When to properly use "voltage"

[greypilgrim]

Hi.

I'm confused about the usage of "voltage". Some scripts I read introduce it in electrostatic as potential difference (where there's only the scalar potential), but continue using it when changing magnetic fields are present ("induced voltage"). Others make a clear distinction and introduce the term "electromagnetic force" or EMF.

Is there a compelling reason to distinguish between them, or should one use "voltage" for anything that's measured in volts?

 

[Dale]

There are a variety of opinions on this topic. I don’t think there is a universal consensus so I think you can pick your preference.

should one use "voltage" for anything that's measured in volts?

Personally, this is my preference. A voltmeter measures voltage so if it can be measured with a voltmeter then I am comfortable calling it a voltage.

Other people have strong opinions about distinguishing between voltages and EMFs. @vanhees71 perhaps you can better represent that viewpoint than I can.

 

[vanhees71]

There is no variety of opinions on this topic but just sloppy use of words. Indeed a "voltage" is a potential difference, i.e., it applies to electrostatics only.

Also a voltmeter measures not only potential differences but all kinds of EMFs, including induced ones from a time-varying magnetic field or that of a Galvanic cell/battery.

 

[greypilgrim]

Indeed a "voltage" is a potential difference, i.e., it applies to electrostatics only.

So "battery voltage" is technically wrong as well, or whenever voltage is mentioned when it comes to AC?

 

[vanhees71]

Yes, it's an EMF.

 

[f95toli]

So "battery voltage" is technically wrong as well, or whenever voltage is mentioned when it comes to AC?

No, AC voltage is definitely a "proper" voltage. Electromotive force (EMF) is used when talking about energy transfer, but that does not mean that AC voltage is always a EMF.
Much (but not all) of this about convention, but if the question is if there is such as thing as "AC Voltage" the answer is yes; it is part of the SI.

For batteries the EMF and the voltage are indeed not the same thing.

 

[Dale]

And that is why you always measure the battery EMF with an emfmeter and never a voltmeter.

 

[vanhees71]

A "voltmeter" measures always an EMF! Remember our extended discussion about the experiment in Lewin's E&M lecture ;-)).

 

[Dale]

I remember I wasn’t very convinced there or here.

Certainly, my voltmeter user manual says it measures voltage

https://manuals.harborfreight.com/manuals/98000-98999/98025.pdf

 

[vanhees71]

Well, the terminology in physics is not always very accurate. My argument is that both voltages and emf's are measured in Volts ;-).

 

[greypilgrim]

No, AC voltage is definitely a "proper" voltage.

Are you sure about this? Alternating voltages aren't in the realm of electrostatics, or so I thought.

 

[vanhees71]

For time-dependent fields you have $\vec{\nabla} \times \vec{E}=-\partial_t \vec{B}$, i.e., in AC circuits $\vec{E}$ in general has no potential and thus the use of the term "voltage", though very common, can lead to confusion.

There is this nice experiment by Lewin about the dependence of the read "voltage" on a voltmeter on the geometry of the wiring when there's time-varying magnetic flux involved, which is very illuminating in understanding the fundamental difference between potential differences ("voltage" in the proper sense) and more general "electromotive forces" (which is what's measured by a volt-meter).

https://web.mit.edu/8.02/www/Spring...edu/8.02/www/Spring02/lectures/lecsup3-15.pdf

 

[f95toli]

Are you sure about this? Alternating voltages aren't in the realm of electrostatics, or so I thought.

Yes, I understand that there are subtle points about the physics here; but the fact is that "AC Voltage" is a well developed field in electrical metrology and officially part of the SI. Hence, by convention as well as according to international standards it is correct to call it a voltage.

 

[vanhees71]

Where in the SI is the quasistationary approximation of electrodynamics explicitly used? The "new SI" is rather founded on the fundamental natural constants and quantum theory.

Also, as with any words, it's only important to know, what's really meant by them, and if you use "voltage" in AC circuit theory you should be aware that it's going beyond the usual meaning of an electric potential (at least as soon as inductances and transformers are relevant in a circuit).

 

[f95toli]

Where in the SI is the quasistationary approximation of electrodynamics explicitly used? The "new SI" is rather founded on the fundamental natural constants and quantum theory.

