Does Kirchhoff's Law Hold? Disagreeing with a Master

[ajb]

He even takes this argument so far to the point of saying that Kirchoff's voltage law does not apply to circuits with inductors, because they have a changing magnetic field:
http://web.mit.edu/8.02/www/Spring02/lectures/lecsup4-1.pdf

From that same supplement, emphasis mine:

Suppose you put the probes of a voltmeter across the terminals of an inductor (with very small resistance) in a circuit. What will you measure? What you will measure on the meter of the voltmeter is a "voltage drop" of Ldi/dt. But that is not because there is an electric field in the inductor! It is because putting the voltmeter in the circuit will result in a time changing magnetic flux through the voltmeter circuit, consisting of the inductor, the voltmeter leads, and the large internal resistor in the voltmeter

I think that shows pretty clearly that he is not making a measurement mistake, and that he understands exactly why he got the result he did in his demonstration.  So I guess he's so dismissive of KVL not because it's wrong, but because it gets the right answer via an insufficiently rigorous method, even when lumped inductors are added to his resistor model.

a case of theoretical physics vs practical engineering approaches.

Just so.

[RoGeorge]

The meter wires are part of the circuit and the orientation of the wires determines the results.

What happens if we remove the voltmeters?  How do we measure the voltage without the voltmeters?  We will need to take an electric charge and drag it through the circuit from A to B.  How much energy do we need to move our charge from A to B?

The answer is: it depends.  If we go from A to B through the left side, or through the right side.  Not only that the energy is different for each half of the circuit, but it has an opposite sign.  No chance to get a zero for the whole loop.

[SiliconWizard]

He even takes this argument so far to the point of saying that Kirchoff's voltage law does not apply to circuits with inductors, because they have a changing magnetic field:
http://web.mit.edu/8.02/www/Spring02/lectures/lecsup4-1.pdf

Thanks for the reference. This helps making it much clearer what he was meaning - especially on page 3.

We've discussed this many times in previous threads.  Dr. Lewin gave his world famous SUPER DEMO as he refers to it in 2002, I guess.  But he didn't invent it.  It is an exact recreation of the experiment in this 1982 paper:
http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf

In the paper, everything is explained very simply without drama.  It's no mystery.  The meter wires are part of the circuit and the orientation of the wires determines the results.

Absolutely, and this is exactly what several of us have been saying all along.
The experiment itself and the drama add no value.

There's still one valid point in what he says in how EEs interpret Kirchhoff's 2nd law. This doesn't change anything in practice.

[rfeecs]

The meter wires are part of the circuit and the orientation of the wires determines the results.

What happens if we remove the voltmeters?  How do we measure the voltage without the voltmeters?  We will need to take an electric charge and drag it through the circuit from A to B.  How much energy do we need to move our charge from A to B?

The answer is: it depends.  If we go from A to B through the left side, or through the right side.  Not only that the energy is different for each half of the circuit, but it has an opposite sign.  No chance to get a zero for the whole loop.

Yes, the wires are determining the path from A to B.

So you are supposed to get the amount of work by multiplying the charge by the E field and integrating that over the path.  But that only works for electrostatics.  We have a changing magnetic field so the electrostatic potential is not defined.  We can make up a potential that still works for electrodynamics and Faraday's law, the magnetic vector potential:
https://en.wikipedia.org/wiki/Electric_potential

As the article points out, there is confusion over the language.  What is meant by potential, voltage drop, potential difference, EMF?  They tend to be used interchangeably but they can mean different things.

[RoGeorge]

http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf

Question:
If we remove the voltmeters and their leads, what is the voltage between A and B?

An even simpler question:
No voltmeters, no leads, no wires. Is the voltage between A and B positive, or negative?  <- drama, it's both!   

[ArthurDent]

As a relevant point of interest, you cannot have a half-turn transformer winding.

