What is the r.m.s. value of a current?
What is the r.m.s. value of a current?
(OP)
I responded to a question of this forum (cable selection based on duty cycle) where I afirmed that the r.m.s. value is similar to the thermal equivalent current. I realized this may be a stupidity (in fact, I am pretty sure).
I analyzed the problem and now I believe that the r.m.s. value of a current is the so called "effective" value of the current (for ac currents).
I.e. for an ac current i(t) = I*sin(omega*t - fi), the effective value is sqrt(2)*I, where I is the amplitude.
Can anyone explain me what the r.m.s. value is?
I analyzed the problem and now I believe that the r.m.s. value of a current is the so called "effective" value of the current (for ac currents).
I.e. for an ac current i(t) = I*sin(omega*t - fi), the effective value is sqrt(2)*I, where I is the amplitude.
Can anyone explain me what the r.m.s. value is?






RE: What is the r.m.s. value of a current?
Am I missing something in your question?
RE: What is the r.m.s. value of a current?
RE: What is the r.m.s. value of a current?
Yrms=sqrt[(1/T)(integral from a to (a+T) of y(t)^2 x dt)]
(there is a typo in the dictionary, namely t should be T)
Also,
y=sqrt[A1^2 + A2^2 + ..... + An^2]
where A1, A2, ... An are the rms values of the fundamental component, second harmonic, .... , nth harmonic, respectively.
Refresh the Fourier Series theory.
RE: What is the r.m.s. value of a current?
I tried to put the algebra on here, but it looked awful. The RMS value includes all frequencies contained in a waveform, not just the fundamental. A college-level textbook in your library should give you the algebraic form of the calculation.
RE: What is the r.m.s. value of a current?
http://search.netscape.com/ns/boomframe.jsp?query=%22rm...
for:
RMS application note
etc, for more info
RE: What is the r.m.s. value of a current?
You are being much too hard on yourself when you say "...the r.m.s. value is similar to the thermal equivalent current. I realized this may be a stupidity (in fact, I am pretty sure)."
You are in fact correct. The RMS value is the constant (or dc) value of a time varying current that would produce the same heat. "Effective" may be a better term because it applies to real energy other than heat as well. RMS, or root mean square, is the square root of integral of the square of the time varying current over a time period divided by the time period. It is the thermal equivalent because the heat produced by a current through a resistance is proportional to the square of the current.
For a sinusoidal current over an integral number of cycles, the integration works out to make the equivalent constant value equal the peak value divided by sqrt(2).
RE: What is the r.m.s. value of a current?
FWIW, {no offense intended} IEEE 100-1992 tags the term “effective value” as deprecated.
RE: What is the r.m.s. value of a current?
any conductor is proportional to the square of either
measured value current through or voltage across.
P=I*I*R or P=(V*V)/R
RMS allows to account for the expected heating to be a
non-linear function of the current or voltage.
So which wire will run hotter.
12A at a 50% duty cycle.
6A at a 100% duty cycle.
The average current is the same but the 12A wire is hotter.
Rodar
RE: What is the r.m.s. value of a current?
Loss = R * I^2
In the AC world, we would like use the same formula. Therefore the concept of r.m.s was invented, such that we can do
Loss = R * I(r.m.s)^2
In certain sence, r.m.s is an equivalent current for loss calculation. Since heating is propotional to loss, sometimes people think r.m.s is the thermal equivalent current.
RE: What is the r.m.s. value of a current?
However, if the waveform is a pure sinusoid, then Irms is different from Idc. Irms is a mathematical approach to waveforms to obtain a constant value that is convenient to use, e.g. Irms of Vmax x sin(wt) = Vmax/sqrt2.
Irms = constant is often called Irms dc and
Vrms = constant is often called Vrms dc. This is by a coincidence that a constant value of some function, e.g. Vmax sinwt happens to be equal to a constant=Vmax/sqrt2.
RE: What is the r.m.s. value of a current?
RE: What is the r.m.s. value of a current?
RE: What is the r.m.s. value of a current?
RE: What is the r.m.s. value of a current?
No longer the Queen's English, I guess
RE: What is the r.m.s. value of a current?
RE: What is the r.m.s. value of a current?
The area under the sinusoid would be positive for 1/2 cycle then negative for the other 1/2 cycle. Total area over one cycle would be zero. Yet the evil Utility charges for the rms value of something that averages out to nothing!!!
RE: What is the r.m.s. value of a current?
electricpete, what "Wutz" does mean? Is your irony strictly limited to my English or is extended over my person too?
To the rest of the members: thank you all replying to my question. I have got the answer I have been looking for.
