Is MIT Prof. Lewin wrong about Kirchhoff's law?

[Antiphon]

Hey Antiphon

I want to clarify with you so there is no mis-understanding:

1) You imply the real circuit like what I did has real physical size. With physical size resistors and wires, electric and magnetic field come into play.

2)Where the professor only draw the circuit loop with two resistors, he automatically imply there is no physical size of the resistors and no length between the connections. He cannot just simply put it into a real circuit and hope that the real circuit is still only two resistor in a loop with no physical size. AND it just happen the method of measurement just happen to give the same result he was looking for.

3)Is that the reason in #2 above that you said the circuit model that the professor gave and his experiment don't match and he cross the line? That he mixed the theoractical circuit diagram ( with no physical size) and he did the experiment that the EM effect come into play.


I guess this is similar to what I said before that, if he want to use his experiment, he has to put in the extra "real life" circuit elements of the emf generator due to the transformer effect of the loop of wire that pick up the flux etc. AND his experiment was frauded with the EM interference.

Please reply point by point to my questions with different color fonds right below my questions so we have a clear understanding with each other. As I said so many time, I only challenge his experiment.

Thanks

PS: I think this is the first argument that make sense to me. Now we wait for the ones that disagree to come in and present their case.

Sorry, I don't know how to color the responses.

1) Yes. The assumptions of circuit analysis are that a circuit has zero physical extent and that the circuit elements types do not cross-couple. That means a capacitor only exhibits capacitance, not inductance or resistance. In a microwave circuit you assume that a capacitor has all three. In a field analysis of a physical capacitor you could construct an equivalent circuit that would have to have an infinite number of resistors, capacitors and inductors to model a physical capacitor.

2) Essentially, yes. It isn't just the two resistors but as you pont out also the wires and the voltage source, everything. Any time you draw a circuit it is implicit that it has zero physical size. The professor's sleight of hand was not precisely in assuming that the circuit was of zero size; all circuits in circuit theory are. His feint was in assuming that it was *not* of zero size by allowing a magnetic field to couple to it. He construced a hybrid circuit which was partly idealized as in circuit theory and partly an electromagentic induction loop, a field analysis.

3) Yes.

 

[Antiphon]

Can you read German?

Because that is not what Kirchoff actually said or for that matter what appeared in Maxwell's translation of it.
His actual exposition make a huge difference to this problem.

Ja, ich deutsch lesen und schreiben. Ich lebte in Bayern für ein Jahr.

But my fluency in German isn't germain. You aksed me for *my* version of KVL. Which is what is taught in today's schools.

What's *your* version Studiot?

 

[Studiot]

As Kirchoff originally stated, of course.

Here is an English translation

The conditions of a linear system

1) At any point of the system the sum of all currents which flow towards that point is zero.

2) In any complete circuit formed by the conductors the sum of the electromotive forces taken around the circuit is equal to the sum of the products of the currents in each conductor multiplied by the resistance of that conductor.


(2) is, of course the paragraph we are talking about here.

If you had bothered to read back in this thread you would have seen that I had already published this along with links to Maxwell's discussion of it where he explicitly states that he considers this is 'avoids consideration of potential' which is my objection to Professor Lewin's version.
As I said only a few posts ago I have already posted in this thread the simple application of Kirchoff's own words to this eliminate this problem.

 

[yungman]

Hey Studiot

I know you have been following this thread closely from day one. I wish you would join in and give your opinion. So far you only pick on the definition of emf and KVL etc. and not involve in the major point of discussion.

I think at this point it is very clear. I challenged the experiment and I proofed my point. StevenB insisted on this is still path dependent and proofed the professor was right. So since you are very into definition, tell us whether this is path dependent or not.

I said many times that I am not particularly strong in theory, but I do have a gift with my nose to smell out spin!( If you watch O'Rielly's no spin zoo, you know what I mean! lol!). And I worked a full career successfully trusting my nose. I am about making things work and find out why when it does not. I can't sit 3 days arguing about the definition of some abstract theory and definition. That's why when it came to this point, I stopped! I am not going to spent a day more to argue about the definition of path dependent! This is for the theractical physis to do.

