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Q.

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

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a

0

b

$frac{{{I_0}}}{2}$

c

$frac{{2{I_0}}}{pi }$

d

${I_0}$

answer is C.

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Detailed Solution

${I_{av}} = frac{{int_0^{T/2} {,,,,,i,dt} }}{{int_0^{T/2} {,,,,,dt} }}$ $= frac{{int_0^{T/2} {,,,,,{I_0}sin (omega ,t)dt} }}{{T/2}}$

$= frac{{2{I_0}}}{T}left[ {frac{{ - cos omega ,t}}{omega }} right]_0^{T/2}$ $=frac{2I_0}{T}$ $left[ {-frac{{ cos frac{omega ,T}{2}}}{omega }} +frac{cos,0^o}{omega}right]$

$= frac{{2{I_0}}}{{omega ,T}}[ - cos pi + cos {0^o}]$ $= frac{{2{I_0}}}{{2pi }}[1 + 1] = frac{{2{I_0}}}{pi }$

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