RE: What is the r.m.s. value of a current?
Indeed, because successive half cycles are positive and negative, the area enclosed by the sinusoidal waveform will equate to zero for an integer number of full cycles.
That is why root-mean-square was invented - because when you square a negative value you get a positive one. You then work out the mean of the "positively forced" waveform and square root it !!
RE: What is the r.m.s. value of a current?
If the utility (mean, vile and nasty people as they seem to be) refused to pay you the return current (the negative half-cycles) and charged you for the RMS value of the positive half-cycles - would that help?
davrom,
I have a hard time reading the native's tounge myself (being Swedish). I think that FWIW means "For What it is Worth" and that "Wutz" is a (German influenced?) way of saying "What does". But then again, I'm more of a technician than a linguist. So I might be wrong there. But I am sure that no-one meant to hurt or ridicule you.
RE: What is the r.m.s. value of a current?
FWIW = for what it's worth
RE: What is the r.m.s. value of a current?
TTFN
RE: What is the r.m.s. value of a current?
Sorry for inadvertence.
RE: What is the r.m.s. value of a current?
jbartos,
The area under the sinusoid would be positive for 1/2 cycle then negative for the other 1/2 cycle. Total area over one cycle would be zero.
///True.\\\
Yet the evil Utility charges for the rms value of something that averages out to nothing!!!
///Not quite. For example, a heating element will produce amount of heat during positive area proportional to the plus area and during the negative area amount of heat proportional to the negative area. Now, I am being charged by the Utility for areas plus and minus for Energy EWhrs,rms=Vrms x Irms x time, which amounts to more than EWhrs,av=Vav x Iav x time = Vdc x Idc x time = Ewhrs,dc.
It is hard to beat this engineering and scientific fact, which has been around for long time. I would much appreciate to have the Utility supplying EWhrs,dc instead of EWhrs,rms for my heaters. I feel more comfy around the wormer heaters. What about others?\\\
RE: What is the r.m.s. value of a current?
"...which amounts to more than EWhrs,av=Vav x Iav x time = Vdc x Idc x time = Ewhrs,dc."
Except that EWhrs,av does not equal Vav x Iav x time. The average power equals the average of the product V·I which equals Vrms·Irms, not the product of the averages.
In the case of current through the heater, W = I²·R. The average of I² is Irms² (by definition of rms). Average energy is Whrsavg = Irms²·R·time.
RE: What is the r.m.s. value of a current?
Nothing to do with German, just sounded funny at the time.
I think the subject of rms just makes me giddy. There are some classic discussions in the following links.
Thread237-68161
http://www.brazosport.edu/~pschimpf/forums/vitreousenam...
I am tempted to take up the discussion of rms but based on past experience maybe I better just pass. I recognize the name jghrist has been around a long time and very capable of bringing order to the chaos.
RE: What is the r.m.s. value of a current?
Try the square root of the area under the square of the sinusoid. Wutz a wormer heater? Sounds nasty.
RE: What is the r.m.s. value of a current?
RE: What is the r.m.s. value of a current?
RE: What is the r.m.s. value of a current?
Wasn't Faber College’s Dean Wormerheater a character in the 'Animal House' movie?
RE: What is the r.m.s. value of a current?
jbartos wrote,
"...which amounts to more than EWhrs,av=Vav x Iav x time = Vdc x Idc x time = Ewhrs,dc."
///This is extracted out of context.\\\
Except that EWhrs,av does not equal Vav x Iav x time.
///Not true. For dc where dc=av, it does. By any chance, have you ever designed any electronics circuits where ac and dc are frequently superimposed or combined?\\\
The average power equals the average of the product V•I which equals Vrms•Irms, not the product of the averages.
///Yes, however, in this case you are addressing average rms power not average dc power. There is a big difference between those two. Please, what is your educational level?\\\
In the case of current through the heater, W = I²•R.
///Not clear what you mean by I. Do you mean Idc=Iav or Irms?\\\
The average of I² is Irms² (by definition of rms).
///Yes, the average is Irms average of sinusoidal wave not the absolute value of sinusoid, i.e. |sinwt| often obtained from a full wave rectifier. However, this is an average of Irms not Idc=Iav. It would be better to go to the engineering paper with squares and see those differences. There is a big difference between (sinwt)^2 leading to Irms and obtaining Iav from |sinwt| (including Iav^2).
Average energy is Whrsavg = Irms²•R•time.
