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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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$\frac{I_{0}}{2}$

$\frac{2 I_{0}}{π}$

$I_{0}$

answer is C.

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Detailed Solution

$I_{av} = \frac{\int_{0}^{T / 2} idt}{\int_{0}^{T / 2} dt} = \frac{\int_{0}^{T / 2} I_{0} \sin (ωt) dt}{T / 2}$

$= \frac{2 I_{0}}{T} {[\frac{- cosωt}{ω}]}_{0}^{T / 2}$

$= \frac{2 I_{0}}{T} [- \frac{\cos (\frac{ωT}{2})}{ω} + \frac{\cos 0^{\circ}}{ω}]$

$= \frac{2 I_{0}}{ωT} [- cosπ + \cos 0^{\circ}] = \frac{2 I_{0}}{2 π} [1 + 1]$

$= \frac{2 I_{0}}{π}$

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