Does Kirchhoff's Law Hold? Disagreeing with a Master

[bsfeechannel]

Arguing about unwanted and wanted fields... putting the 'P' in PhD.

I used those terms for humorous effect. There are varying fields that I don't want to interfere with my measurement so I cancel out their effects when probing. But I can't cancel out the effect of the very field I want to measure.

This is stupid.

I side with Mehdi on this.

Mehdi is my friend. But truth is a better friend.

The fields are effecting the probes, the only reason why the voltage changes is due to how the probe wires are affected by the probes. In such a way the laws are put in place, we talk of an ideal circuit.

If I was to make the same mistake while trying to measure a current sensor's voltage while wrapping the wires around the probe, I'd be laughed out of the room.

Lewin's demonstration is a reductio ad absurdum. He assumes for a moment that Kirchhoff always holds, and then shows that if you keep thinking like that you are going to reach the wrong conclusions.

This thread is a monument to that truth.

[Berni]

About this:


Yes in order to do this you need the components to be lumped. Something you claim can not be done for any circuit in a magnetic field.

As for "correct probing" no it does NOT mean canceling out the EMF on the voltmeter. Its about canceling out EMF on the wires leading to the meter. If you are trying to get voltage in the formal textbook definition then Dr. Lewins wire path is such a path that gives 0V over the probe wires, if you are trying to measure the conservative component of voltage then then such a path is both wires heading towards the origin of the field. If you calculate the EMF on the probe wires and subtract it then you can place the wires in any path you like and still get the correct result. So you ether place your wires so that there is no error due to probing, or you calculate the error and subtract it out. So Dr. Lewin is indeed using correct probing to measure the thing he wants to measure, but it is never explained that the probing is just as important as the circuit to get the correct result.

As for there being two forms of Kirchhoffs law:


This is what you get when you turn maxwells equations into KVL. Notice that it has an extra voltage in it. That is because Maxwells equations work fine with magnetic fields around so deriving KVL from it also gets you a form of KVL that works with magnetic fields. If you use this form of KVL in Dr. Lewins example it works out just fine, nothing surprising about that. It is very similar to the form of KVL we all know, but its not the same. When you are using it in cirucit meshes you have to throw away Vi because its impossible to calculate it due to circuit meshes not having any fields inside them. Without Vi you get the well known form of KVL that's meant for use in circuit meshes, but as Dr. Lewin has demonstrated breaks in the real world. Cirucit meshes are NOT supposed to be the underlying workings of the universe. they are just a close enough approximation that works pretty much the same, yet it faster to work with.

Its the similar as the classical kinematics equation we all know from physics:
d=s*t

This equation is WRONG! It only works in a universe where the speed of light is infinite or in one where space and time are not related to each other in the form of a spacetime field. So is that for the birds too? But the thing is that at any reasonable speeds we might encounter on earth the error in the result due to ignoring special relativity is pretty much in the parts per million or even smaller. So we use it anyway because it gives results that are still within margin of error, yet its much easier and faster to work with. In fact most physics equations we see in highschool only work in this fictional universe with infinite, speed of light, no atmosphere or drag and spherical cows. Yet a lot of these cut down formulas are still close enough to the real deal to be perfectly usable. Circuit meshes are the same sort of thing, not quite real but real enough for what they are supposed to do.

If you are going to use the classical simple form of KVL use it in circuit meshes where it indeed always works. If you want your circuit mesh to behave like the real circuit in the universe we live in then also use proper circuit modeling methods (where wires are modeled as having inductance). If you don't want to do that then don't just directly slap on KVL and expect it to work every time.

Instead you can use the version of KVL that is derived from Maxwell equations in the physical world, since that does work. Calculate it however you want, just don't carelessly mix formulas from our universe and formulas from circuit meshes. A lot of the times they work fine, but not always (As Dr. Lewin clearly demonstrates)

If you can't handle abstraction then just ignore circuit meshes and focus on pure Maxwells equations instead.

I can make sense of Dr. Lewins circuit both in the form of fields and in the form of a circuit mesh model. Both work just fine and give identical results. If you can't make sense of the circuit using a mesh model then try to learn how, otherwise don't complain about it being wrong just because you don't seam to understand it. I don't want to come across rude or anything, but any answer to why its wrong to mesh model this circuit is along the lines of "It can't be done because i said so" rather than getting an explanation why i am getting the right results out of my mesh model despite it being supposedly wrong for some mysterious reason.

[Berni]

I do agree with Sredini here.

Tho yeah if your goal is to measure the voltage at the terminals of the current sensor then warping the probe wires around it is a rather non optimal way of doing it. Unless its a rather high gain type of sensor (Like a high ratio current transformer of a heavily amplified HAL), then it doesn't really matter since your scopes front end is probably too noisy and drifty to notice.

[ogden]

EDIT: Bernie, it's Sredni, not Sredini.

I am Sredni Vashtar the beautiful.
My thoughts are red thoughts
and my teeth are white.
My enemies call for peace,
but I bring them death.

So try not to piss me off, uh? 

https://en.wikipedia.org/wiki/Narcissism

[Berni]

Ah sorry for the typo in your name Sredni

[In Vacuo Veritas]

The real question is: would it measure the same in space, or indeed, Mars?