///Yes, however, this is rms energy, i.e. Whrs,rms=Irms^2 x R x time, not av=dc energy of |sinwt| Whrs,av=Iav^2 x R x time. Please, notice that electronic engineering books have not changed anything in this area, only electrical power engineering started downplaying the form factor and differences between Irms and Iav=Idc. I know why, do you? Please, notice that this has been around for some time and will stay in here for some time, like it or not, since this is a scientific fact, not any engineering interpretation or twisting. Please notice that Irms = sqrt [(1/T) x Integral (Imax x sinwt)^2 dt] = (Imax / Sqrt2) is different from Irms = sqrt [(1/T) x Integral {[(1/T) x Integral (Imax x |sinwt| x dt)]^2 x dt}] = (2 x Imax / pi) = 0.6366 Imax = sqrt2 x 2 x Imax / (sqrt2 x pi) = (sqrt2 x 2 /pi) x Irms = 0.9 x Irms = Iav
As it can be seen, the Irms of Imax x |sinwt| is different from Irms of Imax x sinwt.
See Reference:
L.J. Giacoletto “Electronics Designers’ Handbook,” 2nd Edition, McGraw-Hill Book Company, 1977, Table 4.3 Characteristics of Periodic Waveforms.\\\
RE: What is the r.m.s. value of a current?
I can see that you are busy convincing the engineering community that they have been using the wrong definition of RMS for about one hundred years. Would it not be worth while to sit down and think. You might find that you and Don Quixote are in the same business.
RE: What is the r.m.s. value of a current?
"(quoting me)'In the case of current through the heater, W = I²•R.'
///Not clear what you mean by I. Do you mean Idc=Iav or Irms?\\\"
I mean that the instantaneous power is equal to the instantaneous current squared time the resistance. It doesn't matter if the current is dc, sinusoidal, exponential, square wave, or worm shaped. To get the energy, you integrate the instantaneous power over whatever time period you want. The result is the integral of I²·dt over that time period.
Also,
"Please notice that Irms = sqrt [(1/T) x Integral (Imax x sinwt)^2 dt] = (Imax / Sqrt2) is different from Irms = sqrt [(1/T) x Integral {[(1/T) x Integral (Imax x |sinwt| x dt)]^2 x dt}]"
Actually, no it isn't because the square of sin(ωt) is equal to the square of what you call |sin(ωt)|. Even someone with my limited educational level knows that the square of -n equals the square of +n.
When I said "Except that EWhrs,av does not equal Vav x Iav x time", I was not completely correct. They would be equal in the unique case of constant voltage and current. But this is the only case.
RE: What is the r.m.s. value of a current?
Thread237-81315
RE: What is the r.m.s. value of a current?
Hi Buzzp
This is not true in a circuit with reactive loads (C,L). If your current is a mix of many frequencies (harmonics), your RMS-Current depends on the harmonic mix and in this case the heating effect of different harmonic currents with the same RMS-Current-Value may be different.
If you have a pure C-Load, you will not have any DC heating in your circuit. I think that this is obvious.
RE: What is the r.m.s. value of a current?
For the case presented and as stated time and time again, this is assuming a purely RESISTIVE LOAD. Whatever the rms level, if you get the rms level and apply the same amplitude, DC, to a purely resistive load, the steady state temperature will be the same as with the AC rms current. The discussion of reactive components has never been brought up unless I overlooked a post.
As far as harmonics, the rms current takes into account harmonic current. This is the reason it is used because when you have harmonics you do not have a pure sine wave so finding the average a scaling it as though it were a pure sine wave results in errors. Even with the ugliest waves around, if you find the real RMS value, apply this to a resistive load and apply the same value in DC, the heating effect will be the same.
RE: What is the r.m.s. value of a current?
Whether we are talking dc current, ac sinusoidal current or non-sinusoidal current, only the resistance in the circuit generates heat (not the L or C).
As long as we specify the current (we are talking about heating as a function of current), the existence of L and C elements is irrelevant.
Maybe you are thinking of a circuit with constant voltage applied. Add C's and L's in series and you change the ac and dc currents and therefore the resulting heating. That does not seem relevant to a discussion of heating as a function of current, where current is the independent/controlled variable under discussion.
If the resistance is fixed and the rms of the current is specified, those TWO quantities are all that is needed to determine the heating (Irms^2*R). It doesn't matter whether that rms is associated with dc or ac or non-sinusoidal waveforms.
For dc currents, the rms value is the same as the dc value.
For ac currents the rms value is the Peak/sqrt(2)
For general currents the rms value is
sqrt(<i(t)^2>) = sqrt{(1/T) Integral(i(t)^2)dt}
BTW, depending on the size of the cable and frequency of the current, skin effect could alter the effective resistance. It is a completely different subject from what we have discussed here but important for large cables.
RE: What is the r.m.s. value of a current?
