Question

An electric current has both $DC$ and $AC$ components. $DC$ component of $8A$ and $AC$ component is given as $I=6\sin \omega t$. So $I_{rms}$ value of resultant current is

• A. $9.05A$
• B. $8.05A$
• C. $11.58A$
• D. $13.58A$

Answer 1

Answer: (A)

$9.05A$

Given,

DC current, $I_{DC}=8A$ ....(i)

AC current, $I_{AC}=6\sin \omega t$ ....(ii)

Total current, $I=I_{DC}+I_{AC}$

$I=8+6\sin \omega t$

Squaring on both sides,

$I^2={(8+6\sin \omega t)}^2$

$I^2=64+36{\sin }^2\omega t+96\sin \omega t$

$I^2=64+36\times \frac{1}{2}+96\times 0$

$I^2=64+18=82$

$I_{rms}=\sqrt{82}=9.05A$