The output current versus time curve of a rec | vedclass

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(C) The given curve represents a full-wave rectified output current. The current $I$ varies as $I = I_0 \sin(\omega t)$ for the duration of each half-

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$2i_0/\pi$

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(C) The given curve represents a full-wave rectified output current. The current $I$ varies as $I = I_0 \sin(\omega t)$ for the duration of each half-cycle.To find the average value $(I_{avg})$ over one complete cycle of the rectified output (which has a period of $T/2 = \pi/\omega$),we integrate the current over one half-cycle and divide by the time interval:$I_{avg} = \frac{1}{T/2} \int_0^{T/2} I_0 \sin(\omega t) dt$$I_{avg} = \frac{\omega}{\pi} \int_0^{\pi/\omega} I_0 \sin(\omega t) dt$$I_{avg} = \frac{\omega I_0}{\pi} \left[ -\frac{\cos(\omega t)}{\omega} \right]_0^{\pi/\omega}$$I_{avg} = \frac{I_0}{\pi} [-\cos(\pi) + \cos(0)]$$I_{avg} = \frac{I_0}{\pi} [1 + 1] = \frac{2I_0}{\pi}$

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

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