The output sinusoidal current versus time cur | vedclass

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(C) The given figure represents a full-wave rectified output. The current varies as $I = I_0 \sin \omega t$ for the interval $0$ to $T/2$,where $T$ is

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

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(C) The given figure represents a full-wave rectified output. The current varies as $I = I_0 \sin \omega t$ for the interval $0$ to $T/2$,where $T$ is the time period of the original $AC$ input. The time period of the rectified output is $T/2$.The average value of the output current is given by:$I_{av} = \frac{1}{T/2} \int_{0}^{T/2} I_0 \sin \omega t \, dt$Substituting $\omega = \frac{2\pi}{T}$:$I_{av} = \frac{2}{T} I_0 \int_{0}^{T/2} \sin \left( \frac{2\pi}{T} t \right) dt$$I_{av} = \frac{2 I_0}{T} \left[ -\frac{\cos(\frac{2\pi}{T} t)}{\frac{2\pi}{T}} \right]_{0}^{T/2}$$I_{av} = \frac{2 I_0}{T} \cdot \frac{T}{2\pi} \left[ -\cos(\pi) + \cos(0) \right]$$I_{av} = \frac{I_0}{\pi} [ -(-1) + 1 ] = \frac{I_0}{\pi} [ 1 + 1 ] = \frac{2I_0}{\pi}$

The output sinusoidal 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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