„RMS of any ac signal has the same heating effect as the same value in DC, period.“
„Even with the ugliest waves around, if you find the real RMS value, apply this to a resistive load and apply the same value in DC, the heating effect will be the same.“
buzzp,
You didn’t mention in your first posting that you apply in your model a resistive load and simulate the “ugly current” in your model.
I agree that the heating of a resistive load is an equivalent of RMS-Value of the current and that the RMS-Value can be calculated or measured.
But this fact has only a theoretical value.
Current is always a function of the impedance and voltage (I=U/Z). In a real circuit there is no pure resistance or inductance, and there is a feedback between the non-linear load and the voltage source. RMS-Values of a current is just a figure with little practical value.
RE: What is the r.m.s. value of a current?
How can you say that RMS-Values of a current is just a figure with little practical value? The RMS value governs the thermal losses in a circuit, whether it is the resistance of a 'pure' resistance or the inevitable resistance of a real-world inductance. The resistances of all the non-ideal components we are forced to live with in this imperfect world will dissipate energy as heat when current flows through the resistance in question. The energy dissipation will depend on the RMS value of the current, and on the resistance.
RE: What is the r.m.s. value of a current?
I do understand that impedances and such are important in calculating the current. This discussion has nothing to do with calculating the current and everything to do with measuring the current. Take your cheap clamp on meter and measure the output of a drive. Use that to calculate temperature rise of cable and equipment and you will be in serious trouble. Take your rms clamp-on and do the same measurement and calculations and you will be right on (ignoring skin effects).
RE: What is the r.m.s. value of a current?
You have a generator which can generate a voltage with different frequencies (from zero Herz , i.e. DC, to 100 Giga-Herz). You have a device, that can measure the RMS-Value of the current. You have a real resistor and you can measure the temperature on this resistor.
1) You generate DC-Voltage and measure the RMS-Value of the DC-Current and the temperature on the resistor.
2) You generate 100-GHz-Voltage and measure the RMS-Value of the DC-Current and the temperature on the resistor.
In this case you will measure the same RMS-Value of the current (you can adjust your generator), but the temperature on your resistor will be different, because there is no pure resistance in this resistor. There is also a L and C resistance. Then you have to take into account the skin effect (you cannot ignore this phenomenon!) and the electromagnetic radiation in a 100-GHz-circuit.
As you see, only in and ideal circuit with an ideal resistance is the RMS-Value of a current an equivalent of the temperature on this resistance.
RE: What is the r.m.s. value of a current?
I'm a power engineer posting in a power engineering forum. This sounds like microwave engineering, where the conductors are replaced with pipes, and the 'normal' electrical laws get mixed in with waveguide theory and the like.
However, the thermal losses are still determined by the RMS value of current passing through the resistance.
The capacitance and inductance of the resistor do not dissipate energy as heat, although I agree that current may be shunted through a capacitance and therefore not pass though the resistor. The shunted current will not contribute to the heat loss.
Skin effect (and proximity effect) are relevant to the thermal calculations, but as noted by electricpete on Dec 15th are an entirely different subject to calculation of RMS, and only have practical significance to conductors which are 'large', although large is a somewhat loose term as it is frequency-dependent. Skin effect does not magically add L and C to the 'pure' resistance, it just makes the effective resistance, still pure, higher than its DC value. The effective resistance still dissipates energy as heat; the heat loss may be calculated as (RMS current)^2 x (effective R). The only change is that the effective resistance is substituted for the DC resistance normally used in the calulation.
RE: What is the r.m.s. value of a current?
Hi ScottyUK,
RMS means Root-Mean-Square, that indicates that we are talking about a mathematical model.
Can you understand the difference between a mathematical model and a real circuit?
RMS-model works with a DC-Current or with a Sine-Current, but only approximately.
If there is a “distorted” current, you have to represent this current as a mix of different sine curves with different frequencies (Fourrier Analysis).
You can calculate the RMS-Value of a sine current as:
I rms = squ(sum( In mom ^2)/n); n- number of the instant-currents
As you see, you have to split your real current curve into n instant-currents to find out your “root mean square”, which means that you can only find out an approximate value of the real current curve, because you are operating with a limited number (n).
If your current is “ugly”, you have to do your calculation with a limited number of sine curves and then find the total RMS of the sine-mix.
I rms-total = squ(sum Im rms ^2 ); m – the number of sines
As you can see, there is a big fault in this model. You cannot take into account the phase-displacement of different frequencies.
In circuits with “ugly current” you have to distinguish between DPF (displacement power factor) and TPF (true power factor).
