An alternating current is given by the equation $i=i_{1}cos\omega t+i_{2}sin\omega t$. The r.m.s. current is given by

• A. $\frac{1}{\sqrt{2}}(i_1+i_2)$
• B. $\frac{1}{\sqrt{2}}(i_1+i_2{)}^2$
• C. $\frac{1}{\sqrt{2}}(i_1^2+i_2^2{)}^{\frac{1}{2}}$
• D. $\frac{1}{2}(i_1^2+i_2^2{)}^{\frac{1}{2}}$

Answer 1

The correct option is C $\frac{1}{\sqrt{2}}(i_1^2+i_2^2{)}^{\frac{1}{2}}$

$i_{rms}=\sqrt{\frac{i_1^2+i_2^2}{2}}=\frac{1}{\sqrt{2}}(i_1^2+i_2^2{)}^{\frac{1}{2}}$