RR said:

Hi,

As I understand it, RMS is calculated on the area under the sine or cosine

wave for the AC supply and the peak voltage.

Sort of, but you'll get a better idea of what it's really all about simply

by going through what "RMS" stands for in the first place.

The problem is one of determining the "effective" voltage, current, or

whatever of an alternating source; in other words - and to use the most

popular example - if I pass an AC current through a resistor, how much

power is dissipated in that resistor? How can I compare AC to DC in

this sense?

You clearly can't use the peak voltage or current - the waveform isn't

at the peak but for an instant, so obviously doing a power or some

other such calculation based on that value would be wrong. The next

idea would probably be to try to find the "average" value of the

waveform, but that winds up even worse - if you average any "pure"

AC (meaning that it is symmetrical, regardless of the form of the wave,

and spends as much time above zero as below), you get a result of

exactly zero. That's obviously not right, either, since the resistor DOES

heat up.

So instead, we start by squaring the function that describes the AC

waveform; if you square such a wave, everything winds up above

zero, right? Then find the average, or mean, of the squared waveform

(so now you have a constant value), and to correct for the squaring

operation you did in the first place,

find the square root of that average

value.

In short, you are finding the (square) Root of the Mean of the Square.

"RMS," see?

It happens to work out to 0.707 peak for a pure sinusoid; other

waveforms wind up with different fractions of the peak value, and

this is really only a shortcut which can be applied to those examples

where one of these "regular" waveforms is in question. But the

above process - square the wave, average it, and take the square

root of the result - applies to all.

Obviously, frequency does not enter into this at all - RMS is 0.707

of peak for ANY sinusoid, regardless of frequency.

I've attempted to follow the calculations here:

http://www.alpharubicon.com/altenergy/understandingAC.htm
and the frequency seems to always reduce to a factor of 0.5.

The final result is just a numeric value - it has no frequency (that

is the result of averaging the squared waveform - an average has

no frequency, since it's a constant value, right?). You seem to get

into some unexpected frequencies during all of this because the

squared waveform is itself a periodic wave with a frequency 2X

the original (at least for anything but a 50% duty-cycle square

wave).

So, why does an appliance designed for 240volts 50Hz care whether you supply

240volts 60Hz or 240volts 100Hz, for that matter?

When an appliance "cares" about the line frequency, one of two

things are generally at issue:

1. The appliance relies on the frequency of the line in order to

run at the proper speed - e.g., the motor in an electric clock.

2. The appliance contains components (typically, transformers or

similar magnetics) which are designed to operate at one frequency,

and will be less efficient at others.

Bob M.