The term “effective current” refers to a low-frequency-sine-current that causes the same thermal “effect” in a resistor as a DC-Current. You just measure the temperature in this resistor and if the temperatures are equal, you can say that the “effective” values of these currents are equal.
As you see, the “Effective Value” (heating effect in a resistor) and the “RMS-Value” of a current are different things. "Effective value" can be measured with a thermometer, the "RMS-Value" can be calculated, but only approximately, not taking into account many important things.
Have you got my drift, ScottyUK?
RE: What is the r.m.s. value of a current?
You don't have to do a Fourier analysis to determine the rms value of the current. If you can define the current as any function of time, you can do the integration on that function. If you can't define the current as a function, but can measure it with a digital meter and capture the sample values, you can square each sample, sum the squares, take the square root, and divide by the number of samples. You could even develop a digital meter that does this automatically and market it as a "true rms" DMM. Your accuracy would be limited by the sample rate.
I guess you could measure the "effective value" with a thermometer by measuring the temperature rise of a "real resistor" with the test current passing through it, then run dc current through it and adjust the current until the temperature rise was the same for the same period of time. You could call the resultant dc current level the "effective value" of the test current. This would make current measurements a little more time consuming than using a "true rms" DMM.
The normal way to account for the frequency effects is to adjust the resistance to get an "effective resistance" instead of using dc resistance and developing an "effective value" of current. But hey, if you want to market your method of current measurement, go ahead. I'll try to get a patent on my "true rms" DMM and we can compete in the marketplace. Hope I'm not too late.
RE: What is the r.m.s. value of a current?
Precisely that is the problem! There are no true rms current meters!
The first digital rms-meters just measured the amplitude of the current and multiplied it with the factor 1/1,4142... (1/squ(2)). The manufacturers assumed that the current is a pure sine. The old-fashioned electromagnetic meters were more accurate than the firs digital meters.
Most modern digital meters make use of numerical sampling and Fourier Analysis.
RE: What is the r.m.s. value of a current?
As ScottyUK said, this is a power engineering topic at the 50-60Hz level. The exception you mentioned in your post:
"The term “effective current” refers to a low-frequency-sine-current that causes the same thermal “effect” in a resistor as a DC-Current. You just measure the temperature in this resistor and if the temperatures are equal, you can say that the “effective” values of these currents are equal. "
We are strictly dealing with low frequency current. There may or may not be significant harmonics in our 50-60Hz sinusoids and their effects will be negligable to a resistive heating element.
*Military uses 400Hz power systems to save on weight, but that is an exception to this "civilian" discussion about a simplistic concept under general terms.
RE: What is the r.m.s. value of a current?
Are you a physicist?
This world must really irritate you! Our instrument manufacturers can't make instruments with infinite bandwidth, our mechanical colleagues can't make anything flat (always some pesky atom sticking up), the electronics guys among us have not yet managed to get rid of thermal noise...
The mathematical definition of RMS, and any calculations based upon it, certainly appear inviolable. I spent a long time on Google looking for any evidence to the contrary, and couldn't find anything. The problem you perceive is that we, in our imperfect world, cannot measure what can be modelled by equations so well.
You are indeed correct that none of the sampling meters can measure from DC to infinite frequency, which is theoretically what is needed for a true rms instrument. But for most real-world measurements the minute error introduced by a bandwidth of a few hundred kHz on a high-end bench meter, or the 50MHz bandwidth of the excellent Tektronix current probe connected to a 'scope with a math function, is of no practical significance. The typical engineer has to work with primary transducers which are at best 0.1% accurate. The inaccuracy caused by the bandwidth limitation is likely to be at least one order of magnitude below this except in specific applications, for example where measurements may have to be made on the broad-spectrum pollution caused by an arc furnace. In these specific applications, instrument (and transducer)bandwidth is undoubtably important. Knowing when it is important, and when it isn't, is part of an engineer's job.
For applications such as the microwave engineering example you chose, the plumbers
RE: What is the r.m.s. value of a current?
This is good. In the context, the rms value is equal to the effective value.
Yes you can find the RMS value of any waveform by squaring the sample summing it with the other squared samples, take the average and then square root this. The whole idea of doing it this way (rather than the averaging method) is to get the real rms value, which includes other "frequencies" of the fundamental. Ultimately, there is only one waveform to measure. It does not break itself down. So if you sample a waveform over some specific time period and do the math above, you will get the rms value (harmonics and all).
No true rms meters? Yes there is and there are also averaging rms meters (as the salesman like to call them). See http://www.fluke.com/products/specifications.asp?SID=5&...
RE: What is the r.m.s. value of a current?
Hi Laplacian,
I’m German and I work in a Public Utility and my job is power quality maintenance.