Also, as with any words, it's only important to know, what's really meant by them, and if you use "voltage" in AC circuit theory you should be aware that it's going beyond the usual meaning of an electric potential (at least as soon as inductances and transformers are relevant in a circuit).

Yes, I do understand the difference. However, the concept of "voltage" has been used for time varying quantities for a very, very long time even in "proper" electrical metrology . AC voltage is traceable to DC voltage standards via power measurement or more recently programmable Josephson voltage arrays.

Note also that the Volt in the SI is realized using the Josephson effect; meaning what is actually is measured is NOT actually a static potential but a filtered AC signal.
Again, this is not a question about physics but about convention; whether it conforms to the original meaning of volt as being limited to static potentials is not really relevant.

 

[vanhees71]

You mean in "proper" electrical engineering, not "metrology". The "metrology" of electromagnetic phenomena is of course very confusing, but in the SI it's pretty clear. There you simply define the C via setting the elementary charge to the corresponding now fixed value. The Volt is a derived quantity.

Of course, the mis en pratique is through quantum measures (magnetic flux quanta, Josephson junctions, etc., because the provide the most accurate realization of the "new SI" units), and of course "Volt" is the unit of general EMFs, not only "electrostatic potential differences".

 

[f95toli]

You mean in "proper" electrical engineering, not "metrology". The "metrology" of electromagnetic phenomena is of course very confusing, but in the SI it's pretty clear. There you simply define the C via setting the elementary charge to the corresponding now fixed value. The Volt is a derived quantity.

No, I meant metrology (as in metrology institutes such as NIST, PTB and NPL), most people who work in electrical metrology are physicists; not electrical engineers.
The mis en pratique for electrical units hasn't really changed with the new SI (so far the only real practical difference is that it now allows for the Ampere to be realized using electron pumps, so technically they can be used for traceable calibration).
The volt has been realized using the Josephson effect for decades (early 90s, then using CODATA values for the Josephson constant), the new SI is conceptually new but so far it hasn't really changed how traceable electrical calibration is done.

 

[Herman Trivilino]

A "voltmeter" measures always an EMF!

That's not common usage. In a circuit you can measure the voltage drop across a resistor with a voltmeter. It is not a measurement of an EMF.

EMF is an outdated term, introduced into the lexicon of physics before voltage was fully understood. Unfortunately, it is still used in cases where the voltage is across an element that's putting energy into a circuit, but it is never used to describe a the voltage across a circuit element that is extracting energy from a circuit.

At least I have never seen it used in this context.

 

[vanhees71]

The voltage drop across a resistor is indeed a potential difference, but it's also an EMF. An EMF is defined as the line integral along a closed path. It includes the potential differences across a resistor or capacitors, but also the EMF of a source. This closed line-integral does not vanish in general but give the time change of the enclosed magnetic flux. The general formula, including the case of moving parts of the surface enclosed by the boundary line and this line itself, is
$$\int_{\partial A} \mathrm{d} \vec{x} \cdot (\vec{E} + \vec{v} \times \vec{B})=-\frac{\mathrm{d}}{\mathrm{d} t} \int_A \mathrm{d}^2 \vec{f} \cdot \vec{B}.$$
That's all, I'm saying.

Admittedly "electromotive force" is an old-fashioned terminology. Of course, "force" her refers to an energy-like quantity rather than force in the Newtonian sense. BTW. Helmholtz's famous paper about the energy-conservation law was titled "Über die Erhaltung der Kraft" ("On the conservation of force"). However, I've also not found another more modern name for it.

 

[Herman Trivilino]

However, I've also not found another more modern name for it.

Voltage source.

 

[vanhees71]

Yes, but then you have "voltage" again. Many students confuse it with potential differences... I think, unfortunately there's not really a good solution. It's very hard to change the use of technical terms, even when they are problematic as in this case.

 

[DaveE]

However, I've also not found another more modern name for it.

It's "induced voltage" to me.

 

[Dale]

The voltage drop across a resistor is indeed a potential difference, but it's also an EMF.

Which is also one of the main reasons that I feel comfortable just calling them all voltages.

An EMF is defined as the line integral along a closed path. It includes the potential differences across a resistor or capacitors, but also the EMF of a source.