Without the clear distinction like Antiphon, I think we charllenge the same thing about the real life experiment has more components that what was drawn in the professor's assumption of only two resistors. So you being very strong on definition, you should start putting in your opinion beyond what is KVL in german.



How about all the other mentors and contributors? This is down to definition now!

 

[Antiphon]

As Kirchoff originally stated, of course.

Here is an English translation

The conditions of a linear system

1) At any point of the system the sum of all currents which flow towards that point is zero.

2) In any complete circuit formed by the conductors the sum of the electromotive forces taken around the circuit is equal to the sum of the products of the currents in each conductor multiplied by the resistance of that conductor.


(2) is, of course the paragraph we are talking about here.

If you had bothered to read back in this thread you would have seen that I had already published this along with links to Maxwell's discussion of it where he explicitly states that he considers this is 'avoids consideration of potential' which is my objection to Professor Lewin's version.
As I said only a few posts ago I have already posted in this thread the simple application of Kirchoff's own words to this eliminate this problem.

I saw the discussion, but I didn't consider it in any way illuminating to the topic at hand. But I'll address them now since they are also your version of KVL and since you're advancing this version as the correct one. Don't build any circuits with it though or you'll be very disappointed.

As Kirchoff stated it he's totaling up the IR drops around the circuit and equating that to the available EMF. That way, if there is induction or batteries (or both) driving a current he's got that all in there. That's fine since circuit analysis hadn't yet been refined to the point it is today. Kirchoff was doing physics in the lab, not electrical engineering as we know it today. To see what I mean, try applying the as-stated Kirchoff Voltage law to a circuit consisting of a battery, resistor and a capacitor. It doesn't work.

Of course you can see what's happeneing here. When the authors of a new principle start fleshing it out, its often not as well defined as it is later on. That's why the KVL of modern electrical enegineering is the one we really need to be using in circuit analysis, where the only sources of EMF around the circuit are the voltage sources on the schematic, not the fields perpendicular to the blackboard.

 

[Studiot]

As Kirchoff stated it he's totaling up the IR drops around the circuit and equating that to the available EMF. That way, if there is induction or batteries (or both) driving a current he's got that all in there. That's fine since circuit analysis hadn't yet been refined to the point it is today. Kirchoff was doing physics in the lab, not electrical engineering as we know it today. To see what I mean, try applying the as-stated Kirchoff voltage law to a circuit consisting of a battery, resistor and a capacitor. It doesn't work.

Of course you can see what's happeneing here. When the authors of a new principle start fleshing it out, its often not as well defined as it is later on. That's why the KVL of modern electrical enegineering is the one we really need to be using in circuit analysis, where the only sources of EMF around the circuit are the voltage sources on the schematic, not the fields perpendicular to the blackboard.

How arrogant can you get?

Your example for analysis is easy. It does not conform to the boundary conditions which state "In any complete circuit formed by the conductors".
Of course a capacitor is not a conductor so there is no complete circuit formed by the conductors to analyse.

I have never claimed KVL to be universally applicable, in fact I stated the opposite a couple of posts back and posted a link to the (rather good for Wikipedia) article detailing one of the exceptions viz non planar circuits.

Yet this thread was entitled 'Was Prof Lewin Wrong?'

My answer is yes, not because of a sleight of laboratory handiwork, but because in this case correct application of KVL will yield a correct result.
This would not be the situation in every case.

So what my answer means is that Prof Lewin was correct to say that sometimes KVL does not work, but his IMHO his example was flawed.

 

[yungman]

why don't we concentrate on the professor's claim which he backed by the experiment. We cannot exactly separate the two. For all I care he cound be right in some cases, but not with his example and with the experiment he did. As Antiphon put is so nicely that if you look at it as a circuit model, you cannot have the wires and physical size of the resistors that can be acted on by the EM produced. If you use the circuit model, you are going to have to put in the parasitic components that come with the finite physical size. Using a physical wire and resistor around a physical coil get us immediately into a real life circuit and it is an electromagnetic experiment instead of a theoractical circuit model. That was the reason I jumped in because I smell the flaw. That is the reason I conclude the professor is wrong on his claim with his experment.

