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. $\frac{2I_0}{\pi }$
• D. $I_0$

Answer 1

Answer: (C)

$I_{av}=\frac{{\int }_0^{T/2}idt}{{\int }_0^{T/2}dt}=\frac{{\int }_0^{T/2}{I}_{0}sin\left(\omega t\right)dt}{T/2}$
$=\frac{2I_0}{T}{\left(\left[\frac{-cos\omega t}{\omega }\right]\right)}_0^{T/2}=\frac{2I_0}{T}\left[-\frac{cos\left(\frac{\omega T}{2}\right)}{\omega }+\frac{cos{0}^{\circ }}{\omega }\right]$
$=\frac{2I_0}{\omega T}\left[-cos\pi +cos{0}^{\circ }\right]=\frac{2I_0}{2\pi }\left[1+1\right]=\frac{2I_0}{\pi }$