Does Kirchhoff's Law Hold? Disagreeing with a Master

[EEVblog]

I'm putting this here instead of in the other blog section, as it's an important technical discussion.
Mehdi claims Walter Lewin is wrong about his infamous KVL violation video, and I've always felt the same but have never investigated myself.

[ataradov]

Wow. I was not even aware that there is such a controversy over Kirchhoff's law.

I though Kirchhoff's laws were derivable from Faraday's law and Maxwell equations in general. But quick search shows that it is not very easy.

[bson]

KVL only applies in static fields.  KCL still applies in fields under flux.

A meter used to measure across points in an induction loop in field flux becomes part of the loop, and the voltage will depend on where the meter and leads are placed relative to the loop.  Move it from one side to the other and the voltage reverses.

The current induced in a loop is fixed.  The voltage depends on the impedance - the higher the impedance, the higher the voltage between any two points in the loop.  This is actually normal inductor behavior if you think about it.

[beenosam]

The worst part of this is the way Lewin is acting on YouTube on his own video. He's being pretty childish and refuses to discuss it at all.

[chris_leyson]

When I first watched Walter Lewins video the first thing that struck me was the experimental setup and that the test leads were also part of the experiment. Mehdi's got it right an you can't fault his experimental setup and explanation. KVL still holds true in an varying magnetic field if you draw the circuit correctly by including the test leads. I think Walter Lewin knows this and is just being controversial to get students to think about the problem. Mehdi's experimental setup is nicely done and very easy to replicate and hopefully it will teach EEs a little about good wiring practice when there are stray magnetic fields.

[chris_leyson]

Mehdi Sadaghdar's lecture and experiment is also a good way of showing how you should attach twisted pair into a circuit to make a measurement, think twice before you measure.
As an aside, I wonder how the electrostatic "dual" of the experiment would be arranged ?

[HackedFridgeMagnet]

The nub of the discussion seems to be do the sum of the voltages around a circuit always add to zero.

You have to admit Maxwells-Faradays law seem to be on Walter Lewins side.

Also
From Wikipedia

KVL is based on the assumption that there is no fluctuating magnetic field linking the closed loop. This is not a safe assumption for high-frequency (short-wavelength) AC circuits.[2] In the presence of a changing magnetic field the electric field is not a conservative vector field. Therefore, the electric field cannot be the gradient of any potential. That is to say, the line integral of the electric field around the loop is not zero, directly contradicting KVL.

It is often possible to improve the applicability of KVL by considering "parasitic inductances" (including mutual inductances) distributed along the conductors.[2] These are treated as imaginary circuit elements that produce a voltage drop equal to the rate-of-change of the flux.

But then Electrobooms arguments are convincing too.

Maybe the demonstration by Walter Lewin doesn't really show what he is trying to show? the loop seems to include the path to the scope.
How would you measure EMF in a closed loop anyway?

IDK but I really would like to understand this better.

[ajb]

From Wikipedia

It is often possible to improve the applicability of KVL by considering "parasitic inductances" (including mutual inductances) distributed along the conductors.

Et voila.

The crux of the matter is that Lewin didn't account for the fact that KCL require the EE equivalent of spherical cows.  In the real world wires have resistance and inductance and mutual capacitance, and are not the simple indications of equivalence that they are assumed to be in KCL.  So for the math to be accurate you have to consider them as lots of little spherical cows all stuck together in different ways.

If you have a whole lot of little spherical cows you get to call that finite element analysis.

[chris_leyson]

Thanks HackedFridgeMagnet, "KVL is based on the assumption that there is no fluctuating magnetic field linking the closed loop" which is true and KVL only holds up for a static field. However, if you take into account all of the parasitic and stray circuit elements then KVL still holds up if you have a vaying magnetic field, however, you've got a different circuit than what you started with. Both Lewin and Electroboom are right, all depends on whether you model in the parasitics. KVL still holds for varying magnetic field if and only if you model in the parasitic circuit elements

[HackedFridgeMagnet]

Thanks HackedFridgeMagnet, "KVL is based on the assumption that there is no fluctuating magnetic field linking the closed loop" which is true and KVL only holds up for a static field. However, if you take into account all of the parasitic and stray circuit elements then KVL still holds up if you have a vaying magnetic field, however, you've got a different circuit than what you started with. Both Lewin and Electroboom are right, all depends on whether you model in the parasitics. KVL still holds for varying magnetic field if and only if you model in the parasitic circuit elements

Hmm.. it seems to say it differently below.
Apparently it needs to be in a conservative vector field but I can't even see that the field within a resistor is a conservative vector field because it is dissipating energy.