BTW, I think I mis-used the work Fraud instead of flaw. I don't mean he intentionally decieve people, I meant his experiment is flawed that don't back up what he claimed because of all the reason we presented. Excuse me on my English as this is not my primary language.

 

[Antiphon]

How arrogant can you get?

Your example for analysis is easy. It does not conform to the boundary conditions which state "In any complete circuit formed by the conductors".
Of course a capacitor is not a conductor so there is no complete circuit formed by the conductors to analyse.

I have never claimed KVL to be universally applicable, in fact I stated the opposite a couple of posts back and posted a link to the (rather good for Wikipedia) article detailing one of the exceptions viz non planar circuits.

Yet this thread was entitled 'Was Prof Lewin Wrong?'

My answer is yes, not because of a sleight of laboratory handiwork, but because in this case correct application of KVL will yield a correct result.
This would not be the situation in every case.

So what my answer means is that Prof Lewin was correct to say that sometimes KVL does not work, but his IMHO his example was flawed.

First let's correct your errors. A capacitor is a conductor. The current flowing in one end is the exact same current coming out the other. But since you prefer wires, the stated KVL doesn't work for a battery, resistor and inductor either. That's a circuit that can be constructed out of a battery and one big long piece of wire. So no, I'm not arrogant, I'm informed.

I guess I'm confused about what your view is exactly. If Kirchoff's own KVL applies in this case and gets the right answer, why is the professor wrong?

 

[Studiot]

guess I'm confused about what your view is exactly. If Kirchoff's own KVL applies in this case and gets the right answer, why is the professor wrong?

I can't put it any better than steveB did in post#4 of this thread it is an excellent summary.

We will have to agree to disagree about 'what comes out of the other end of a capacitor'.

I do, however, note that often your posts are just statements, without working or backup, although I have several times unsuccessfully invited you to provide the same.
I try to offer my working and backup when I make statements so that others may judge for themselves. Sometimes they have then proved me wrong and I have been the ultimate winner in that I have learned something new.

 

[Antiphon]

I can't put it any better than steveB did in post#4 of this thread it is an excellent summary.

We will have to agree to disagree about 'what comes out of the other end of a capacitor'.

I do, however, note that often your posts are just statements, without working or backup, although I have several times unsuccessfully invited you to provide the same.

SteveB did sum it up nicely but he drew the wrong conclusion (to include Faraday's law in KVL.) The distinction he's not making is the one I've been pointing out.

I don't know what's coming out the back of *your* capacitor, but I can tell you mine is clean as a whistle. :)

I missed your invitations but ok. My favorite treatment of this topic begins on page 264 of "Electromagnetic Fields, Energy and Forces" by Fano, Chu, and Adler. This is an out-of-print MIT texbook from 1963 so I'll do you and everyone the courtesy of making a trip to the library unnecessary. I've added some of my comments in bracket in caps. I'm not shouting, its just that I don't want what I wrote to be confiused with the book's text.]

