Question

A direct current of $5A$ is superimposed on an alternating current $I=10\sin \omega t$ flowing through a wire. The effective value of the resulting current will be:

• A. $\left(15/2\right)A$
• B. $5\sqrt{3}A$
• C. $5\sqrt{5}A$
• D. $15A$

Answer 1

The correct option is B $5\sqrt{3}A$

$I_{ac}=\frac{10}{\sqrt{2}}$

$I_{dc}=5$

The effective value of resulting current will be,

$I=\sqrt{I_{ac}^2+I_{dc}^2}$

$I=\sqrt{{\left(10/\sqrt{2}\right)}^2+5^2}$

$I=\sqrt{50+25}$

$I=5\sqrt{3}A$