Lumpable (lumped and not lumped) and unlumpable for Dummies
What makes a circuit lumpable? First of all its physical dimension have to be negligible compared to the wavelength of the electrical oscillations, and then voltages and currents 'offered' at the terminals must be well defined at any time. You want your circuit to be independent on how you measure voltage between two points or current along the same branch.
Here is a snapshot from page 2 of "Basic Circuit Theory", by Desoer and Kuh (don't let the title deceive you: this is the Bentley of circuit theory books).
Source: Desoer, Kuh "Basic Circuit Theory"
https://i.postimg.cc/sf4j3HbF/Desoer-Kuh.jpg
Note: in the case of Lewin's ring we know that the frequency is so low that retardation effects play no role; the condition that voltages and current be well defined is what we must be careful about. In particular, it's voltage the variable in discussion.
If we can interact with the component only through its terminals and we are not allowed to get inside, the only paths along which we can evaluate voltage (which is a path integral) are those 'outside' the component. And we require that the voltage be the same no matter how we choose the path joining the terminals.
In the case of magnetic components, we know that voltage along the path joining two points depends on the path, when we can go from one side of the magnetic flux region to the other. This is a direct consequence of one of Maxwell's equations (Faraday's law: curl E = -dB/dt) and basic vector integral calculus (Stokes theorem, the definitions of circulation and the definition of flux).
In order for voltage to be well defined, we must avoid paths that go through or 'on the other side' of the variable magnetic flux. The reason is simple: if the same starting and ending points admit two paths that are on opposite sides of the magnetic region, then the closed path formed by joining these two paths will enclose a variable flux and they must necessarily sum up to a nonzero value
Fig. two paths and the area enclosed (to be added later)
Now we know how to make voltage unique: allow only paths that cannot get into the forbidden zone. We enclose the component inside a black box (or an impenetrable wall) and we do not question what is inside. We must also ensure that our circuit path - the orange dashed line - does not contain variable magnetic flux itself.
Here is a lumpable circuit. The same circuit can be considered
- lumpED, when we avoid the forbidden paths by erecting an impenetrable wall and we only access the magnetic component through its terminals (note the circuit path that does not go into the forbidden zone, but instead jumps at the terminals). KVL works inside the green circuit path.
- NOT lumped, when we consider a circuit path (for the same physical system that we usually address with the name 'circuit') that encloses part or all of the variable magnetic flux region. In this case any path inside the orange dashed line that represent the circuit's premises is allowed. Some of these paths - not all, but only one would suffice - can 'go on the other side' of the magnetic region, making voltage between two points NOT WELL DEFINED.
Fig. the same lumpable circuit can be considered either lumped or not lumped
https://i.postimg.cc/8kFQxNqc/Lumpable-can-be-lumped-or-not.jpg
So far, so good: it looks like we have freedom to choose when we can make KVL works.
NO. There are circuits that are not lumpABLE. There are circuits where the circuit path is REQUIRED by definition or physical constraint to include the variable flux region. In this case it is not possible to find a green circuit path that connects the lumped components AND does not contain the variable flux region at its interior. Only orange paths are available.
Lewin's ring is an example of such a circuit. The resistors R1 and R2 are required to be on the opposite sides of the solenoid, i.e. the variable flux region. And you cannot find a circuit path that connects them without enclosing such forbidden zone. Voltages for points on your circuit will be path dependent.
Fig. an unlumpable circuit: you cannot exclude dB/dt region from the circuit path
https://i.postimg.cc/5NyZDPVS/Unlumpable-circuit.jpg
And, no. You cannot model it with several tiny little transformer secondaries distributed along the perimeter, because you would forfeit the constraint that the two resistors be on the opposite sides of the variable magnetic region. It's exactly that constrain - your circuit path containing the dB/dt region - that makes Lewin's ring so special.
If you change the magnetic field region you are considering a different problem
Fig. an unlumpable circuit: you cannot exclude dB/dt region from the circuit path
https://i.postimg.cc/x1KgZHcP/Spot-the-differences.png
In order to model it with two or four lumped coils, the magnetic field region must be split to accommodate a circuit path that does not include any of it. I used the same 'stellated' path style used by Feynman in figure 22-9 on page 22-7 of his second volume of lectures.
You have nothing else but to resort to the "Moral High Ground Fallacy". On the other hand, the KVL side has provided theoretical results and experimental results that perfectly agree with each other. What have you provide? Just a big pile of steaming BS.