I mean the Earth is just a rock with nothing on it. Those rocks in space however, are the Future. We better figure out how to measure voltages there.

[Sredni]

The real question is: would it measure the same in space, or indeed, Mars?

I mean the Earth is just a rock with nothing on it. Those rocks in space however, are the Future. We better figure out how to measure voltages there.

Dude, I've heard Canada is experimenting with making marijuana legal.
How's it going so far?
 

[jesuscf]

And yet, the voltage between A and B can have two different values.

At the same exact time?

Yep. That's a snapshot at a given time.
The field will oscillate going one way, then the other, at - I do not remember exactly, maybe... 300 Hz?
At any rate, well within the limit of quasi static electrodynamics.

Maybe you have to take into account the magnetic field generated by the flowing current through the wire...

Nope, self-inductance is negligible, and there are no retardation effects.

The same two points, at the same moment in time, can have different voltages between them.
And there are no voltmeters, no probes, no measurement errors.
That's just the way it is.

Whatever you say man.  I just want to point out what "Engineering Electromagnetics" by Hyat and Buck, Seventh Edition, says in page 94:

"Equation (21) (Curl integral of E.dl=0) is therefore just a more general form of Kirchhoff's circuital law for voltages, more general in that we can apply it to any region where an electric field exists and we are not restricted to a conventional circuit composed of wires, resistances, and batteries.  Equation (21) must be amended before we can apply it to time-varying fields.  We shall take care of this in Chapter 10, and in Chapter 13 we will them be able to establish the general form of Kirchhoff's voltage law for circuits in which currents and voltages vary with time."

[bsfeechannel]

As for there being two forms of Kirchhoffs law:

Unfortunately that is not Kirhchhoff's law. That is Kirchhoff's law.



And it is not difficult to see why.

Let's get back to the infamous Lewin's circuit. Kirchhoff says that all voltages around a circuit add up to zero. So I'm going to do exactly what he says. I will "walk" around the circuit with my voltmeter. Since "bad probing" would give me the wrong results and I would probably be  laughed out of the room, I'm taking the proper precautions not to allow any stinking varying magnetic field to induce unwanted voltages on my probes. So, here we go.



So far so good. As an added precaution, I will measure the voltage across the wire, just to make sure it's what I expect.



And, bingo! Zero volts. No wonder. The wire is a dead short. Now it's time for the other resistor.



Notice that I'm maintaining the polarity of the meter coherent with the anticlockwise path that I chose. Now, let's check the voltage across the other piece of wire and add up the voltages.



Surprise! They do not add up to zero.

For Kirchhoff to hold there should be a V₅ somewhere measuring exactly -1V. But I checked every corner of this circuit and didn't find any other voltage than the four I measured.

So, either Kirchhoff is a liar, or didn't see it coming. I prefer to believe in the second hypothesis.

But you are going to say, Aha! Gotcha! The loop is nothing more than the secondary of a transformer. But where exactly is that generator in the circuit? My measurements show that this generator is nowhere to be found.

So the logic conclusion is that voltages do not necessarily obey the observation made by Kirchhoff, petrified in his laws. There must be another phenomenon that, when present, brakes those laws.

Its the similar as the classical kinematics equation we all know from physics:
d=s*t

This equation is WRONG! It only works in a universe where the speed of light is infinite or in one where space and time are not related to each other in the form of a spacetime field. So is that for the birds too?

From the point of view of Einstein's relativity, yes, Newton is for the birds. You cling to Newton, you won't be able to predict what Einstein did. Newton reveals an even worse relationship to Einstein, than Kirchhoff to Maxwell. The speed of light can't be infinite in practice, as you said. While we can have a zero magnetic field.

But the thing is that at any reasonable speeds we might encounter on earth the error in the result due to ignoring special relativity is pretty much in the parts per million or even smaller. So we use it anyway because it gives results that are still within margin of error, yet its much easier and faster to work with. In fact most physics equations we see in highschool only work in this fictional universe with infinite, speed of light, no atmosphere or drag and spherical cows. Yet a lot of these cut down formulas are still close enough to the real deal to be perfectly usable. Circuit meshes are the same sort of thing, not quite real but real enough for what they are supposed to do.

Such approximations work fine because we live under a relatively low constant gravitational field. We would only notice something wrong at astronomical scale. In fact we did, already in the 19th century. And that's why we have relativity today.

However the electromagnetic force is 10³⁶ times stronger than gravity. Noticeable deviations from the approximations such as those that we do to deduce Kirchhoff can be noticeable at a scale of millimeters. So they must be taken care of with much more attention.

If you are going to use the classical simple form of KVL use it in circuit meshes where it indeed always works. If you want your circuit mesh to behave like the real circuit in the universe we live in then also use proper circuit modeling methods (where wires are modeled as having inductance). If you don't want to do that then don't just directly slap on KVL and expect it to work every time.

