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(D) In a full-wave rectifier,the output current consists of a series of half-sinusoidal pulses. To find the average current $(I_{avg})$,we integrate t

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

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(D) In a full-wave rectifier,the output current consists of a series of half-sinusoidal pulses. To find the average current $(I_{avg})$,we integrate the current over one complete cycle (from $t=0$ to $t=T/2$) and divide by the time interval $(T/2)$. The current is given by $I = I_0 \sin(\omega t)$. $I_{avg} = \frac{1}{T/2} \int_{0}^{T/2} I_0 \sin(\omega t) dt$ $I_{avg} = \frac{2}{T} \cdot I_0 \left[ -\frac{\cos(\omega t)}{\omega} \right]_{0}^{T/2}$ Since $\omega = \frac{2\pi}{T}$,we have $\omega \cdot \frac{T}{2} = \pi$. $I_{avg} = \frac{2 I_0}{T \omega} [-\cos(\pi) + \cos(0)] = \frac{2 I_0}{T (2\pi/T)} [1 + 1] = \frac{2 I_0}{2\pi} \cdot 2 = \frac{2 I_0}{\pi}$.

The figure shows the current as a function of time at the output of a full-wave rectifier. The average value of this current is:

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