Other than the previous link on fractional turns dated 2003, an engineer named Franklin d'Entremont who worked for GE in Somersworth, NH got a patent in 1942 for fractional turns in line frequency transformers.

http://www.freepatentsonline.com/2284406.html

An easy way to get a half turn on a winding with multiple turns is to have 2 windings in parallel with 1 turn difference between the two windings. If one winding has 100 turns and the other has 101 turns, the average is 100.5 turns. It does waste a little power but if there are quite a few turns for the two windings it won't make much difference.   

 

[rfeecs]

http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf

Question:
If we remove the voltmeters and their leads, what is the voltage between A and B?

An even simpler question:
No voltmeters, no leads, no wires. Is the voltage between A and B positive, or negative?  <- drama, it's both!   

OK, no voltmeter, no wires.  Calculate the voltage between A and B (using physics, Maxwell's equations or whatever).  You will probably need to know the length of the wire segments.  Assume 4 equal segments and the resistors have negligible length.  Do you get more than one number?  No.

[bsfeechannel]

The problem with Kirchhoff is that he's not thinking fourth-dimensionally. The strict adherence to Kirchhoff's laws is what makes it difficult for people to grasp RF.

[Simon]

It is not like he taught advanced physics. From what I've seen his lectures were more like physically themed perfo rmances rather than actual lectures. This was fine for the first year EEs that have never seen physics before.

Yes I have to admit that the videos I have seen don't go into anything too profound and I guess with the more public profile that he has if that is what he is into then it's far enough for educating the average person. He has always striked me as a fairly decent fellow and of his lectures that I have seen I enjoyed most the ones that were indeed more performance in nature. I think he did an excellent job at giving physics a practical angle and perhaps inspiring people. I found his parting public lecture very entertaining and a little informative and greatly enjoyed the lecture he gave to children on the nature of sounds.

In this case though he has suffered the beginner mistake of poor probing and allowing his probe to become part of the circuit.

It is fairly a common problem with people that don't have to deal with the hard physics to miss "real world" factors like stray capacitance. I tried in vain to explain this to a guy at work that has just gotten into radio and is going by rules he is being taught in radio class. He thought that he could solve my EMC issue with standard aerial chokes until I explained what common mode noise is and that that inductor in real life is not an inductor but a tuned circuit and that for RFI purposes 2 inductors of the same value could behave differently because of this thing called stray capacitance.

[KL27x]

What happens if we remove the voltmeters?  How do we measure the voltage without the voltmeters?  We will need to take an electric charge and drag it through the circuit from A to B.  How much energy do we need to move our charge from A to B?

The answer is: it depends.  If we go from A to B through the left side, or through the right side.  Not only that the energy is different for each half of the circuit, but it has an opposite sign.  No chance to get a zero for the whole loop.

Well, when measuring voltage, why are we "dragging the electron" where it doesn't want to go? Isn't the usual way to do this to let the electron go where it wants? If you have to drag it one way and input energy, and the opposite is true for the other direction, it will take the other way every time. This is why the electrons go in a circle, here, right? From A to B via route 1, and B to A via route 2? You make it sound like there's some random chance electricity will spontaneously take the uphill direction against the merry-go-round and is therefore the voltage undefined. The electron is not going to go A to B via route 2, because it doesn't want to. Oh.. wait. yeah. i'm in way over my head, here. I think I'm starting to see where I have no idea what the grown ups are talking about. 

I should probably watch lectures 8, 5, 11, 7 and 15.

[In Vacuo Veritas]

We've discussed this many times in previous threads.  Dr. Lewin gave his world famous SUPER DEMO as he refers to it in 2002, I guess.  But he didn't invent it.  It is an exact recreation of the experiment in this 1982 paper:
http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf

In the paper, everything is explained very simply without drama.  It's no mystery.  The meter wires are part of the circuit and the orientation of the wires determines the results.

LOL this Lewin guy is sounding more and more like the typical academic bitter old crank. Not attributing previous work and acting like a fool? Time to push him out on an ice floe, seems to me.
He's the Leo Kronecker of the physics world...

