Question

The output sinusoidal current versus time graph of a rectifier is shown in the figure. The average value of output current :

• A. 0
• B. $\frac{I_o}{2}$
• C. $\frac{I_o}{4}$
• D. None of these

Answer 1

The correct option is D None of these

Average value of a function is defined as;

$f_{av}=\frac{\int f\left(x\right)dt}{\int dt}$

Here,

$I=I_0\sin \omega t$ $0\le \omega t\le \pi$

$I=-I_0\sin \omega t$ $\pi \le \omega t\le 2\pi$

$I_{av}=\frac{\int Id\left(\omega t\right)}{\int d\left(\omega t\right)}=[-[\cos \omega t{]}_0^{\pi }+\left[\cos \omega t{]}_{\pi }^{2\pi }\right]=\frac{2I_O}{2\pi }=\frac{I_0}{\pi }$