KVL is based on the assumption that there is no fluctuating magnetic field linking the closed loop. This is not a safe assumption for high-frequency (short-wavelength) AC circuits.[2] In the presence of a changing magnetic field the electric field is not a conservative vector field. Therefore, the electric field cannot be the gradient of any potential. That is to say, the line integral of the electric field around the loop is not zero, directly contradicting KVL.

It is often possible to improve the applicability of KVL by considering "parasitic inductances" (including mutual inductances) distributed along the conductors.[2] These are treated as imaginary circuit elements that produce a voltage drop equal to the rate-of-change of the flux.

So is the line integral of the electric field around the loop zero in all cases (KVL) or not?
If it is non zero (Maxwell Faraday) then how would you measure it? Because measuring it with a scope would seem to prove KVL.
Of course there is also the unlikely scenario where Wikipedia is wrong. 

[riyadh144]

I have thought about this question way too much since high school, but I always convinced myself that KVL doesn't hold under external EMF.

BUT Walter's setup is really bad probing.
I will be working on getting a good experiment.

[EEVblog]

Maybe the demonstration by Walter Lewin doesn't really show what he is trying to show?

That's possible. He could be right in theory, but may be using a poorly thought out experiment to try and show it.
And maybe it's deliberately a bit dodgy because it's not easy to demonstrate?, and maybe he knows that?

Kinda reminds me of my current flowing through a capacitor video. That was bit of a troll on my part in order to show a "controversial" way of thinking about theoretic current and maxwells law. The old theoretical physicist vs practical engineer viewpoint discrepancy.

[Berni]

I would also say that both are right in a certain way.

Kirchoffs law doesn't hold in a magnetic field if you don't model the effect of the field on the inductance. But does work if you model the parasitics of the wire as instructors.

If you have taken the DC voltage source in his lecture example and replaced it with a 1GHz AC source then Kirchoffs law again would not hold because your schematic is ignoring parasitic effects that the real circuit can't simply ignore.

A similar argument to this is how to calculate kinetic energy in physics. Its commonly used that kinetic energy E = (m*v^2)/2 and it turns out this works perfectly in practical experiments. However due to relativistic effects things appear heavier as they get closer to the speed of light, this is sort of a 'parasitic' effect that we are ignoring in that formula because the speeds we normally work with are so low that the effect is practically zero and everything works great. But when you get to these higher speeds this effect starts to contribute more and more to the total energy and then yes that equation is broken. But its not broken because the equation is wrong. Its just ignoring a insignificant detail of the physics model that turned out to become significant in this particular set of circumstances.

But i do have to say that Dr. Lewin explains it a slightly odd direction that is kinda misleading. Its not that this special case with magnetic fields breaks Kichhoffs law, but its just that the mathematical model of the cirucit ignores magnetic effects that should not be ignored in this case. Ideal wires with 0 voltage drop would need to also be 0 units long in the physical world so that they don't have inductance. If all the wires are 0 units long this means the physical circumference of the circuit must also be 0 (Resistors are considered to be 0 length too or they would also be inductors). A circle with 0 circumference must also have a surface area of 0 as such it has 0 magnetic loop area and as such can't get a voltage induced in it no matter how strong or fast changing of a magnetic field you place it in. With that that the voltage on both resistors would calculate to be 0V as you would get trough the analysts of the circuit because the circuit contains no voltage sources.

The correct model for his physical circuit would include inductors on all lengths of wire(including probes going to the scope) and all these inductors should have a dot marked on them showing if they go clockwise or counterclockwise along the magnetic field. Additionally arrows should be drawn between all of them to show they are all coupling together via a magnetic field and the coupling factor written on each arrow. This circuit now has a voltage source in it, its the voltage source that is powering the inductor representing the solenoid. You could then calculate the voltages at each point of the circuit and you would get results that are very close to what the scope is showing.