[RoGeorge]

What happens if we remove the voltmeters?  How do we measure the voltage without the voltmeters?  We will need to take an electric charge and drag it through the circuit from A to B.  How much energy do we need to move our charge from A to B?

The answer is: it depends.  If we go from A to B through the left side, or through the right side.  Not only that the energy is different for each half of the circuit, but it has an opposite sign.  No chance to get a zero for the whole loop.

Well, when measuring voltage, why are we "dragging the electron" where it doesn't want to go? Isn't the usual way to do this to let the electron go where it wants? If you have to drag it one way and input energy, and the opposite is true for the other direction, it will take the other way every time. This is why the electrons go in a circle, here, right? From A to B via route 1, and B to A via route 2?

Very good idea, looks much clear if we move the probing electron as you say.

Let's drag our probing electron with the flow. From A to B via route 1, and B to A via route 2.  Our electron will gain some energy on route 1, then will gain some more energy on route 2.  After circling a full loop, from A to A, we end up with some extra energy in our probing electron.  That energy is the voltage around the loop.  So, the sum of voltages around the loop is NOT zero, as Kirchhoff Voltage Law predicted.

This is the contradiction that makes the professor saying "Kirchhoff is for the birds" here.

[KL27x]

so hmm. it this a close analogy?

A mobius strip doesn't have a front and a back.... So therefore all the dummies using the term front and back are really talking about a special case (which is pretty much everything except a contrived thought experiment). So it is therefore an OUTRAGE for textbooks to be incorrectly stating that things have fronts and backs when it is not universally the case?

[SiliconWizard]

so hmm. it this a close analogy?

A mobius strip doesn't have a front and a back.... So therefore all the dummies using the term front and back are really talking about a special case (which is pretty much everything except a contrived thought experiment). So it is therefore an OUTRAGE for textbooks to be incorrectly stating that things have fronts and backs when it is not universally the case?

You're pushing it a little too far, but that was quite fun.

[KL27x]

Ok, trying to be serious, and sticking my neck out. Is this close at all?

Kirchoff's law is not valid in a changing magnetic field. This is given fact. It's accepted. But this is only because of what we define as a closed circuit. We can add "invisible strings" in the form of magnetic flux, and by convention, the circuit is still closed. Which would be sorta like doing a momentum analysis between two colliding steel balls without figuring the effect of a magnet under the table. But by convention, this is the case, and thus Kirchoff's Law is considered invalid in a magnetic flux.

The good Doc has chosen a strange example to make this point, when a must better example would have been to show one loop in a transformer (well that's not a closed circuit!) another example where you could include in the effect of magnetic flux to show how that make Kirchoffs law correct. In fact, the example/experiment is obfuscating to the actual point, and further weirded by completely ignoring the magnet under the table. But it does make you go ooh, and want to watch lectures 8, 5, 7, 11, and 15.

If he makes more of it that this, then he knows something the rest of the world doesn't? Or he is making a mobius strip out of a molehill? (Hmm, maybe that should be "mountain out of a mobius strip?")

[Simon]

oh for christs sake how hard is it to see that voltage is also induced into the probe wires that were being ignored as part of the circuity are. In magnetic's any length of wire cannot be ignored like we do in DC, in AC it can start to be a problem and in magnetic's well tin foil hat time and don't breath the wrong way.

[RoGeorge]

[Kirchhoff's Voltages Law (KVL) failure] would be sorta like doing a momentum analysis between two colliding steel balls without figuring the effect of a magnet under the table.

 

That's exactly our kind of problem.

Of course, we were trained to identify and deal with it.  But it was not so obvious that, in fact, we are "patching" the KVL by adding imaginary batteries to our circuit loop, isn't it?  If it were so obvious, we wouldn't bother to talk about it.  We are doing that in order to include the external influences of a variable flux.  KVL was not meant to include the external influences.  Kirchhoff derived the KVL for circuits with batteries and no external fields.

The other Kirchhoff's law, Kirchhoff's Currents Law (KCL) still works just fine no matter the externally magnetic fields.  Only KVL doesn't hold, and only in a variable magnetic flux.  KVL in a constant flux, again no problem.