Instead you can use the version of KVL that is derived from Maxwell equations in the physical world, since that does work. Calculate it however you want, just don't carelessly mix formulas from our universe and formulas from circuit meshes. A lot of the times they work fine, but not always (As Dr. Lewin clearly demonstrates)

If you can't handle abstraction then just ignore circuit meshes and focus on pure Maxwells equations instead.

I can make sense of Dr. Lewins circuit both in the form of fields and in the form of a circuit mesh model. Both work just fine and give identical results. If you can't make sense of the circuit using a mesh model then try to learn how, otherwise don't complain about it being wrong just because you don't seam to understand it. I don't want to come across rude or anything, but any answer to why its wrong to mesh model this circuit is along the lines of "It can't be done because i said so" rather than getting an explanation why i am getting the right results out of my mesh model despite it being supposedly wrong for some mysterious reason.

You're absolutely right. I can't handle the "abstraction". I must admit. So I humbly ask you a favor. Please, show me how to solve the circuit below using exclusively Kirchhoff.



Thank you in advance.

[Berni]

Unfortunately that is not Kirhchhoff's law. That is Kirchhoff's law.



And it is not difficult to see why.

Yes it looks like that when used in cirucit meshes. It has the extra voltage in it when you try to derive a "KVL like" equation from Maxwells equations. It has to be there otherwise there is a mistake in the process or Maxwells equations are wrong (And that's highly unlikely)

Let's get back to the infamous Lewin's circuit. Kirchhoff says that all voltages around a circuit add up to zero. So I'm going to do exactly what he says. I will "walk" around the circuit with my voltmeter. Since "bad probing" would give me the wrong results and I would probably be  laughed out of the room, I'm taking the proper precautions not to allow any stinking varying magnetic field to induce unwanted voltages on my probes. So, here we go.



So far so good. As an added precaution, I will measure the voltage across the wire, just to make sure it's what I expect.



And, bingo! Zero volts. No wonder. The wire is a dead short. Now it's time for the other resistor.



Notice that I'm maintaining the polarity of the meter coherent with the anticlockwise path that I chose. Now, let's check the voltage across the other piece of wire and add up the voltages.



Surprise! They do not add up to zero.

For Kirchhoff to hold there should be a V₅ somewhere measuring exactly -1V. But I checked every corner of this circuit and didn't find any other voltage than the four I measured.

So, either Kirchhoff is a liar, or didn't see it coming. I prefer to believe in the second hypothesis.

But you are going to say, Aha! Gotcha! The loop is nothing more than the secondary of a transformer. But where exactly is that generator in the circuit? My measurements show that this generator is nowhere to be found.

So the logic conclusion is that voltages do not necessarily obey the observation made by Kirchhoff, petrified in his laws. There must be another phenomenon that, when present, brakes those laws.

Yes i completely agree you get those voltages, what else would you expect there?

The fact that you contain the field on the inside does not mean it has no effect on the probes going around it. It just makes it a special case where induced voltage in the probes is 0V for the formal definition. If the probes pass trough the middle then you get voltage and voltmeters show wrong results hence why probe path matters. Since this behavior does not mirror circuit mesh behavior directly (It does if you model the indutance tho) means KVL does not work. If you apply the Maxwell derived version of KVL it does work cause it has that Vi component in it.

If you do the same thing again with the conservative component of voltage and again place the voltmeter in such a case that it shows 0V across the probes you would get identical voltages across resistors and a voltage gradient across the wires and the whole loop adds up to zero as conservative fields always do. So if you plug those voltages into KVL it also adds up to zero.

Its just a matter of perspective. There is nothing special about the two cases. Both work just fine. And its not my problem if you only agree with one case.

From the point of view of Einstein's relativity, yes, Newton is for the birds. You cling to Newton, you won't be able to predict what Einstein did. Newton reveals an even worse relationship to Einstein, than Kirchhoff to Maxwell. The speed of light can't be infinite in practice, as you said. While we can have a zero magnetic field.

But the thing is that at any reasonable speeds we might encounter on earth the error in the result due to ignoring special relativity is pretty much in the parts per million or even smaller. So we use it anyway because it gives results that are still within margin of error, yet its much easier and faster to work with. In fact most physics equations we see in highschool only work in this fictional universe with infinite, speed of light, no atmosphere or drag and spherical cows. Yet a lot of these cut down formulas are still close enough to the real deal to be perfectly usable. Circuit meshes are the same sort of thing, not quite real but real enough for what they are supposed to do.

Such approximations work fine because we live under a relatively low constant gravitational field. We would only notice something wrong at astronomical scale. In fact we did, already in the 19th century. And that's why we have relativity today.

However the electromagnetic force is 10³⁶ times stronger than gravity. Noticeable deviations from the approximations such as those that we do to deduce Kirchhoff can be noticeable at a scale of millimeters. So they must be taken care of with much more attention.

Well you can get problems due to this approximation on earth just as well. Particles on earth that approach the speed of light start preciving time slower, tho this is not directly observable outside of a lab experiment. Also anything that moves a very small fraction of light speed but has a very accurate sense of time can observe the effects. Such as putting atomic clocks on a plane and flying it around, or to get an even bigger effect putting them into orbit around the earth such as GPS does. The part about gravity is a different effect. Infact the two effects are fighting each other in the case of GPS satellites. The fact that satellites are moving quickly is making them run slower while the fact that they experience less gravity up there is making them run faster, but the effects are not the same in magnitude so they don't cancel out and we do need to tweak the clocks on the satellites ever so slightly to fix it.

