First slide

Alternating Current and voltage

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

Moderate

A

0
B

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

$\frac{2 I_{0}}{π}$
D

$I_{0}$

Solution

$I_{av} = \frac{\int_{0}^{T / 2} i dt}{\int_{0}^{T / 2} dt} = \frac{\int_{0}^{T / 2} I_{0} \sin (ω t) dt}{T / 2}$
$= \frac{2 I_{0}}{T} {[\frac{- cosω t}{ω}]}_{0}^{T / 2} = \frac{2 I_{0}}{T} [- \frac{\cos (\frac{ωT}{2})}{ω} + \frac{\cos 0^{o}}{ω}]$
$= \frac{2 I_{0}}{ω T} [- cosπ + \cos 0^{o}] = \frac{2 I_{0}}{2 π} [1 + 1] = \frac{2 I_{0}}{π}$

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