Question

If a direct current of value $a$ ampere is superimposed on an alternative current $I=b\sin \omega t$ ampere flowing through a wire, what is the effective value of the resulting current in the circuit?

• A. ${[a^2-\frac{1}{2}{b}^2]}^{1/2}$
• B. $[a^2+b^2{]}^{1/2}$
• C. ${\left[\frac{a^2}{2}+b^2\right]}^{1/2}$
• D. ${[a^2+\frac{1}{2}{b}^2]}^{1/2}$

Answer 1

The correct option is D ${[a^2+\frac{1}{2}{b}^2]}^{1/2}$

$I_{dc}\left(rms\right)=aA$
$I_{ac}(rm{s}_{=}b/\sqrt{2}A$
effective rms value of current =$\sqrt{\left(I_{dc}\right(rms){)}^2+(I_{ac}\left(rms\right){)}^2}=\sqrt{a^2+\frac{b^2}{2}}$