# Vdc and vrms

1. Oct 14, 2011

i have read that vrms is the same as equivalent dc voltage but i have also read that vav and vdc are same but vav and vrms is not same vrms of sinosoid is zero but vav of sinousoid is not zero where i am wrong?

2. Oct 14, 2011

### vk6kro

You have most of that wrong.

http://en.wikipedia.org/wiki/Root_mean_square

However, the average voltage of a sinewave (over a whole 360 degrees) is zero, but the power isn't zero because positive and negative voltages are equally effective at producing power, assuming a constant resistive load.
The average over a half wave is 0.637 times the peak value.

The RMS voltage of a sinewave is 1/√2 times the peak voltage level or 0.707 times the peak voltage.

Last edited: Oct 14, 2011
3. Oct 14, 2011

### Bob S

Vrms = sqrt[Vmeansquare(t)] =sqrt[∫V(t)2dt/∫dt] integrated over a complete cycle.

Vav = ∫V(t)dt/∫dt.

4. Oct 14, 2011

### jim hardy

RMS mnemonic:
it's backwards.

instant by instant:
Square the instantaneous value
find Mean (average) of those squared values
square Root of that mean is RMS

and clearly that's a lot different from a simple average of the instantaneous values.
for one thing squaring them discards their signs.

but i think backwards so it's natural to me...