In Germany they do not use the term RMS, they still say “effective value” (Effektivwert).
You cannot neglect the harmonics in a public utility net. If the THD of your voltage is less than 8% and U5 less than 6%, you do not have to take any measures.
There are no limitations to the harmonics level in the current (according to DIN EN 50160). The current you measure in a public net has nothing to do with a sine wave, it is always very “ugly”.
A public utility sells to their customers 50-Hz-Power, but the induction meter (Ferraris) measures the RMS of the total active power. Customers can sue the utility, because they didn’t agree to pay for harmonics.
An electronic power meter can measure the fundamental frequency of 50 Hz, but the customer may profit from harmonics if he uses the power for heating.
The utilities have big problems with the correct measurements of the electric power.
Besides, you have to derate the power of your transformers, because they can get overheated through the harmonics. You have to increase the diameter of your PEN. You have very high 150-Hz-Currents in the PEN, even if you have a balanced burden. The 150-Hz-Current in the PEN is a sum of the 150-H-Curents in your three phases.
Laplacian, how can you say that “their effects will be negligable to a resistive heating element“.
RE: What is the r.m.s. value of a current?
I'm going to let someone else post some comments, but I just wanted to compliment you on your technical English. I'm very impressed. I can barely ask for a large beer politely in German!
RE: What is the r.m.s. value of a current?
Thanks, Schotty. My English is far from perfect, but I try my best.
PS:
You do not have to speak German when you ask for a bear in Germany. Every German speaks basic English.
RE: What is the r.m.s. value of a current?
You were doing great until you mispelled beer!
I have found that even if you don't find someone who speaks English in Europe, a variation of the words "beer" or "bier" will get you a very good brew just about anywhere.
RE: What is the r.m.s. value of a current?
I noticed right away that I misspelled “Scotty” and “beer”, but you cannot edit your postings in this forum, can you?
Ich wollte keinen Baeren aufbinden!
P.S.
In Spain you have to say: Una cerveza, por favor
RE: What is the r.m.s. value of a current?
There is a possibility, however, that he was trying to say "a lager beer" and in that case, he misspelled "lager" when he wrote "large". Is not that an important aspect in this discussion?
I mean, if we are discussing the difference between RMS and effective value, we could as well discuss the spelling of "beer" and "large".
Those who think that secondary effects are proof that RMS and effective value and DC are different should rethink. All these terms are definitions and, as such, equivalent. Any difference that you might think that you notice is the result of inadequate instrumentation and/or badly designed experiments. Or pure lack of understanding.
But we can agree - I hope - that there is nothing like a large beer.
RE: What is the r.m.s. value of a current?
Prost!!
RCC
RE: What is the r.m.s. value of a current?
English spelling and beer are really very interesting matters to discuss, but I guess that you are referring to the posting of Scotty, when you talk about a “large beer”. I just typed “bear” instead of “beer”. I couldn’t correct my spelling, because I cannot find in this forum the “edit” button.
P.S. English spelling is really very tricky. You can even misspell the word “mis(s)pell”.
RE: What is the r.m.s. value of a current?
The areas for RMS are different from areas for Average values.
Therefore, there is the relationships between Iav=0.634 Imax
and Irms=0.707 Imax. This has not been properly addressed by most postings above.
RE: What is the r.m.s. value of a current?
and Irms=0.707 Imax. This has not been properly addressed by most postings above.“
jbartos,
We are not talking about sine waves, we are talking about „ugly current“.
RE: What is the r.m.s. value of a current?
You have filled one thread with ill-founded nonsense based on your misunderstanding of RMS and average. Please desist from filling this one too.
RE: What is the r.m.s. value of a current?
jbartos - Iav which you have described as average absolute value has no relevance to heating.
RE: What is the r.m.s. value of a current?
http://cybertron.vlsi.uwindsor.ca/85-124/Docs/85-124-La...
for:
""Average Responding Type RMS Meter
An average responding type RMS analog meter is designed for sinewave use only and rectifies (full-wave rectification) the input sinewave to form a DC waveform with an average value of 0.636 VMAX. The meter movement responds to the average DC value. An internal multiplying scale factor of 1.11 (=0.707/0.636) is used to obtain the correct RMS value.""
Where the meter without adjustment to rms would be indicating Iav, therefore, there would be smaller amount of heat calculated or measured over voltage and current. This is a basic principle between sinusoidal rms and average.
I am surprised that such basics of electrical engineering are posing so big problems to so many. Perhaps, an additional coursework at University, e.g. Windsor (originator of the above link content), would be beneficial.
RE: What is the r.m.s. value of a current?
Jbart,
Try the square root of the area under the square of the sinusoid.