If both your theory and experiments depend on each other, that'll do you no good.
Because the experimental data presented here was obtained by more or less blindly poking around circuits with a volt meter, and without any understanding of what is actually going on. So the measurements taken do not support in any form the claim that "KVL holds".
Talk for yourself! Don't reflect your ignorance into other people. When I saw Lewin's experiment for the first time I thought immediately: he is ignoring the induced voltage in the scope probes! The other day I showed Lewin's circuit to a friend of mine and almost instantaneously he also said "he is measuring the voltages incorrectly". I bet that is the case with the vast majority of people that know how to use an oscilloscope.
As for "If both your theory and experiments depend on each other, that'll do you no good", well, last time I checked that is how science works. That is exactly how Maxwell equations were derived.
It's not possible to measure two different voltages in the same spot.
Why does the wall have to be there? How about I put my wall here, in the very center of the toroid just to keep idiots from dropping their volt meter leads through there, as shown in the diagram below - it's functionally identical to your wall, yes? And its a lot less bricks!
https://i.postimg.cc/qqG0vgRV/20211124-213839.jpg
Above: See the crosshatched wall inside of the core.
Actually, your ring above is COMPLETELY lumpable as a 1 turn transformer output in series with two resistors.
Just like shown with my Lewin Clock, there are planes along which probe leads may be run where there is no non-conservative field which allows unambiguous physical measurements to be made of the two half-turns.
No, it all boils down to certain people being unable to understand what they read, and being incapable of assimilating new concepts that go beyond their limited knowledge. Like trying to explain the orbit of planets with epicycloids: it works numerically, but it betrays a fundamental ignorance of the actual physical phenomena behind the motion.
Do you really think that by now these guys haven't already figured out that their rhetoric is pointless? They know darn well that Lewin is right, Mehdi is wrong, KVL doesn't hold under a varying magnetic field, static wires are just low ohm resistors that can't generate voltages, you can measure two different voltages across the same two points in a circuit, etc., etc., etc.
So, if they are not intellectually impaired, why do they keep producing assertions that deny the evidence and reject facts and logic? Even when repeatedly debunked left and right?
As I said in an early post, stupidity is a moral issue. Even when you give them the answer they expect, they'll say you're wrong. This is because they determined arbitrarily that you're wrong. No matter what.
Although discussing with them may sometimes produce an interesting socratic-like dialog, it also may give the occasional reader the impression that their questioning is legitimate.
You have nothing else but to resort to the "Moral High Ground Fallacy". On the other hand, the KVL side has provided theoretical results and experimental results that perfectly agree with each other. What have you provide? Just a big pile of steaming BS.
It really is their religion, isn't it? I hate to say it, but that seems to be what it comes down to.
No, it all boils down to certain people being unable to understand what they read, and being incapable of assimilating new concepts that go beyond their limited knowledge. Like trying to explain the orbit of planets with epicycloids: it works numerically, but it betrays a fundamental ignorance of the actual physical phenomena behind the motion.
Do you really think that by now these guys haven't already figured out that their rhetoric is pointless? They know darn well that Lewin is right, Mehdi is wrong, KVL doesn't hold under a varying magnetic field, static wires are just low ohm resistors that can't generate voltages, you can measure two different voltages across the same two points in a circuit, etc., etc., etc.
So, if they are not intellectually impaired, why do they keep producing assertions that deny the evidence and reject facts and logic? Even when repeatedly debunked left and right?
As I said in an early post, stupidity is a moral issue. Even when you give them the answer they expect, they'll say you're wrong. This is because they determined arbitrarily that you're wrong. No matter what.
Although discussing with them may sometimes produce an interesting socratic-like dialog, it also may give the occasional reader the impression that their questioning is legitimate.
You have nothing else but to resort to the "Moral High Ground Fallacy". On the other hand, the KVL side has provided theoretical results and experimental results that perfectly agree with each other. What have you provide? Just a big pile of steaming BS.
It really is their religion, isn't it? I hate to say it, but that seems to be what it comes down to.
Yet the only thing you managed to prove is that Lewin is right and you are wrong.
Keep on trying.
Who knows you manage to win converts to the cause of stubborn ignorance.
Why does the wall have to be there? How about I put my wall here, in the very center of the toroid just to keep idiots from dropping their volt meter leads through there, as shown in the diagram below - it's functionally identical to your wall, yes? And its a lot less bricks!
https://i.postimg.cc/qqG0vgRV/20211124-213839.jpg
Above: See the crosshatched wall inside of the core.