But those are rare cases where it matters, for everything else you can use the quick and simple formulas that work on spherical cows in a vacuum. Gets you the result quicker while being just as accurate once margins of error are considered. Its a matter of understanding the limitations of your abstraction.

If you want to include the effects of time dilation due to special relativity when calculating how long its going to take to to walk across town on foot be my guest. But don't expect everyone else to do it too.

Keep in mind Maxwells equations are an just an abstraction of Quantum electrodynamics. But not that it matters, they work for what they are meant to do. Just like circuit theory being a abstraction of Maxwells equations.

You're absolutely right. I can't handle the "abstraction". I must admit. So I humbly ask you a favor. Please, show me how to solve the circuit below using exclusively Kirchhoff.



Thank you in advance.

Can't do it using just Kirchhoff. But even if there was no magnetic field you couldn't solve it using only Kirchhoffs circuit laws. That's because the circuit contains resistors and KVL has no way to deal with that, it can only deal with voltages. So it requires the assistance of circuit mesh analysis tools to join it to a resistor model by using Ohms law to calculate the voltage and then present that to KVL.

In the same way Faradays law alone can't be used to solve this circuit. It will tell you the magnitude of the non conservative E field around this circuit and that is very helpful since we have a magnetic field but that's where its assistance ends. You have the total voltage but you have no idea where it is.

Id solve your particular circuit with numbers but the size of the loop area is not provided so a numeric result is not possible.

But a typical path to solve this circuit would be as follows:
1) Use Faradays law to get the induced voltage
2) Use Thevenins theorem to reduce the circuit to a single voltage source and resistor (Involves the use of series lumping to get there)
3) Use Ohms law to find the current flowing in this reduced cirucit
4) Use Kirchhoff current law to deduct this same current must flow trough all components (If there was a junction node there would be more work here) to find the current flowing on each resistor
5) Use Ohms law to turn the current on both resistors to the voltages on resistors.

There now all voltages and currents in the circuit are known. Notice that this involved 4 different formulas/procedures to get there. Any single one of them alone could not fully solve the circuit, thats because they don't spit out the voltages and currents for every point, or that they need extra input information that gets provided by a different formula.

[bsfeechannel]

Its just a matter of perspective.

Yes. The perspective of those who study Maxwell for real and understand the physical phenomenon with which they're dealing, and those who don't.

Keep in mind Maxwells equations are an just an abstraction of Quantum electrodynamics.

Poor Feynman. Won the Nobel Prize for nothing.

Can't do it using just Kirchhoff.

That's a pity. I was already picturing you being invited by the King of Sweden for a banquet.

But even if there was no magnetic field you couldn't solve it using only Kirchhoffs circuit laws.

You said you could calculate Lewin's circuit using Kirchhoff with the exclusion of Maxwell.

Id solve your particular circuit with numbers but the size of the loop area is not provided so a numeric result is not possible.

Didn't you say that Kirchhoff is an abstraction of Maxwell? Doesn't Kirchhoff hide the ugly underlying details of Maxwell? Why do you need them now? Isn't it because Kirchhoff is in fact a special case of Maxwell?

This is just yet another contradiction that shows that such claims are nothing but false.

[Berni]

Yes. The perspective of those who study Maxwell for real and understand the physical phenomenon with which they're dealing, and those who don't.

I understand both of the of the perspectives just fine, so there is a problem behind knowing too much? That makes no sense.

Poor Feynman. Won the Nobel Prize for nothing.

Feynman won the nobel prize exactly on the topic of quantum electrodynamics. His diagrams are also widely used to describe interactions in this theory. I can't know how he feels about his nobel prize but this stuff is still at the cutting edge of physics research.

Just because quantum electrodynamics are even more fundamental than Maxwells equations doesn't mean that they are suddenly useless. If you are looking for the underlying workings of the universe they are indeed not the place to look, but if you just want to deal with electromagnetic fields then they are great (Since that's exactly what those equations are supposed to do). If you just want a voltage on a resistor in a typical cirucit then all you need is circuit analysis theory. Use the appropriate theory for the task at hand and everything is fine.

You said you could calculate Lewin's circuit using Kirchhoff with the exclusion of Maxwell.

I said that you can properly model Dr. Lewins circuit as a circuit mesh to have KVL work just fine on it. Notice that in my procedure for solving the circuit i never used KVL.

Can you show me where i said that we don't need Maxwells equations or Faraday law? (Cause i don't remember it)

Didn't you say that Kirchhoff is an abstraction of Maxwell? Doesn't Kirchhoff hide the ugly underlying details of Maxwell? Why do you need them now? Isn't it because Kirchhoff is in fact a special case of Maxwell?

This is just yet another contradiction that shows that such claims are nothing but false.

Call it an abstraction or special case or whatever you want. Its all because of the way circuit mesh analysis works and KVL fits into that. Maxwell deals with it using fields, cirucit analysis deals with it using inductance, just a different way of going about it that gives the same result.

