# Rectifier – Why Output DC Voltage of Full Wave Rectifier is Not Equal to RMS of AC Input

acdcrectifierrms

https://www.electronics-tutorials.ws/accircuits/average-voltage.html

https://www.electronics-tutorials.ws/accircuits/rms-voltage.html

I understand that the RMS of an AC voltage is the magnitude of the equivalent DC voltage in terms of power produced,so I expected that when the AC voltage is rectified, the output DC voltage would be equal to the RMS of the original AC (assuming no other voltage drops for diodes.)

When used to compare the equivalent RMS voltage value of an alternating sinusoidal waveform that supplies the same electrical power to a given load as an equivalent DC circuit, the RMS value is called the “effective value” and is generally presented as: V eff or I eff.

In other words, the effective value is an equivalent DC value which tells you how many volts or amps of DC that a time-varying sinusoidal waveform is equal to in terms of its ability to produce the same power.

V DC = 0.9 * V RMS

The $$\\boxed{\text{average of }|x|}\$$ is $$\\color{red}{\text{not mathematically the same as the}}\$$ $$\\sqrt{\text{average of } |x|^2}\$$