///O.K. This yields Irms=0.707xImax, and Vrms=0.707xVmax
Prms=Vrms x Irms=0.707xImax x 0.707xVmax=(1/2) x Imax x Vmax
\\\
Wutz a wormer heater?
///RMS figures or values of the sinusoidal wave are bigger than Average values of rectified sinusoid. The most practical way to obtain the dc equivalent of the sinusoidal waveform is over the sinusoid full wave rectification, i.e. by absolute value of |sinwt|.\\\
Sounds nasty.
///Not necessarily, if a proper education is in the place.\\\
RE: What is the r.m.s. value of a current?
jb,
I can see that you are busy convincing the engineering community that they have been using the wrong definition of RMS for about one hundred years.
///To the contrary, the rms has been used very shrewdly, especially by the Utility, since the ac values for power show 19% higher values than DC values for power. What this means is that the Utility would lose 19% of profits by supplying customers DC electricity. I would love to get 19% more heat energy for the same money; especially in cold weather.\\\
Would it not be worth while to sit down and think.
///About what?\\\
You might find that you and Don Quixote are in the same business.
///I have clearly been seeing what is going on for quite a some time, have you? If not, try to figure out why the meter has to be adjusted in the following link:
http://cybertron.vlsi.uwindsor.ca/85-124/Docs/85-124-La...
\\\
RE: What is the r.m.s. value of a current?
jb wrote:
"(quoting me)'In the case of current through the heater, W = I²•R.'
///Not clear what you mean by I. Do you mean Idc=Iav or Irms?\\\"
I mean that the instantaneous power is equal to the instantaneous current squared time the resistance. It doesn't matter if the current is dc, sinusoidal, exponential, square wave, or worm shaped.
////True.\\\\
To get the energy, you integrate the instantaneous power over whatever time period you want.
////True.\\\\
The result is the integral of I²·dt over that time period.
////True. However, for sinusoidal waveforms:
Prms x t = kWhr = (1/2) Vmax x Imax x t = (0.707 x Vmax) x (0.707 x Imax) x t = (0.5) x Vmax x Imax x t = Vrms x Irms x t
For absolute value of sinusoid, |sinwt| averaged to dc:
Pav x t = kWhr = (2/pi) x Vmax x (2/pi) x Imax x t = 0.64 x Vmax x 0.64 x Imax x t = (0.405) x Vmax x Imax x t = Vav x Iav x t
The 19% is coming from (1-0.405/0.5)x100%=19%.\\\\
RE: What is the r.m.s. value of a current?
Where the meter without adjustment to rms would be indicating Iav, therefore, there would be smaller amount of heat calculated or measured over voltage and current.
Exactly the point. The meter without adjustment would indicate a value that would calculate the wrong amount of heat.
jbartos writes a lot about rectified sinewaves. The rms value of a full-wave rectified sinewave is the same as the rms value of unrectified ac. Since power equals I²·R, to get the average power, you have to average I², not I. The average of unrectified sinusoidal current squared equals the average of full-wave rectified current squared. This comes from the well-known fact that
(+N)² = (-N)² = |N|² where N is any number.
RE: What is the r.m.s. value of a current?
jbartos wrote:
Where the meter without adjustment to rms would be indicating Iav, therefore, there would be smaller amount of heat calculated or measured over voltage and current.
Exactly the point. The meter without adjustment would indicate a value that would calculate the wrong amount of heat.
///Finally, got it.\\\
jbartos writes a lot about rectified sinewaves. The rms value of a full-wave rectified sinewave is the same as the rms value of unrectified ac.
///Exactly true, never denied.\\\
Since power equals I²•R, to get the average power, you have to average I², not I.
///Yes, you can average I^2, however, the result is Irms^2 as I showed in my previous posting, not Iav^2. Therefore, there is a DC average and AC average (often expressed in in rms values. See the reference below.\\\
The average of unrectified sinusoidal current squared equals the average of full-wave rectified current squared. This comes from the well-known fact that
(+N)² = (-N)² = |N|² where N is any number.
///True, never denied. However, the average of the |Imax x sinwt| is Iav=0.64 x Imax, which is different from Irms=0.707 x Imax
There have been several postings on this issue within past four years in this Forum.
The following reference is available:
Ned Mohan, Tore M. Undeland, William P. Robbins, “Power Electronics, Converters, Applications, and Design,” Third Edition, John Wiley & Sons, Inc., 2003.
Page 14 Section 1-7
The uppercase symbols V and I refer to their values computed from their instantaneous waveforms. They generally refer to an average value in dc quantities and root-mean-square (rms) value in ac quantities.
