Question

The output current versus time curve of $a$ rectifier is shown in the figure. The average value of output current in this case is :-

• A. $0$
• B. $\frac{I_{0}}{2}$
• C. $\frac{2 I_{0}}{\pi }$
• D. $I_{0}$

Answer 1

Answer: (C)

$I_{a v}=\frac{\displaystyle \int _{0}^{T / 2} idt}{\displaystyle \int _{0}^{T / 2} dt}=\frac{\displaystyle \int _{0}^{T / 2} I_{0} sin \left(ωt\right) dt}{T / 2}$
$=\frac{2 I_{0}}{T}\left(\left[\frac{- cosωt}{\omega }\right]\right)_{0}^{T / 2}=\frac{2 I_{0}}{T}\left[- \frac{cos \left(\frac{\omega T}{2}\right)}{\omega } + \frac{cos 0 ^\circ }{\omega }\right]$
$=\frac{2 I_{0}}{\omega T}\left[- cos \pi + cos 0 ^\circ \right]=\frac{2 I_{0}}{2 \pi }\left[1 + 1\right]=\frac{2 I_{0}}{\pi }$