Question

If a direct current of $3\text{A}$ is superimposed on an alternating current $i=4\sqrt{2}\sin \omega t\text{A}$, flowing through a wire, what is the average value of current in one complete cycle ?

• A. $5\text{A}$
• B. $4\sqrt{2}\text{A}$
• C. $3\text{A}$
• D. $(3+4\sqrt{2})\text{A}$

Answer 1

The correct option is C $3\text{A}$

Current at any instant in the wire will be,

$i=i_{dc}+i_{ac}=3+4\sqrt{2}\sin \omega t$

Therefore, the average current in the wire,

$i_{avg}=\frac{{\int }_0^{T}idt}{{\int }_0^{T}dt}$

$\Rightarrow i_{avg}=\frac{1}{T}\left[{\int }_0^T(3+4\sqrt{2}\sin \omega t)dt\right]$

$=\frac{[3t+0{]}_0^T}{T}[\because {\int }_0^T\sin \omega tdt=0]$

$=3\text{A}$

Hence, $\left(\text{C}\right)$ is the correct answer.