Question

The average current of a sinusoidally varying alternating current of peak value 5A and initial phase zero, between the instants $t=T/8$ to $t=T/4$ is:(Where $T$ is the time period)

• A. $\frac{10}{\pi }\sqrt{2}A$
• B. $\frac{5}{\pi }\sqrt{2}A$
• C. $\frac{20\sqrt{2}}{\pi }A$
• D. $\frac{10}{\pi }A$

Answer 1

The correct option is A $\frac{10}{\pi }\sqrt{2}A$

$i=5sin\left(wt\right)$

$<i>=\frac{{\int }_{t_1}^{t_2}idk}{t_2-t_1}$

$=\frac{{\int }_{T/8}^{T/4}5sin\left(wt\right)dt}{\frac{T}{4}-\frac{T}{8}}$
$=\frac{{5[-\frac{cos\left(wt\right)}{w}]}_{T/8}^{T/4}}{T/8}$
$=\frac{51/\sqrt{2}\times 1/w}{T/8}$

$=\frac{5}{T/8}\times \frac{1}{\sqrt{2}}\times \frac{T}{2\pi }$

$=\frac{10}{\pi }\sqrt{2}A$