Okay can you then calculate the voltage for me without making up a random value for the area?

[bsfeechannel]

Call it an abstraction or special case or whatever you want.

You urgently need to know the huge difference between the two.

[Sredni]

Whatever you say man.  I just want to point out what "Engineering Electromagnetics" by Hyat and Buck, Seventh Edition, says in page 94:

"Equation (21) (Curl integral of E.dl=0) is therefore just a more general form of Kirchhoff's circuital law for voltages, more general in that we can apply it to any region where an electric field exists and we are not restricted to a conventional circuit composed of wires, resistances, and batteries.  Equation (21) must be amended before we can apply it to time-varying fields.  We shall take care of this in Chapter 10, and in Chapter 13 we will them be able to establish the general form of Kirchhoff's voltage law for circuits in which currents and voltages vary with time."

Yep, it's talking about 'new' or 'extended' or 'amended' KVL that is used with lumped circuits.
But it's really Faraday and Lenz carrying around Kirchhoff's corpse.

https://i.ibb.co/bWNhLK8/screenshot-9.png

But this breaks as well when you try to apply a lumped circuit rule to a non-lumped circuit such as the Romer-Lewin ring.

[Sredni]

What probe wires???
There are no probes wires in the computation of the path integrals I've shown above.
The two different values we get, for the two possibile path along the circuit, are the result of induction. But that's how the system is. If you remove the induced part of the field, you are analyzing a different (unrealistic) system.

It's as if you subtracted the field generated by the point charge near a piece of copper to come to the conclusion that there is a nonzero field inside the metal (and then came up with tiny generators inside the metal) that produce the observed surface charge.

The ones that connect his oscilloscope to points A and B, since the BNC connector on a scope does not conveniently have the exact contact spacing to touch the two points of interest.

Im not saying that the two voltages result is due to the probe wires. I am trying to say that the path that the probe wires take is important.

You saw the field, you saw the computation of the integral along the two branches. It has nothing to do with the probes. It's the circuit itself that is path-dependent. When you are outside of the loop the voltmeters show this dependency as well, but they are not necessary to know this is happening to the circuit and has nothing to do with the measurement.
And in fact, as long as you do not cross the flux region (meaning also you cannot go 'on the other side' with your voltmeter) the probes path is not affecting the 'exterior' measurement.

If you take probing into account you can run the wires in any path you want and get the same result. Still two voltages across A and B.

This is inconsistent. Either you get the same result, or you get two voltages.

Can you please solve the circuit using your method?
You had to stop because the area was not given, so make it up. 10 cm^2 or any values that gives you a nice round value for the emf, such as 1V, 5V, 10V, you make it up BUT please make sure not to lose sight of the phase relationship between the flux, the emf and the 'effective' voltage. Because I believe, if you do, there are bad news in sight for Mabilde and co.

[Berni]

Alright then. Lets assume the area is 10cm2. I just copy pasted my procedure and filled in numbers
 
1) Use Faradays law to get the induced voltage
Integ(E)=-Integ(∂B/∂t*dA)
Integ(E)=-Integ(∂sin(100*t)/∂t*0.001)
Integ(E)= -100 * cos(100*t) * 0.001
Vi = -0.1 * cos(100*t)
So this gives us 0.1 Vrms that is leading by 90 degrees

2) Use Thevenins theorem to reduce the circuit to a single voltage source and resistor (Involves the use of series lumping to get there)
U=Vi=0.1 * -cos(100*t)
R=R1+R2=100+900= 1000 Ohm

3) Use Ohms law to find the current flowing in this reduced cirucit
I=U/R=0.1 * -cos(100*t) / 1000
I= 100 * -cos(100*t) µA

4) Use Kirchhoff current law to deduct this same current must flow trough all components (If there was a junction node there would be more work here) to find the current flowing on each resistor
I_R1 = I_R2 = I =  100 * -cos(100*t) µA

5) Use Ohms law to turn the current on both resistors to the voltages on resistors.
U=I*R
U_R1=I_R1*R1 = 100E-6 * -cos(100*t) * 100 =  10 * -cos(100*t) mV
U_R1=I_R1*R1 = 100E-6 * -cos(100*t) * 900 =  90 * -cos(100*t) mV

There now voltages and current across all components are visible. The conditionality for all values is in the clockwise direction around the circuit diagram. This is pretty much what Dr. Lewin did on his whiteboard except it includes phase. What is so special about this?

[Sredni]

I am sorry I wasn't clear, what I meant was to solve it to give the 'true' or 'effective' or 'coulombian' or 'unique' voltage. The one that in the case of an emf of 1V gives 0.4V between the midpoints. If you use ohm's law to the arc composed of piece of wire + resistor + piece of wire for the two half-circles, you end up with two different values for the voltage between the same points (something that Kirchhoffian would not tolerate).

Can you give the voltage at points between resistors to show, like Mabilde did, that you get a gradually changing voltage from one resistor to the other?

I am showing you my cards, here: my point is that, if that's the voltage associated with the conservative part of the total electric field, it will give contributes that are actually opposing the emf.

