What is the mathematical expression for the average value of a rectified voltage sinusoid?

What is the mathematical expression for the average value of a rectified voltage sinusoid?

• A. (1/π)Vm
• B. (2/π)Vm
• C. (π/2)Vm
• D. Vm/2

Answer: (B)

The average value of a rectified voltage sinusoid is calculated based on the properties of the waveform and the process of rectification. For a sinusoidal voltage represented as \( V(t) = V_m \sin(\omega t) \), where \( V_m \) is the peak voltage, the rectified output removes the negative portion of the waveform, resulting in a signal that only takes positive values. When determining the average value of this rectified sinusoidal voltage over one complete cycle, we consider only the positive half of the waveform. The average value \( V_{avg} \) for a full cycle of a sinusoid (considering rectification) can be derived from the integral of the positive half from 0 to \( \pi \) and then normalized over the full cycle of \( 2\pi \): \[ V_{avg} = \frac{1}{\pi} \int_0^{\pi} V_m \sin(t) \, dt = \frac{V_m}{\pi} \left[-\cos(t)\right]^0_{\pi} = \frac{V_m}{\pi} [1 - (-1)] = \frac{2}{\pi}V_m

The average value of a rectified voltage sinusoid is calculated based on the properties of the waveform and the process of rectification. For a sinusoidal voltage represented as ( V(t) = V_m \sin(\omega t) ), where ( V_m ) is the peak voltage, the rectified output removes the negative portion of the waveform, resulting in a signal that only takes positive values.

When determining the average value of this rectified sinusoidal voltage over one complete cycle, we consider only the positive half of the waveform. The average value ( V_{avg} ) for a full cycle of a sinusoid (considering rectification) can be derived from the integral of the positive half from 0 to ( \pi ) and then normalized over the full cycle of ( 2\pi ):

[

V_{avg} = \frac{1}{\pi} \int_0^{\pi} V_m \sin(t) , dt = \frac{V_m}{\pi} \left[-\cos(t)\right]^0_{\pi} = \frac{V_m}{\pi} [1 - (-1)] = \frac{2}{\pi}V_m