And here, even very well informed proponents of the EMF terminology such as yourself, do what seems contradictory to me. You say that the EMF is defined as a line integral along a closed path, but then in the very next sentence you speak of the EMF of a source which is a single component and not a closed path.

Even very high end voltmeters explicitly state that they measure voltages, not EMF's,
https://download.tek.com/manual/2182A-900-01_May_2017.pdf
https://mse.engin.umich.edu/interna...nano-volt-micro-ohm-meter/agilent-34420-90001
and only speak of (thermal) EMF as something that introduces a bias in the voltage measurement.

If metrologists, manufacturers, and users all call the quantity measured by a voltmeter a "voltage", then I am perfectly comfortable doing so too even if some physicists insist that it is an EMF. In this sense there is indeed a variety of opinions on this topic. The metrologists, manufacturers, and users do in fact use different terminology of the physicists.

 

[DaveE]

Which is also one of the main reasons that I feel comfortable just calling them all voltages.

And here, even very well informed proponents of the EMF terminology such as yourself, do what seems contradictory to me. You say that the EMF is defined as a line integral along a closed path, but then in the very next sentence you speak of the EMF of a source which is a single component and not a closed path.

Even very high end voltmeters explicitly state that they measure voltages, not EMF's,
https://download.tek.com/manual/2182A-900-01_May_2017.pdf
https://mse.engin.umich.edu/interna...nano-volt-micro-ohm-meter/agilent-34420-90001
and only speak of (thermal) EMF as something that introduces a bias in the voltage measurement.

If metrologists, manufacturers, and users all call the quantity measured by a voltmeter a "voltage", then I am perfectly comfortable doing so too even if some physicists insist that it is an EMF. In this sense there is indeed a variety of opinions on this topic. The metrologists, manufacturers, and users do in fact use different terminology of the physicists.

Yes, quite a pedantic thread (again). I worked for over 30 years in analog circuit design, control systems, power conversion, etc. Everyone called everything voltage in that world. Lasers and satellites still worked just fine regardless.

 

[vanhees71]

Which is also one of the main reasons that I feel comfortable just calling them all voltages.

And here, even very well informed proponents of the EMF terminology such as yourself, do what seems contradictory to me. You say that the EMF is defined as a line integral along a closed path, but then in the very next sentence you speak of the EMF of a source which is a single component and not a closed path.

There's no contradiction. If you measure the "voltage drop" along a resistor, you connect a voltmeter, and then you measure the EMF along the closed circuit consisting of the resistor and the voltmeter. To get the voltage drop across the resistor of the original circuit the resistance of the voltmeter must be much greater than the resistance of the resistor.

Even very high end voltmeters explicitly state that they measure voltages, not EMF's,
https://download.tek.com/manual/2182A-900-01_May_2017.pdf
https://mse.engin.umich.edu/interna...nano-volt-micro-ohm-meter/agilent-34420-90001
and only speak of (thermal) EMF as something that introduces a bias in the voltage measurement.

If metrologists, manufacturers, and users all call the quantity measured by a voltmeter a "voltage", then I am perfectly comfortable doing so too even if some physicists insist that it is an EMF. In this sense there is indeed a variety of opinions on this topic. The metrologists, manufacturers, and users do in fact use different terminology of the physicists.

Then voltage=emf! This is just a fight about semantics. One has just to make clear, what's meant when using a word. If voltage=emf in this community it's fine with me. I only know that there's a lot of confusion when misunderstanding it as "potential difference" when there is no potential.

 

[SredniVashtar]

Personally, I think that differentiating between voltage (path integral of the total electric field) and scalar potential difference (path independent integral of the conservative part of the electric field) can remove most if not all of the ambiguities associated with this concept.

A few ways (and notations, which should be self explanatory) to see this decomposition:

Etot = Ec + Enc
= Ecoul + Eind
= Erot + Esol
= - Grad phi + (-dA/dt)

The path integral of the lhs is voltage, the path integral of the first part of the rhs is the potential scalar difference, and the rest is the EMF contribute that makes voltage - in general - path dependent.

A minus sign can apply to all path integrals, depending on convention.

(Sorry, I have all integral relation in markdown, but on my PC and for some reason I can't post from there, and reentering them all by smartphone keyboard is not gonna happen).