[Berni]

The effective voltage across the resistors is the same so above calculations still hold. The circuit in question had no midpoint node marked in it so everything between the resistors was assumed to be an ideal wire.

If you want to add two points in the middle this makes it the same as the inner part of Dr. Lewins experiment and i already put that together 2 months ago:
https://www.eevblog.com/forum/chat/does-kirchhoffs-law-hold-disagreeing-with-a-master/msg1945312/#msg1945312
Remember to interact a circuit mesh with magnetic fields the circuit has to have inductors otherwise all loop areas are 0 cm2

Okay it was done with SPICE, but its no problem to do it manually too.
We need to find the voltage on each lumped inductor. All four inductors form the entire loop so they are considered fractional turns around the given coupled field and the coupling factor is 1 so all inductance is in the form of coupled inductance. Considering that points A and B are in the middle gives each inductor an equal 1/4 share of the total turn ratio. This means that they basically catch 1/4 of the total field trough it. So we simply solve Faradays Law with a field 1/4 the strength.

But we already calculated it for the whole loop before so we can simply reuse the result and divide it by 4 (Since that's what we get if we put 1/4 the field in) and since the wires all also go in  the same direction around this gives them the same sign too however the effective voltage is the opposite sign to the EMF voltage due to charge separation (And in general voltage sources in circuits act like this because they essentially have a negative 'voltage drop'):
U_L2=U_L3=U_L4=U_L5= -(-0.1 * cos(100*t)) / 4 = 0.025 * cos(100*t) V

The circuit is again fully solved because we know the current and voltage on every component.

So now then lets test the result a bit by calculating the voltage across A and B in two ways.
1) Going trough L5 R1 L2:
U_AB = U_L5+U_R1+U_L2 = 0.025 * cos(100*t) +(-0.010 * cos(100*t)) + 0.025 * cos(100*t) = 0.040 * cos(100*t) V
2) Going trough L4 R2 L3:
U_AB = -U_L4-U_R2-U_L3 = -0.025 * cos(100*t) -(-0.090 * cos(100*t)) + 0.025 * cos(100*t) = 0.040 * cos(100*t) V

There you go, same voltage no matter what path you take

To top it off lets also show that KVL works, so all voltages should add up to zero:
U_loop= U_R1+U_L2+U_L3+U_R2+U_L4+U_L5 =
-0.010 * cos(100*t) + 0.025 * cos(100*t) + 0.025 * cos(100*t) + (-0.090 * cos(100*t) + 0.025 * cos(100*t) + 0.025 * cos(100*t) = 0 V
So KVL works as we got zero

You can also add the voltages of the other 4 inductors in the outer circuit and get the voltages at the voltmeter terminals. Or the points A and B can be moved to any other location by recalculating the inductor turns ratio to match.

Oh and i should  also note that this calculation is valid for the case where the applied field "1T * sin(100*t)" is constantly maintained by whatever is generating it (Such as a superconducting coil fed by a ideal voltage source), if not then the current flowing in the circuit would reduce the strength of the field inside the loop area and this would need to be accounted for with fairly complex math. Tho in this case with a field strength of 1T and 100uA of current the difference in the result would be very small.

[rfeecs]

Alright then. Lets assume the area is 10cm2. I just copy pasted my procedure and filled in numbers
 
1) Use Faradays law to get the induced voltage
...
2) Use Thevenins theorem to reduce the circuit to a single voltage source and resistor (Involves the use of series lumping to get there)
...
3) Use Ohms law to find the current flowing in this reduced cirucit
...
4) Use Kirchhoff current law to deduct this same current must flow trough all components (If there was a junction node there would be more work here) to find the current flowing on each resistor
...
5) Use Ohms law to turn the current on both resistors to the voltages on resistors.
...
There now voltages and current across all components are visible. The conditionality for all values is in the clockwise direction around the circuit diagram. This is pretty much what Dr. Lewin did on his whiteboard except it includes phase. What is so special about this?

You could simplify to:
1)  Use Faraday's law to find the EMF in the loop.
2)  Use ohms law to find the total current in the loop (I = Total EMF / total resistance).
3)  Use ohms law to calculate the voltage drop across each resistor (V = IR).

Notice that you MUST use Faraday's law to solve this, and you do not use Kirchhoff's loop rule at all to solve it.

Doesn't that say something?

[jesuscf]

Whatever you say man.  I just want to point out what "Engineering Electromagnetics" by Hyat and Buck, Seventh Edition, says in page 94:

"Equation (21) (Curl integral of E.dl=0) is therefore just a more general form of Kirchhoff's circuital law for voltages, more general in that we can apply it to any region where an electric field exists and we are not restricted to a conventional circuit composed of wires, resistances, and batteries.  Equation (21) must be amended before we can apply it to time-varying fields.  We shall take care of this in Chapter 10, and in Chapter 13 we will them be able to establish the general form of Kirchhoff's voltage law for circuits in which currents and voltages vary with time."

Yep, it's talking about 'new' or 'extended' or 'amended' KVL that is used with lumped circuits.
But it's really Faraday and Lenz carrying around Kirchhoff's corpse.

https://i.ibb.co/bWNhLK8/screenshot-9.png

But this breaks as well when you try to apply a lumped circuit rule to a non-lumped circuit such as the Romer-Lewin ring.