Now, is the professor correct, or not?  Does Kirchhoff derived his KVL before, or after adding the virtual sources representing induced voltages caused by a variable flux?  All the clues indicates that Kirchhoff was not concerned about induced voltages from external fields.  He was not even looking for KVL.  Kirchhoff was trying to find a way to calculate all the currents in a mesh of linear wires, so he was looking for KCL, not KVL.  If I understood it correctly, Kirchhoff was thinking about telegraph wires when he derived KCL and, unintendly, KVL too.  (see https://www.jstor.org/stable/20021539 starting from the last paragraph)

Before taking his degree, Kirchhoff had begun his work in original
 research, and published a remarkable paper on electrical conduction in
 a thin plate, especially a circular one. His problem was to find the
 current in any branch of a network of linear conductors. Starting

 from Ohm's familiar law, he derived two results long recognized in
 electrical science as Kirchhoff 's laws.

I couldn't find the original papers with the KCL and KVL published by Kirchhoff.  All I could find is a followup of the KCL and KVL paper, (which, by the way, seems to be the first analysis of a transmission line: https://www.ifi.unicamp.br/~assis/Apeiron-V19-p19-25(1994).pdf ). In this followup paper, Kirchhoff started from a real problem of those times: What happens in underwater telegraph wires.  Again, the influence caused by an external variable magnetic flux was not a concern for the problem of submarine telegraph cables.  All clues indicates that KCL and KVL were originally meant to be used for normal circuits, with batteries, and without considering external induced voltages.

I'll say the professor was correct when he said we can not always apply KVL.  Of course, if we first transform the real circuit into a lumped circuit, where we add the externally induced voltages as voltage sources internal to our circuit, then we obtain a new circuit that obeys KVL.

[MT]

Come to re-think of it, and as he's clearly not an idiot, I was then willing to believe that he actually did that on purpose, just to make young students aware of the question: using simplistic models while thinking they hold true in the real world, which is a very common pitfall. This would be all good if he made it clear in the end that it was his intent instead of making it even more confusing, to the point that he even managed to confuse some very experienced engineers, using his position of authority.

Now if he was genuinely trying to instill advanced physics notions in young heads, I think this was a very bad way of doing it from a pedagogical standpoint.

Precisely.

The attitude of some professors to initially troll up some drama then later express the correct explanation in their lecturers but newer really make it clear is just crap mentality and bad pedagogics just causing confusion on everyone else expense. I have seen Prof Leonard Susskind do the same in some of his quantum physics lectures.

[bsfeechannel]

I'll say the professor was correct when he said we can not always apply KVL.  Of course, if we first transform the real circuit into a lumped circuit, where we add the externally induced voltages as voltage sources internal to our circuit, then we obtain a new circuit that obeys KVL.

We engineers do that all the time. We tend to reduce a complicated problem to a simpler one for practical purposes. What Professor Lewin is probably trying to do is to call the attention to the fact that you'll have a hard time if you always think that way.

You see, Faraday-Maxwell is not easy. It involves vector calculus and a bunch of non intuitive concepts. That kind of study takes several semesters of an engineering course. Many consider that theory impenetrable.

For those who have Kirchhoff as second nature, this is an additional difficulty. Since Kirchhoff is simpler and easier to apply, Faraday-Maxwell seems unnecessarily complicated and a pain to reconcile.

He probably noticed that in his students and decided to demonstrate with an experiment what kind of confusion this may lead to. But as someone has pointed out, it ended up causing more confusion than convergence.

[HackedFridgeMagnet]

I'll say the professor was correct when he said we can not always apply KVL.  Of course, if we first transform the real circuit into a lumped circuit, where we add the externally induced voltages as voltage sources internal to our circuit, then we obtain a new circuit that obeys KVL.

They are always just going to be two mathematical models of the same circuit, the real circuit is in the lab.

