Is RMS Frequency Variant?

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Discussion Overview

The discussion revolves around the concept of root mean square (RMS) values in the context of alternating current (AC) frequencies, particularly in relation to a wind-driven alternator design. Participants explore whether the RMS value is influenced by the frequency of the AC signal and its implications for power generation and heating in resistive loads.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that for a pure sinewave, the RMS value is constant at 0.707 times the peak value and does not depend on frequency.
  • Others question whether the effective power output differs at varying frequencies, suggesting that lower frequencies might yield less effective power integration over time.
  • One participant proposes that while RMS measures power effectively, the relationship between frequency and power generation may require different considerations, particularly in practical applications.
  • Concerns are raised about the heating effects in resistive loads when subjected to different voltage levels, emphasizing that RMS accounts for the heating potential of both positive and negative voltages.
  • Another viewpoint suggests that operating at higher frequencies could lead to higher voltage outputs, potentially affecting power generation efficiency.
  • Some participants express a willingness to conduct practical experiments to clarify the relationship between frequency and RMS values, indicating a preference for empirical evidence over theoretical discussion.

Areas of Agreement / Disagreement

Participants generally agree that RMS is a useful measure for power calculations, but there is disagreement regarding the implications of frequency on effective power generation and heating in resistive loads. The discussion remains unresolved as multiple competing views are presented.

Contextual Notes

Some participants express uncertainty about the definitions and implications of RMS in relation to frequency, indicating a potential gap in understanding that may affect their conclusions. The discussion also highlights the need for practical measurements to validate theoretical claims.

Who May Find This Useful

This discussion may be useful for individuals involved in electrical engineering, particularly those working with AC systems, power generation, and the design of electrical machines.

ormusgold
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Hi folks,

this might be a stupid question, I don't know, but I'm working on a design for a wind-driven alternator, and while calculating the rms value of the output ac, which is maximum 18Hz AC, sinusoidal, it suddenly struck me that the rms value of a low-frequency wave must surely be much lower than a high-frequency one. That is, if rms is anything like an average? I know it's not an average, but still...

I've looked at many sites, trying to find an equation that had a frequency or time component (and that I could understand; maths is not my strong point) but can't find anything. I'm hoping that someone here can help, or at least point me at something nearer.

All clarifications humbly and gratefully received

thanks,

ormusgold
 
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No, if it is a sinewave, RMS is just 0.707 times the peak value of the sinewave and it doesn't depend on frequency.
 
OK, thanks, vk6kro, much appreciated; however, perhaps I'm misunderstanding some exotic aspect of the meaning of root mean square; that is, if my voltage and current is cycling at say 18Hz, does it do as much work in a resistive load, as it would if cycling at 180Hz? Surely not?

ormusgold
 
There is no difference. Why do you think it should generate more heat at a higher 180 Hz instead of 18 Hz?
 
For a pure sinusoidal voltage source the RMS would measure the same at any frequency. In fact, the RMS value of any shape of waveform will give a measure of the power because it is the average power (V2/R), assuming the load is resistive and that VI = Power. Needless to say, you need to average over many cycles or make sure that you measure over a small number of complete cycles. Finding an instrument that will measure RMS reliably is another matter, though.
 
Averagesupernova said:
There is no difference. Why do you think it should generate more heat at a higher 180 Hz instead of 18 Hz?

I think I'm being tripped up by strict definitions of terms, maybe RMS is not what I mean, but taking an extreme case in good ol' engineering fashion, it seems that if the level was varying with a frequency of once a day or once a week the effective power, integrated over time, would be lower. So there must be a frequency component. I'll probably just finish up building an alternator and measuring the difference, if any, but I thought perhaps it was a known phenomenon, with associated equation. I've concluded that RMS is not the term or quantity that I'm looking for and that benchwork will be more useful than headscratching. I'm grateful for the opinions of the respondents, and thanks for your input. My education continues...

ormusgold
 
RMS is a very good concept although you may be looking for something different.

If you had a big resistor and I sent you +100 volts DC for a week and then -100 volts DC for another week, the average would be zero, but you could have had your resistor running very hot for all that time. The RMS voltage would be 100 volts.

Then if I sent you +/- 200 volts, can you see that you could have disspated 4 times as much heat in your resistor for all that time, because the power = E * E / R ?

RMS allows for this extra heating ability for different parts of the sinewave and it also allows for the fact that negative voltages are just as effective as positive ones for heating purposes.

The supply is varying very slowly, but the effect is the same as if you got the power at 60 Hz or any other frequency.

Intuitively, you would think that it is harder to turn a generator fast than to turn it slowly. However, to generate the same power while turning it slowly, you would have to apply greater force to a different generator which was designed with bigger coils and bigger magnets.
 
OK, vk6kro, thanks; I get it now - good explanation. I can relax in the knowledge that I don't need to gear up to a higher speed to achieve my ends.

regards, ormusgold
 
rms value of AC current is that value of a DC current that would liberate the same amount of Joule heat in a resistor.
 
  • #10
You may have to gear up.

Running a generator at twice the frequency produces approximately twice the voltage.
Twice the voltage is twice the power, assuming the same current.

18 hertz is awfully slow.

Why don't you use a car alternator and run it at say 500 RPM?
 
  • #11
As you know the rotation speed of electrical machine is related to its power supply frequency and its coupled mechanical load is function of system speed, for example the mechanical output of fans is proportional with cube of their rotation speed. Indeed the power consumption are independent of frequency just in ohmic consumers (in sinusoidal conditions).
For similar discussion you can refer to Machine Riddle No.16 from http://electrical-riddles.com
 

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