Good, it seems that the top right corner of this image I posted nearly a week ago
has finally reached your brain. A little slow, but better late than never.
Of course, you still don't understand it even though I remade both images using the very same circuit. Voltage is path-dependent in both situations: with or without a wall.
What we choose to do in order to be able to apply KVL in our circuit is limit our circuit path to the region of space where voltage between any two points is the same for all paths within that region of space. In short, we PRETEND voltage is single-valued because we willingly ignore the paths along which it will give multiple values.
The bag of nails in my basement is nodding. It seems to be able to understand this.
Do you?
QuoteActually, your ring above is COMPLETELY lumpable as a 1 turn transformer output in series with two resistors.
Prove it.
QuoteActually, your ring above is COMPLETELY lumpable as a 1 turn transformer output in series with two resistors.
Prove it.
Draw the resistors in that exact position around the shaded dB/dt region, with that shape and size (the one where I write "Example where there is no room to twist it"), and then draw a green dashed line that is your circuit's path. It has to join the resistors' terminals with one another and with the lumped transformer. Note that the shaded disk should all be contained into your lumped transformer, and your green dashed circuit path must NOT INCLUDE the shaded disk.
Go ahead, I'll wait for your picture.
Quote
Just like shown with my Lewin Clock, there are planes along which probe leads may be run where there is no non-conservative field which allows unambiguous physical measurements to be made of the two half-turns.I am not even sure this sentence makes any sense. But I will post the fields for your clock, and you will see that what you are measuring is the path integral of the conservative part of the electric field along the hands of the clock. So much for your good probing...
But let's put this aside for a while, you will comment when I have posted the pictures.
For the moment, let's see that picture where you lump Lewin's rings by enclosing the shaded disk inside your transformer but NOT inside the circuit path that connects it to the resistors.
Remember, the resistor and the disk must remain in the same position, you cannot move them nor split it.
I am waiting.
About the "experiments". It should be abundantly clear by now what is wrong with Jesses EI-core measurements and why they are no proof for "KVL holds". What more than "the solution is in the fields" (plural) can I say.
One cannot consider only the magnetic flux and simply ignore the electric field that is inevitably present as well.
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It's not possible to measure two different voltages in the same spot.
But you aren't measuring the voltages in the same spot, are you? The two voltmeters are in two different spots.
Why does the wall have to be there? How about I put my wall here, in the very center of the toroid just to keep idiots from dropping their volt meter leads through there, as shown in the diagram below - it's functionally identical to your wall, yes? And its a lot less bricks!
https://i.postimg.cc/qqG0vgRV/20211124-213839.jpg
Above: See the crosshatched wall inside of the core.
The real answer is "Don't add undocumented turns to your transformer and expect physics to work."
Your probing method inherently subtracts induced voltage from your reading, leaving you with only the ohmic losses.
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You are, buy definition, only measuring ohmic losses, because you are using a method of measuring which specifically subtracts all induced voltage differences.
QuoteNow the big question is of course, can KVL be somehow made to work in this arrangement, and for that we need to find an equivalent circuit with lumped elements. That will prove to be difficult, because one cannot find a place where to stick a lumped transformer winding or voltage source and still satisfy all the measurements taken in the various places. We can obviously not put it in the wires between the resistors, because we measure 0V across them. It can also not be in "R" and/or in "2R". If we put a 2/3V source "inside" 2R, that would violate the "-1/3V" reading on the rightmost volt meter.
So, where is it? Apparently it is there, but we cannot pinpoint it and measurements between two identical points show different results depending on how we instrument the circuit (1/3V, 2/3V, -1/3V). For circuit theory and KVL this is a nightmare. That's why there are "equivalent circuits" e.g. for transformers which try to model physics with lumped elements full of imaginary numbers and "magic items" like ideal transformers because they relieve engineers of having to think about physics. And to make KVL work. But now and then, when Sir James Clerk Maxwell makes an appearance, everyone is baffled why their circuits don't work.
The only reason we cannot pinpoint it is because it is all the way around. Sure, it MODELS and MEASURES as if it's at the center, but if you look at Faraday, and Maxwell, it's dB/dt inside an area, and measuring it on a solid core of effective infinite length is difficult because the active element of the transformer is no different than our volt meter leads, and they too, suffer from that same effect of induced voltage.