Aren't we talking here about Kirchhoff's circuital law for voltages?  Are you aware of the generalization of Kirchhoff's circuital laws to systems other than linear electric systems?  I can recommend you the book "Physical Networks" by Richard Sanford which explains how to apply KVL and KCL to other "circuits" with potential/flow properties.  The book deals not only with electrical systems, but rotational, translational, and fluids-flow (as water in tanks) systems as well as combinations of all of them via "transformers".  Although not covered in the book, the same rules (as in KCL and KVL) apply to thermal and magnetic circuits as well.

The problem you are having with the so called Romer-Lewin ring is that you are decoupling a circuit that can not be decoupled.  In the so called Romer-Lewin ring the inductor generating the time varying field is part of the circuit and must be included in the solution via the standard equations of transformers.  Then KVL "magically" works as shown by Electroboom.  I don't know man, maybe Richard Feynman was right when he said in one of his lectures on physics (Lecture 25: Linear Systems And Review, at about minute 25:40):

"The difference between a physicist and an electrical engineer is not the difference in anything he knows, except one fact... not the mathematical knowledge or anything else except just one extra fact the physicist knows and that is: electrical systems are not the only linear systems in the world.  All you have the same equations the same problems exactly in electrical engineering and you have in all the rest of physics.  And all the difference between a physicist and electrical engineer is that the physicist knows the same equations apply to another circumstances and he gets in [obviously] and the electrical engineer looks puzzled, and that so is simply why they hired a physicist... I know that but that wasn't an electrical circuit..."

 

[Berni]

You could simplify to:
1)  Use Faraday's law to find the EMF in the loop.
2)  Use ohms law to find the total current in the loop (I = Total EMF / total resistance).
3)  Use ohms law to calculate the voltage drop across each resistor (V = IR).

Notice that you MUST use Faraday's law to solve this, and you do not use Kirchhoff's loop rule at all to solve it.

Doesn't that say something?

Yes in this case you could simplify out the two steps because the circuit is so simple you can see what the total loop resistance is and there is only one path to consider as the circuit does not branch anywhere. But when you describe a procedure you can't just pluck a number from your head because you see it, you have to explain how you got the number. I mention in the procedure that there is not much to do in this step, but in a more complex circuit there could be a significantly more math involved to evaluate all the paths.

And no you can't use only Kirchhoffs circuit laws to solve this, just like you CAN'T use ONLY Faradays law to solve it, you do need it for the first step but you will not be able to find the voltage on the resistors without involving Ohms law. That way my point, circuit analysis makes use of a whole collection of formulas to solve circuits and each formula has its use case.

Its all just a matter of using the right tool for the job. Because the circuit has a magnetic field defined in it you need Faradays law because its a tool for turning changing fields into voltage and once we have voltage we can forget about the field and proceed with circuit analysis as usual.

Aren't we talking here about Kirchhoff's circuital law for voltages?  Are you aware of the generalization of Kirchhoff's circuital laws to systems other than linear electric systems?  I can recommend you the book "Physical Networks" by Richard Sanford which explains how to apply KVL and KCL to other "circuits" with potential/flow properties.  The book deals not only with electrical systems, but rotational, translational, and fluids-flow (as water in tanks) systems as well as combinations of all of them via "transformers".  Although not covered in the book, the same rules (as in KCL and KVL) apply to thermal and magnetic circuits as well.

The problem you are having with the so called Romer-Lewin ring is that you are decoupling a circuit that can not be decoupled.  In the so called Romer-Lewin ring the inductor generating the time varying field is part of the circuit and must be included in the solution via the standard equations of transformers.  Then KVL "magically" works as shown by Electroboom.  I don't know man, maybe Richard Feynman was right when he said in one of his lectures on physics (Lecture 25: Linear Systems And Review, at about minute 25:40):

"The difference between a physicist and an electrical engineer is not the difference in anything he knows, except one fact... not the mathematical knowledge or anything else except just one extra fact the physicist knows and that is: electrical systems are not the only linear systems in the world.  All you have the same equations the same problems exactly in electrical engineering and you have in all the rest of physics.  And all the difference between a physicist and electrical engineer is that the physicist knows the same equations apply to another circumstances and he gets in [obviously] and the electrical engineer looks puzzled, and that so is simply why they hired a physicist... I know that but that wasn't an electrical circuit..."

Yes i did bring that up about 15 pages ago:
https://www.eevblog.com/forum/chat/does-kirchhoffs-law-hold-disagreeing-with-a-master/msg2004740/#msg2004740

The form of KVL we popularly know is meant for use in circuit meshes and it always works there. If a cirucit mesh doesn't behave the same as your circuit that's because you made a mistake in modeling the real circuit as a mesh. But because all other physical systems also show similar behavior as electricity means you can use cirucits to model those too and apply KVL to heat flow, water flow, mechanical motion etc.

Tho to be honest i never seen physicists use circuit schematics to describe anything other than electrical things. It seams to me its more of an electrical engineering thing where engineers have no clue about some random physical system, so they do "when you have hammer every problem looks like a nail" and mold the problem to look like a circuit since that's the one thing they do know how to deal with easily.