It would be necessary to have the formal definition of the law in front of us to see if it is disproved. If anyone can track that down it would be very informative.
Short of that we can use Wikipedia due to it being the most common interpretation of the law.  https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws

No one has yet produced a demonstration that disproves KVL in a dynamic magnetic field.
I would like to see it.
As others have stated if you model the system correctly you can predict results using KVL and reproduce them in a lab. If there is an exception to this I would like to have it demonstrated.

Also I think the way some people are interpreting Maxwell-Faraday is wrong.
They are thinking the sum of voltages around a closed loop which is short circuited will be equal to the rate of change of the magnetic field. I doubt this is the case. Think of a single loop of copper. How would you even measure the two different voltages at the same point.
I am fairly sure Maxwell-Faraday describes a case where the loop is magnetically closed but electrically open circuit.

[ejeffrey]

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.

KVL is only derivable from maxwells equations when dB/dt = 0.  It is basically a statement that the force on an electric charge is representable by a conservative field.  That means that the energy to more a particle between two locations is path independent, or in particular that moving a charge in a loop requires zero net work regardless of path. You can mathematically show that a conservative field can be integrated to create a scalar potential field, which in the case of electric circuits is just the voltage.

You can't do that with changing magnetic fields.  Curl-E = -dB/dt, so there is no scalar potential that describes electron motion.  That is what Walter Lewin was showing.  Everything else is just noise.

[rfeecs]

Dr. Lewin is discussing two apparent problems with Kirchoff's voltage law when a changing magnetic field cuts through the surface of the loop:
1.  The voltage between two points depends on the path you take.
2.  The voltages around the loop don't add up to zero.

He is strictly defining voltage as the integral of E dot dl.  (This is the definition of electrostatic potential so obviously there is a problem here with a changing magnetic field.)

So he goes from point A to point B on one side and adds up the integral of E dot dl.  It's just IR₁.  Then he goes from point A to point B on the other side and adds up the integral of E dot dl.  Its just -IR₂.   OMG! They are not equal!  They are not even the same sign!  This demonstrates point number 1.

So add up the voltages all the way around the loop.  He says this is IR₁ + IR₂ and it doesn't equal zero!  So KVL is for the birds.  In fact it equals the inducted EMF around the loop.  So it agrees with Faraday's law:
IR₁ + IR₂ = EMF
This demonstrates point 2.

He then does his SUPER demo and blows your mind.  End of lecture.

Now people see the YouTube video and start saying:
"As for your demo, you are measuring things wrong.  Your test leads are forming a loop around the magnetic field and that is giving you a false measurement.
KVL still works!  The EMF appears across the ends of the wires connecting the resistors!  It's just like a transformer.  If you add up the voltages,
IR₁ + IR₂ - EMF = 0
The voltages around the loop sum to zero."

Dr. Lewin's response to this is:  You can't do that!  You can't just move the EMF from one side of the equation to the other!  That's dead wrong!  That's criminal. (https://bit.ly/2qzwkh0)

This is the reasoning you are arguing against.

[ajb]

Dr. Lewin's response to this is:  You can't do that!  You can't just move the EMF from one side of the equation to the other!  That's dead wrong!  That's criminal. (https://bit.ly/2qzwkh0)

Wait, one of the top comments on that video is from Mehdi, with responses from Lewin from A YEAR ago.  Then three days ago, Lewin added a new response with the same bunch of links he was putting all over the lecture video comments.  Wow.  He really does get worked up about where you put that EMF, doesn't he?

[EEVblog]

You can't do that with changing magnetic fields.  Curl-E = -dB/dt, so there is no scalar potential that describes electron motion.  That is what Walter Lewin was showing.  Everything else is just noise.

Yeah, but that "noise" is a very big claim that two points on the same circuit measure differently, he states that as a fact and uses a flawed demonstration to try and prove it. This is why many people have a big problem with this.

[RoGeorge]

... is a very big claim that two points on the same circuit measure differently... This is why many people have a big problem with this.

Yes, two points can measure differently.

Why do you think this is not OK?  What rule does it violates?