And then we end up with this crazyness where you claim there is 0 volts across all the wires, but 1 volt across the resistors, where exactly is the voltage coming from?
Oh? It's induced? So it is there. It's just difficult to measure in certain specific situations which have been designed for it to be difficult to measure.
[...]
Sorry man, it's all been explained and shown in pictures and equations. But you just ignore them.
Instead you make up incomplete analogies, like the "wall inside the transformer".
Go back and look at the diagram I made about the ring core transformer. It's all there in red, blue and green. If you don't understand how this transfers to your EI core, sorry, not going to spoonfeed you.
The electric field is there. It cannot be ignored. It cannot be discussed away if you don't want to neglect everything discovered in physics since 1861.
Why does the wall have to be there? How about I put my wall here, in the very center of the toroid just to keep idiots from dropping their volt meter leads through there, as shown in the diagram below - it's functionally identical to your wall, yes? And its a lot less bricks!
https://i.postimg.cc/qqG0vgRV/20211124-213839.jpg
Above: See the crosshatched wall inside of the core.
The real answer is "Don't add undocumented turns to your transformer and expect physics to work."
This "wall inside the transformer" is not equivalent.
It makes people believe they'll be safe if their probe leads do not cross it and so they stop looking at the complete paths and instead concentrate on "forbidden planes". It has certainly not stopped you from adding "undocumented turns" in your EI core experiment.
Your probing method inherently subtracts induced voltage from your reading, leaving you with only the ohmic losses.
[...]
You are, buy definition, only measuring ohmic losses, because you are using a method of measuring which specifically subtracts all induced voltage differences.
But there's no choice, really.Your voltmeter will only show you the sum of the electric fields along the path formed by its probe leads and whatever is between the tips.
This path can either be conservative ("blue") or non-conservative ("red"). But you must treat each path as independent from all other paths. For example in my diagram, the RED path containing the rightmost voltmeter only sums up fields along its path, i.o.w the electric field across "2R" and all external electric field components around the core (green arrows) it encloses! It doesn't matter if the probe leads penetrate your "wall inside the transformer" because "2R" is also on that path, closing the loop. Do you still not see what happened with your EI core?
QuoteNow the big question is of course, can KVL be somehow made to work in this arrangement, and for that we need to find an equivalent circuit with lumped elements. That will prove to be difficult, because one cannot find a place where to stick a lumped transformer winding or voltage source and still satisfy all the measurements taken in the various places. We can obviously not put it in the wires between the resistors, because we measure 0V across them. It can also not be in "R" and/or in "2R". If we put a 2/3V source "inside" 2R, that would violate the "-1/3V" reading on the rightmost volt meter.
So, where is it? Apparently it is there, but we cannot pinpoint it and measurements between two identical points show different results depending on how we instrument the circuit (1/3V, 2/3V, -1/3V). For circuit theory and KVL this is a nightmare. That's why there are "equivalent circuits" e.g. for transformers which try to model physics with lumped elements full of imaginary numbers and "magic items" like ideal transformers because they relieve engineers of having to think about physics. And to make KVL work. But now and then, when Sir James Clerk Maxwell makes an appearance, everyone is baffled why their circuits don't work.
The only reason we cannot pinpoint it is because it is all the way around. Sure, it MODELS and MEASURES as if it's at the center, but if you look at Faraday, and Maxwell, it's dB/dt inside an area, and measuring it on a solid core of effective infinite length is difficult because the active element of the transformer is no different than our volt meter leads, and they too, suffer from that same effect of induced voltage.
Now wait a second. "We cannot pinpoint it because it is all the way around" does not rhyme with treating the red wires in your EI core experiment as lumped voltage sources, right?
Because there you claim (incorrectly) that, since your volt meter leads don't "go through the core" they don't have any voltage induced, right?
So the only voltage source must be the red wire, right? So which way will you have it? It cannot be both.
QuoteAnd then we end up with this crazyness where you claim there is 0 volts across all the wires, but 1 volt across the resistors, where exactly is the voltage coming from?
Oh? It's induced? So it is there. It's just difficult to measure in certain specific situations which have been designed for it to be difficult to measure.
So what you're saying is that Nature is treating poor engineers badly and making it difficult for them on purpose. Bad, bad Nature! I shall put you on my naughty list! No presents for you this Christmas!