At least i never saw this "circuit meshes are not just for electrons" concept even mentioned any of my physics classes, while i have used the trick extensively in a lot of engineering classes to make sense of magnetic circuits, water flow, heat flow etc.. and to actually calculate stuff with it.

[Sredni]

Aren't we talking here about Kirchhoff's circuital law for voltages?  Are you aware of the generalization of Kirchhoff's circuital laws to systems other than linear electric systems?

Oh, Jesus...
How come I have this hunch you did not read all the previous posts?
Are you mistaking me for a kirchhoffian?

I can recommend you the book "Physical Networks" by Richard Sanford which explains how to apply KVL and KCL to other "circuits" with potential/flow properties.  The book deals not only with electrical systems, but rotational, translational, and fluids-flow (as water in tanks) systems as well as combinations of all of them via "transformers".  Although not covered in the book, the same rules (as in KCL and KVL) apply to thermal and magnetic circuits as well.

Good, we discovered analogies. They can be very useful. You might want to go back a couple of tens of pages and read my gravitational analogy with nonconservative drag.
What we are discussing here is the fact that when the electric field is not conservative, you can no longer have a potential function, so that voltage can no longer associated with the difference in the values of said function in two points, but depends on the path as well.
Meaning... when voltage is path dependent you can have two (actually infinitely many but... more than one) different value of voltage between two points. This is no biggie to a physicist and to many engineers. It's just simple math. And if you compute the field inside the ring you can see at a glance that it has nothing to do with probing. Now, I hope you agree that Kirchhoff needs single-valued voltages to live. So Kirchhoff dies inside the Romer-Lewin ring.
And yet there are people (which I call kirchhoffians) insisting that you can still use KVL inside that ring.
(If you want to see why you can use 'extended KVL' with lumped circuit, go read Ramo Whinnery Vanduzer, I am even tired to point out the chapter).

The problem you are having with the so called Romer-Lewin ring is that you are decoupling a circuit that can not be decoupled.  In the so called Romer-Lewin ring the inductor generating the time varying field is part of the circuit

So, you know. Then why...

and must be included in the solution via the standard equations of transformers.  Then KVL "magically" works as shown by Electroboom.

The problem is that if you do that you are lumping the unlumpable.
The circuit with one transformer secondary lumping all the emf in one point is a different circuit. So is the circuit with the emf lumped in four points, or eight, or a thousand.

And if you only consider the conservative part of the total electric field to get a field where you can apply KVL (the McDonald maneuver) you are considering only part of your system, specifically the part with the field that actually opposes the electromotive field generated by the primary coil (or moving magnet). Scalar potential can be very useful, but we must be aware of what it is: only half of the story.

To sum it up, if you believe that KVL can be applied to a non-lumped element circuit, you are mistaken. Neither Feynman nor Hayt ever said that. And while I've never had the pleasure to read Sanford, I am pretty confident he did not either. My bet is that when the system is rotational he uses some analog of Faraday's law and the analog of KVL dies an analog horrible death in a different branch of physics.

[bsfeechannel]

The problem you are having with the so called Romer-Lewin ring is that you are decoupling a circuit that can not be decoupled.  In the so called Romer-Lewin ring the inductor generating the time varying field is part of the circuit and must be included in the solution via the standard equations of transformers. 

What I like about those people who do not study Maxwell and think they understand something about electromagnetism is to get acquainted with the pseudo scientific vocabulary:

"You are decoupling a circuit that cannot be decoupled." HAHAHAHAHA!

Then KVL "magically" works as shown by Electroboom.

The only magical power we have seen Mehdi show, up to now, is the power of attracting those who are lazy enough to understand electromagnetism and need a pseudo-theory to justify their ignorance.

I don't know man, maybe Richard Feynman was right when he said in one of his lectures on physics (Lecture 25: Linear Systems And Review, at about minute 25:40):

Everybody likes to quote Feynman, but no one has the guts to study the subject-matter of his lectures.

[jesuscf]

"You are decoupling a circuit that cannot be decoupled." HAHAHAHAHA!

I wonder... are you an electrical engineer?  If your answer is yes, then you can quickly tell me why an electrical engineer will not use the method Dr. Lewin used to solve his problem #24.

About a year ago, after I watched his series of videos about problem #24, I reached the conclusion that Dr. Lewin's teachings regarding the solution of electric circuits must be carefully considered before accepting them.

The only magical power we have seen Mehdi show, up to now, is the power of attracting those who are lazy enough to understand electromagnetism and need a pseudo-theory to justify their ignorance.

Ad hominem... that will prove you right.  KVL is a pseudo-theory?  Do you know KVL can be derived from Maxwell Equations?

Everybody likes to quote Feynman, but no one has the guts to study the subject-matter of his lectures.

So electrical engineers don't study linear circuits now!  Wow, that must be a new curriculum!

[jesuscf]

The problem is that if you do that you are lumping the unlumpable.

By applying the same logic an inductor is unlumpable...  therefore we can not use KVL in circuit that includes an inductor!?