This is an excellent paradox to get people thinking. But Dr. Lewin should explain that the problem is a bad circuit model ignoring what should not be ignored rather than the ever so useful Kirchhoffs law being wrong.

[nctnico]

I would also say that both are right in a certain way.

Kirchoffs law doesn't hold in a magnetic field if you don't model the effect of the field on the inductance. But does work if you model the parasitics of the wire as instructors.

This is an excellent paradox to get people thinking. But Dr. Lewin should explain that the problem is a bad circuit model ignoring what should not be ignored rather than the ever so useful Kirchhoffs law being wrong.

I agree. Especially with the last part. This has been discussed before and it seems Dr. Lewin is just trolling.

[SparkyFX]

I tend to approach this problem in the following way:
KVL holds true for infinite small dimensioning or as a logical concept - thats when you not happen to use a diagram that includes all inductances and capacitances in the circuit.

For everything else the dimensions and field strength would need to be specified, the logical concept of a circuit designed in a loop does not mean that it physically needs to be a flat loop.

Both are right by themselves, the discrepancy stems from taking the logical concept and converting it directly into a specific physical design.

[madires]

It's easy to forget that wire is a component too, and also the scope with its probes. If you add a changing magnetic field you cant ignore the wire any longer.

[SparkyFX]

All logical concepts ask for ideal elements, this means that side effects can be cancelled out somehow and you are left with the concept itself as the effect.
Ideal switches, ideal wires, ideal ... do obviously not exist, which makes it practically the base of the whole electronics trade to put concepts in physical reality without unwanted/inacceptable side effects (errors or mishaps) by design.

But don´t go ad hominem because of that, as it is just the kind of discrepancy that is thought provoking in a good way, presented as a right/wrong approach although the concept left the realm it was meant to be used in.

[Berni]

I would also say that both are right in a certain way.

Kirchoffs law doesn't hold in a magnetic field if you don't model the effect of the field on the inductance. But does work if you model the parasitics of the wire as instructors.

This is an excellent paradox to get people thinking. But Dr. Lewin should explain that the problem is a bad circuit model ignoring what should not be ignored rather than the ever so useful Kirchhoffs law being wrong.

I agree. Especially with the last part. This has been discussed before and it seems Dr. Lewin is just trolling.

Yeah i get the feeling that he explains it in a way that doesn't give the full picture on purpose. Using it as sort of a way to see what the student are thinking when they try to explain it and perhaps find the rare bright student who figures out the real reason behind this effect.

But it could also be just a case of being exposed to too much theory and too little practical electronics work. I noticed this with some teachers that they get a different perception of a certain subject due to approaching it from pure theory and sort of settle in to certain specific ways of mathematical problem solving that they personally find really neat.

One of my favorite electronics teachers turned out to be a old guy who has been repairing TVs and other equipment for many years. He had an incredible depth of practical knowledge of useful electronic circuits and knew exactly how they work and how to design them. I'm really not saying theory is a waste of time but instead that every bit of theory should be connected to something physical as well, otherwise you just end up going down a rabbit hole full of math describing mythical ideal components. Once enough math abstractions are stacked on top of each other you can get so far away from the physical world that it can be hard to find your way back to what a voltmeter is showing on the bench (Especially when the teacher in question only ever touched a physical voltmeter once a year).

[MiDi]

I am wondering if there is one example KVL does not apply when every "parasitics" and "outer elements" are modeled?

Someone suggested superconductor without giving an example.
So maybe there is an edge case/singularity where KVL does not apply 

[b_force]

I find it a bit nit picky.
Newtons laws also don't work everywhere, that doesn't make them false all of a sudden?
They have their limits, so has Kirchhoffs laws.
Nothing new, can we go on now with the real stuff?

[RoGeorge]

https://www.eevblog.com/forum/chat/kirchhoff_s-loop-rule-is-for-the-birds/
https://www.eevblog.com/forum/beginners/are-kirchoff-laws-useless/msg920903/#msg920903
https://www.eevblog.com/forum/beginners/walter-lewin-8-02-lect-16-super-demo-(correction)/

Internet Rule #0: Search before you post 

[T3sl4co1l]

I'll repeat the comment I made on the video (which I'm sure has been utterly buried under a torrent of less extensive comments, or suppressed outright by algorithm):

The way I see it is structural:

He's using a DC circuit in an AC field, and claiming that the DC circuit still holds, while forcing an AC behavior upon it.