SCNR
PS: the induced potential is not difficult to measure. Just sum up all electric fields along the "R+2R" loop and there you have it: 1V. Just be careful not to accidentally add another non-conservative external electric field to your measurements and forget to account for it.
Sadly, my understanding hasn't changed.
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Dude, the reason your script looks like it stinks to you is because it stinks!
The Maxwell–Faraday version of Faraday's law of induction describes how a time varying magnetic field creates ("induces") an electric field
Oh, goodness me. What a wondrous, copious and melliflously superfluous word salad. All to hide the fact that you cannot lump Lewin's ring. Here, let me repeat the question you are so eloquently avoiding to answer.
Sadly, my understanding hasn't changed.
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Dude, the reason your script looks like it stinks to you is because it stinks!
Oh, goodness me. What a wondrous, copious and melliflously superfluous word salad. All to hide the fact that you cannot lump Lewin's ring. Here, let me repeat the question you are so eloquently avoiding to answer.
This is Lewin's ring: two resistors in a single loop that goes around a circular region (let's consider it of the same size as the loop, so you can see there is no 'room to twist' the wires) of variable magnetic field. The resistors are required to be on the opposite sides of the variable magnetic field region.
https://i.postimg.cc/pLmfyHxZ/Lewin-ring-is-unlumpable.jpg
Please, show everybody you can draw a circuit path (make it green, meaning it's 'flux-free') that joins the resistors' terminals to the "lumped transformer secondary" terminals and DOES NOT INCLUDE the variable magnetic field region in its interior. Like I did for the lumpABLE circuit I decided to see as lumpED (in my post "Lumpable (lumped and not lumped) and not lumpable circuits for dummies").
In addition, you can also show everybody you can draw the path inside your "lumped transformer secondary" that DOES INCLUDE the variable magnetic field region (make it orange) but IS NOT part of the green circuit path.
I will show you that if you can do that you will run into contradiction.
Too bad my armchair is at the quantum mechanic's shop for repairs and I cannot fly away to another galaxy.
Oh, goodness me. What a wondrous, copious and melliflously superfluous word salad. All to hide the fact that you cannot lump Lewin's ring. Here, let me repeat the question you are so eloquently avoiding to answer.Says the guy that when solving Lewin's ring, the first thing he does is to lump the EMF, and then he follows up by using KVL to find the voltages in the resistors!
Oh, goodness me. What a wondrous, copious and melliflously superfluous word salad. All to hide the fact that you cannot lump Lewin's ring. Here, let me repeat the question you are so eloquently avoiding to answer.Says the guy that when solving Lewin's ring, the first thing he does is to lump the EMF, and then he follows up by using KVL to find the voltages in the resistors!No, says the guy who uses Faraday's law and not KVL, but you can't tell the difference.
It seems you're way behind on answering questions -- all you do is ask ask ask ask, but you never answer in the last few days. It's about time you warmed up your crystal ball to get some answers!
Here's some questions I've been asking for days and you're refusing to answer:
You have admitted that in the V1 and V2 voltages in the diagram directly below will both read the same voltage, and you have also admitted that V2 will be suitable as an element in a KVL loop:
Question One:
How can V1 not also be suitable since they both measure the same voltage? Your own trusted source says that if an unambiguous physical measurement of the voltage across the two terminals can be obtained, then KVL holds! How can V1 not work for KVL?
Question Two:
Considering your own trusted source, if a ONE TURN TRANSFORMER SECONDARY on a toroidal transformer has a voltage that is unambiguously physically measurable, then it should qualify as an element for a KVL loop, Correct?
For example, in the following transformer diagram with a safety wall in the center, why would the output winding not be suitable as an element in a KVL loop?
Oh boy, where to even begin...
Okay, first of all: I'm not in denial of observable reality. In fact, I took the reality YOU observed, turned it into a nice, colorful diagram and explained each measurement YOU did using only Ohm, Maxwell and Faraday. I showed in which loops voltage is induced and why not in others, explained every number you obtained.
Here it is again:
Second: I did not "dream up" any "magic electric field". It's existence was found and explained by James Maxwell. It's his second field equation.Quote from: WikipediaThe Maxwell–Faraday version of Faraday's law of induction describes how a time varying magnetic field creates ("induces") an electric field
Third: It is very obvious how to measure it: create a wire loop around any area with changing magnetic flux, create some discontinuity (make a cut, put a resistor in the loop), measure the electric field across it. The probe is just some wire coiled up. It senses non-conservative electric fields. Just the same, each turn around a transformer core "measures" this electric field.
