Question

The r.m.s. value of current for a variable current $i=i_1\cos \omega t+i_2\sin \omega t$ :-

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

Answer 1

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

The average value of the expression

$i=i_1\cos \omega t+i_2\sin \omega t$

is given by :

$\frac{1}{\sqrt{2}}(i_1^2+i_2^2{)}^{1/2}$

(From average value of $sin\theta +cos\theta$ trigonometric identity)