As is always the case in proof by contradiction: we have only proven that our premises were wrong.

It's a similar fiction as the conservation of charge vs. energy when connecting charged capacitors together: if energy is conserved, where does it go?  Well, it turns out that you can't simply short capacitors together without taking account of their resistance, or inductance.  Or, more generally, of the loop area between them, which gives rise to both elements.  So the charge is conserved (a more fundamental quantity), and energy is conserved whether or not you've written in a way for it to do so.

It would be more illustrative if he phrased it as a riddle to the student, to figure out where the disconnect is.


You are quite correct that merely adding a transformer, and keeping track of the probe wires in the field, is all that is missing!

As for failings of Kirchoff's laws: radio waves.  One must get ever more particular about where (spatially speaking) one applies them.  The current flowing into the feedpoint of a dipole antenna, for example, does not equate with the current conducted out of the element tips, which is zero.  The disconnect here is concentrating on conduction, while ignoring displacement current.  In effect, equivalent capacitance carries the current into free space.  But more accurately, it's carried into the fields around every point of the antenna.


At their most general (but perhaps least useful), KVL/KCL reduce to a single point only: they are a differential relation, which must be integrated over the space of interest.  (This, of course, is painful to do by hand for all but the simplest arrangements, so we usually have computers divide the space into millions of finite elements and apply the laws to them, for us.  Hence, FEA (finite element analysis) tools.)

This, in turn, drive home another point about schematics: what we draw is an abstraction, a fiction, a model.  The points are connected instantaneously in time and space, with no concept of distance, or the speed of light (namely, that the distance is effectively zero, or the speed of light is infinite).  To build a realistic model, when the speed of light is relevant, we must introduce enough parameters (whether L and C approximations, or real transmission line elements) to match this.

Tim

[Berni]

Just for the fun of it, here is a LT Spice simulation recreating this cirucit.

The graph shows that the actual voltage between those two points is an average between the two scope readings(Since this cancels out the voltage added and subtracted by the test leads going one or the other way)

EDIT: Do note that this is not a accurate simulation as it still ignores stray capacitance and assumes a perfect coupling between all coils. In reality the coupling between the wires would be slightly less than 1 due to the wires not being able to exist in the same physical location and the coupling to the solenoid coil in the middle should be even less due to it being far away from the current path of all the other wires.

[IanMacdonald]

The reason for the apparent difference in readings is that the magnetic field also induces a voltage into the meter or scope leads. Kirchhoff's Law still holds if you take this into account.

As a relevant point of interest, you cannot have a half-turn transformer winding. It is always an integer number of turns. You have to connect the ends of your 'half turn' winding together somehow, for current to flow. Making the wire longer, as in including the test leads of a meter for example, does not alter the fact that the circuit still completes the same magnetic path as a complete turn would do. The longer wire intercepts a more diffuse magnetic field but over a longer distance, and the induced EMF is the same as if it were a tightly wound turn. 

In this case a fail, but unless people challenge established science there will never be any more breakthroughs. The problem these days is that science has become more like a religion whose tenets MUST NOT be questioned. This is just as bad as allowing complete pseudoscience.

[SiliconWizard]

Interesting question, but I find Dr. Lewin's experimental setup kind of a disgrace for an MIT professor. Anecdotally, the MIT revoked his "professor emeritus" title, but apparently not based on anything related to his scientific merits. Anyway.

I think he hasn't proved anything here. Is there anything else than induced voltages in the probing wires and scope probe in play?
Devising a completely neutral probing setup seems pretty difficult to do, and you won't achieve it with a couple flying wires (however twisted they may be) and basic scope probes.

That said, even if we consider a perfect setup and a real discrepancy, my take here would be that KVL could still perfectly apply. We would just have to consider the loop having extra voltage sources from any induced voltage. That wouldn't defeat it, but make us consider that our circuit model is incomplete.

Just my 2 cents.