Talk:Voltage

Generalization to electrodynamics section

I think the equation

${\begin{aligned}\Delta V_{AB}&=V(\mathbf {r} _{B})-V(\mathbf {r} _{A})\\&=-\int _{\mathbf {r} _{A}}^{\mathbf {r} _{B}}\left(\mathbf {E} +{\frac {\partial \mathbf {A} }{\partial t}}\right)\cdot \mathrm {d} {\boldsymbol {\ell }}\end{aligned}}$

needs a reliable source. I know that it has been in the article a long time, but as far as I can tell, it is unsourced.Constant314 (talk) 12:42, 8 October 2021 (UTC)

I have hopefully fixed this by adding a footnote referencing the theorem that connects this equation to the one before it (and that previous equation is straight from Griffiths). Hopefully that clears it up. Hddharvey (talk) 13:58, 8 October 2021 (UTC)

An explanatory note is not usually considered a sufficient response to a request for a citation. But I agree that it follows directly from the previous (referenced) equation simply by integrating it. SpinningSpark 16:32, 8 October 2021 (UTC)

The math is fine. It needs a citation to show that reliable sources use this definition of voltage in dynamic situations.Constant314 (talk) 18:14, 8 October 2021 (UTC)

You raise a good point. I had been thinking about this a bit. I haven't really seen people talk of "voltage" at all in electrodynamics - they just speak in terms of the potentials but you don't really hear the term "voltage" come up. If you define "voltage" as "difference in electric potential" then the definition in this section makes sense - but I don't think it's really used much. (I could actually argue that electrical engineers indirectly use this definition without realising it, but I'm not sure whether any reliable sources make that argument - no need to overcomplicate it anyway). Usually the term "voltage" is used in the electrostatic (or in an electrostatic approximation at least) or in a lumped or distributed element model where its meaning becomes more and more abstract at higher frequencies. The uses of "voltage" in the electrostatic and lumped element model scenarios work well with voltage as the "work by/against the electric field per unit charge".

To address these issues, I have edited the page to trim down the section on "Generalization to electrodynamics". I think it is nice to still have a passing mention of this topic (and refer to the main article) - however I have avoided explicitly mentioning this "generalization" as a definition of voltage. There was also discussion in the "Definition in electrostatics" section that alluded to the lumped element model - I have moved this discussion to the section that actually discusses the lumped element model. Hddharvey (talk) 02:54, 9 October 2021 (UTC)

All-in-all good improvements. As an engineer, I tend to the common man’s definition. Voltage is what the voltmeter reads. It may vary depending on how you lay the leads down. That’s Ok. The purpose of the math is to predict what the voltmeter will read. Potential and potential difference are nuanced terms and gauge dependent. Voltage is about whether the lights work, regardless of the gauge. Constant314 (talk) 03:31, 9 October 2021 (UTC)

This book page may help here. SpinningSpark 08:43, 9 October 2021 (UTC)

Thanks for the reference. I have seen a few sources (now including this one) generalize the term "voltage" via the integral of E.dl. In electrostatics we have two equivalent definitions: integral E.dl and potential difference. Generalizing to electrodynamics, it is no longer true that both are equivalent and we have to pick one of the two. I'm not sure if there is a consensus one way or the other though (if there was, we could maybe include it in the article). I don't personally like using the term "voltage" in a path-dependent way since it rubs against what we try to do in circuit theory and in the lumped element model. The whole effect of the lumped element model is to ignore the "non-conservative parts" of E by assuming they're contained in each element, leaving the exterior electric field due to charges only so that we can define voltages nicely. Maybe this could be considered equivalent to generalizing voltage as the electric potential difference in the Coulomb gauge (since there is no propagation delay and it gives the same potential as electrostatics - effects of induction and propagation are shoved into the $-\partial \mathbf {A} /\partial t$ component, which can hopefully be modelled with lumped or distributed elements). Hddharvey (talk) 09:17, 9 October 2021 (UTC)

However, I guess there doesn't have to be a consensus to include it in the article - you could always just write that the term "voltage" is ambiguous in electrodynamics and can be used either to refer to the electric potential difference (in some gauge) or integral of E.dl (with ideally a source to back up either case). Hddharvey (talk) 09:22, 9 October 2021 (UTC)

Yes, in cases where there is no consensus we should make that clear and give both views. I'm a simple EE – if a voltmeter doesn't measure it then it's not voltage. SpinningSpark 09:54, 9 October 2021 (UTC)

Okay, I updated the page to mention your reference. I don't have a source for people using voltage in the other sense (in the general case), but the article currently doesn't explicitly state that anyway, so no problemo. And maybe you're right - I'm probably overthinking things when it comes to how I think of voltage. I originally took a deep dive into what "voltage" precisely means a few years ago when I saw this video (there was a follow-up here with an accompanying document here but I'm not very satisfied with the idea that voltage across an inductor is "defined differently" to other components). Hddharvey (talk) 10:49, 9 October 2021 (UTC)

FEC

Topic can't understand 2402:8100:2858:4561:0:0:4C65:D821 (talk) 12:21, 5 December 2021 (UTC)