Page 382 Section 13-5-1 Form Factor = Ia(rms)/Ia(average)..Equation (13-15)
The form factor will be unity only if Ia is a pure dc. The more Ia deviates from a pure dc, the higher will be the value of the form factor. The power input to the motor (and hence the power output) varies proportionally with the average value of Ia whereas the losses in the resistance of the armature winding depend on Ia(rms)^2. Therefore, the higher the form factor of the armature current, the higher the losses in the motor (i.e. higher heating) and, hence, the lower the motor efficiency.
The above paragraph implies that the dc value derived from sinusoidal waveform will produce less heat. This means that the dc value has to be adjusted to match the ac rms value to produce the same value of heat. Therefore, the rms value is somewhat inflated value in comparison with the dc value. I.e. the Utility is selling 19% more energy over the rms than it would be sold over the dc values.
Please, would you kindly support your statements with references, e.g. textbooks, papers, websites, handbooks, etc. to add more credibility to your statements.\\\
\\\
RE: What is the r.m.s. value of a current?
RE: What is the r.m.s. value of a current?
RE: What is the r.m.s. value of a current?
Comment to jghrist (Electrical) Dec 20, 2003 marked ///\\\
jbartos' reference page 382 is discussing dc motors.
///Actually, the paragraph is discussing application of the Form Factor that has been downplayed in the Standard Handbook for Electrical Engineers, and some other electrical engineering publications. By looking at the above posting, it appears that the Irms=10A would produce the same heat, electrical energy, electrical power as Idc=10A. This is essentially what has been discussed as incorrect, at least in my posting.\\\
I will grant him that if he is paying for dc service from his utility, he is getting cheated if the utility is providing a lot of ripple and charging him for the rms value of the current. Note that jbartos' reference states the losses in the motor (i.e. heating) depend on Ia(rms)^2. This is just what everyone else has been trying to convince him of; the rms value of current is the correct value to use when calculating heat produced.
///Yes, the rms value is correct for rms power, i.e. Prms=Irms x Vrms. This one is different from Pav=Pdc=Idc x Vdc.
There is also a statement:
""The power input to the motor (and hence the power output) varies proportionally with the average value of Ia ...""
Now, the dc motor is supplied with Vdc and Idc leading to power consumption Pdc=Vdc x Idc in watts. Corresponding HPs are indicated on the motor nameplate. Now, ac motor is supplied with Irms and Vrms leading to power VArms=Vrms x Irms. Corresponding HPs are posted on the motor nameplate. The input power is then Prms=Vrms x Irms x PF in watts. Considering relationships between Irms=.9 x Idc and Vrms = .9 x Vdc, there are different powers around. I do not see this addressed in many textbooks on AC machinery. If anyone happens to come across this in any literature, please, would you kindly post the reference and the Author. I see that some contributors have access to EPRI literature or industry standards worth of hundreds of thousands of dollars, then perhaps there might be some content dealing with this subject to clarify the differences.\\\
RE: What is the r.m.s. value of a current?
I also learnt what I know about Effective Value, RMS, Average Value and DC value about 40 years ago, but I obviously did not learn the same thing as you did.
I have been applying this knowledge and I have also been doing Fourier analysis (manually in the beginning and using Excel, MatCad and LabView later), working with ABB, Siemens, as a consultant and lecturer and in my own business. My field of work is drive systems, availability and power quality and I can assure you that none of my reports was ever questioned. At least not with regard to the RMS/Average/DC issues.
I also developped DSP based thermal protection relays for Adtranz (now Bombardier) and that is really where you have to consider current waveforms (traction motors with inverter and/or SCR control) and heating. And do you know what? My definitions (and most other engineers' definitions) worked flawlessly and were approved by the customer and the authorities.
So, I urge you to sit down and think again. And I wish you a Merry Christmas (and some insight).
RE: What is the r.m.s. value of a current?
Maybe it could migrate to eigen values. ?
WOC
RE: What is the r.m.s. value of a current?
I believe that everybody knows the definition of the “effective value of a current”, but the discussion is about the measurement and the calculation of this “effective value”.
Mr Ohm discovered his law before the invention of a AC-Generator, but AS-Current can also be used for heating (there were no non-linear loads then). So you have to define a current, which produces the same amount of heat in a resistor.
A true responding Rms-Meter measures the heat dissipated in a reference resistor.
You can also calculate the effective value of a current using the root-mean-squaring, but with less accuracy, because you do not know what frequencies and curves you are measuring.
That’s just a problem of definition!
In a 50-60-Hz-Grind with sinusoidal current there is no difference between Effective-Value and RMS-Value.
I wish you a Merry Christmas and a Happy New Year!