I hope this is not too much to stomach.
You mentioned repeatedly how the magnetic flux is fully contained inside a transformers core (which is not exact but, eh, good enough). Then explain how a conductor (charge particles) outside of the core and thus outside of the magnetic flux, can interact with it. "Spooky action at a distance"? The answer "Dude, because Faraday" is not enough. What is the mechanism behind it?
Btw how's that lumped circuit coming along @Sredni asked you to come up with?
If you honestly answer the above questions and I'll do my best to draw up Lewin's loop and show how I would measure the voltage across the half turns.
It seems you're way behind on answering questions -- all you do is ask ask ask ask, but you never answer in the last few days. It's about time you warmed up your crystal ball to get some answers!
Here's some questions I've been asking for days and you're refusing to answer:
No, I have answered the questions that made some sense. But you have such big holes in your knowledge that you end up asking questions that have little to no sense. I was going to make a post about the misconceptions your posts are full of, but there are way too many. For example, I have written many many times that KVL applies in all regions of space that do not contain/cut a variable magnetic flux. So, in the lumpable circuit with the twisted wire it goes without saying that, since there is no changing flux in the small loop formed by V2, the wires and the jump at the first twist, KVL works.
But you keep asking questions that contain nonsense in themQuoteYou have admitted that in the V1 and V2 voltages in the diagram directly below will both read the same voltage, and you have also admitted that V2 will be suitable as an element in a KVL loop:
What the heck does "V2 (or V1) is suitable as an element in a KVL loop"
V2 is a voltmeter, to begin with, but ....
... let's consider it a branch. A branch alone can be part of a loop to which KVL applies (works) and AT THE SAME TIME be part of a loop to which KVL does NOT apply.
Case in point: Lewin's ring with the two 'external' voltmeters. V1 forms a loop with R1 that you can apply KVL to, but forms with R2 (and V2) loop(s) to which you cannot apply KVL to, you need Faraday.
Therefore:QuoteQuestion One:
How can V1 not also be suitable since they both measure the same voltage? Your own trusted source says that if an unambiguous physical measurement of the voltage across the two terminals can be obtained, then KVL holds! How can V1 not work for KVL?
This question betray your confusion. I cannot answer this question because you are showing not to possess the prerequisite to formulate a rational question. V2 in the twisted circuit can be though as part of a circuit that stops at the first twist.
If you limit yourself to paths that are inside that little loop, V2 will always be part of loops to which KVL can be applied (because in the universe that is the area enclosed by your circuit path there is no dB/dt).
Yes, you can define your circuit path to follow all the twists and go around the core, but that betrays your ignorance of the purpose of making the transformer's terminal so close together: it's to treat the circuit with V2 as lumpED.
V1, on the other hand, is part of a circuit whose circuit path you can immediately see going around the core. Anyway, being a lumpABLE circuit you can choose both ways. If you choose the copper as the trail of your circuit path, you include the dB/dt region inside it. There are paths that when part of a loop along with V1 will go around the core, hence KVL will not apply. Faraday's will.
QuoteQuestion Two:
Considering your own trusted source, if a ONE TURN TRANSFORMER SECONDARY on a toroidal transformer has a voltage that is unambiguously physically measurable, then it should qualify as an element for a KVL loop, Correct?
For example, in the following transformer diagram with a safety wall in the center, why would the output winding not be suitable as an element in a KVL loop?
Again, the question betrays your ignorance. That is a lumpABLE circuit. You can treat it either as NOT LUMPED, by allowing paths that go around the core by considering an orange circuit path that follows the conductor around the core, or lumpED by denying this possibility by considering a green circuit path that jumps at the terminals, excluding this possibility. The wall is just a way to represent the fact that you are denying this possibility and your circuit path skips the innards of the transformer.
If you deny this possibility, then your voltages will be well defined (as Desoer and Kuh require for KVL to hold).
If you allow this possiblity, then your voltage can be multivalued (and Desoer Kuh will say that KVL ceases to work for those loops with a part 'going the other side').
(To tell it all, we should make the terminals close together so that the circuit itself can be shrinked to a point, but I decided not to push this. )
The key property associated with lumped elements is their small size
(compared to the wavelength corresponding to their normal frequency of operation.)
From the more general electromagnetic field point of view, lumped elements
are point singularities; that is, they have negligible physical dimensions.