I’m currently working on a project that deals with controlling an AC heater and it has led to a question that I really should be able to answer… but I can’t.

I understand how to get the values of the average voltage and the RMS voltage of an AC wave, but what I don’t understand is why RMS is used to calculate effective DC voltage. It seems, intuitively, that the area under an AC sine wave could be used to calculate the effective DC voltage. I get that the RMS equation deals nicely with the negative half of the wave, but so would taking the absolute value.

There is a lot of information on the internet about effective DC voltage, but most of it just resorts to the calculus behind the RMS equation; it does not explain why the RMS value is what you need to use instead of the average value. Is there a simple answer?