"6.10 The Concept of Voltage and Kirchoff's Laws
[...] Kirchoff's voltage law states that the sum of the branch voltages along any closed path in the circuit (measured in the same direction) must be equal to zero. This law is the equivalent of Maxwell's first equation, i.e. of Faraday's induction law. This equivalence, however, is not as directly evident as the relation between Kirchoff's current law and the conservation of charge. Indeed, the voltage law depends on how the branch voltages are defined in herms of the electromagnetic field. Although the concept of voltage has already been discussed in Sec. 6.8 in connection with inductive fields, it deserves some further, careful consideration in view of its key role in circuit theory.
To obtain a better feeling for what is involved in in the circuit concept of voltage, it is helpful to consider its definition from an experimental point of view. A little thought will make it obvious that all voltmeters are designed to measure the line intrgral of the electric field along the path formed by the connecting leads. This is evident in the case of electrostatic voltmeters whose operation depends directly on the forces exerted by the electric field. Other more common insturments measure actually the current through a resistor of known value; the current desnity in any such resistor is proportional, by Ohm's law, to the elctric field and, therefore the total current is proportional to the line integral of the electric field between the terminals of the resistor. On the other hand, there are implicit limitations on the use of voltmeters. For instance, nobody in his right mind would wrap the leads of a voltmeter around the core of a transformer in determining the voltage between two points in a circuit. Furthermore, it is understood that the leads of a voltmeter should be kept reasonably short and that little meaning should be attached to an indications which depends on the exact position of the leads. [YOUNGMAN, THIS IS YOUR EXPERIMENT]
These limitations on the use of voltmeters indicate that the voltage between two points has meaning only wjen the line integral of the electric field between two points is closely independent of the path of integration for all reasonably short paths. In mathematical terms, this amounts to saying that a voltage can be defined only between between points of a region in which there exists a scalar potential whose negative gradient is closely euqal to the electric field [VIOLATED BY PROFESSOR LEWIN'S EXPERIMENT]. Thus the concept of voltage in the presence of of time-varying currents is strictly an extension of the concept of voltage as defined in electrostatic systems; this extension is valid only when the path of integration used in the computation of the voltage is contained in a region of space in which the electric field behaves approximately as an electrostatic field."[THIS IS WHY A CIRCUIT HAS TO BE OF INFINITESIMAL SIZE;]

There is much more on the topic but I'll only type it if there is interest.

 

[stevenb]

SteveB did sum it up nicely but he drew the wrong conclusion (to include Faraday's law in KVL.) The distinction he's not making is the one I've been pointing out.

I feel you are slightly misrepresenting what I said here, but I don't blame you because of the length of this thread and certainly it's difficult to absorb it all.

I wasn't really trying to include Faraday's Law in KVL, but mentioned that I prefer a version of KVL which is in some sense consistent (at least more consistent than Lewin's version) with FL. It's not until post number 23 that I clarify this by posting 2 pages from Krauss and clearly state the definition I mean. Interestingly, it's not until post #144 where we bring in the version of KVL you are stressing - the modern circuit version. So, in that post I try to express the main difference between the 3 versions by stating them in an order that clarifies the assumptions.

As to why it took so long to bring in this version to the thread, I'll give my opinion. Essentially, Lewin is not discussing circuit theory at all. You really need to watch his entire course and understand the level of students in the class to understand his point of view. These students (although extremely bright and talented) are freshman level students - most of whom are not heading to be physicist and electrical engineers. This is the general class that all students take along with basic mechanics. So Lewin is not discussing circuit theory, but field theory. His definition of KVL (although I also don't like it) is a field definition. It says that the line integral of electric field is zero. Classical circuit theory is not implied in his discussion. We may not like this, but we should respect the substance of what he is saying, even if we want to point out a criticism of the definition and foundation he applies.

As I mentioned a few times in this thread, personally I have no interest in debating semantics, and I won't go any further down this road than this. So, my position is that if we accept his definitions and previous classwork in full context, he is essentially correct.

The real point of this thread, in my mind, is the issues the OP raised. He objected to the Prof's assertions and made his own prediction that the Prof was not measuring the voltages the way he said he was (basically an accusation of fraud, or at least extreme incompetence). He also made his own predictions of what a proper measurement would yield. He then did an experiment (improperly, mind you) that supporting his conclusions. Then he left thinking he was right. Later, once given enough time, I did the measurements and analysis and posted a full report on the proper way to do the measurements, the causes of error and a clear indication of the mistakes the OP made. I stand by all of this, and am quite confident in what I've put forward, with the motivation of helping others.

 

[yungman]

I feel you are slightly misrepresenting what I said here, but I don't blame you because of the length of this thread and certainly it's difficult to absorb it all.

I wasn't really trying to include Faraday's Law in KVL, but mentioned that I prefer a version of KVL which is in some sense consistent (at least more consistent than Lewin's version) with FL. It's not until post number 23 that I clarify this by posting 2 pages from Krauss and clearly state the definition I mean. Interestingly, it's not until post #144 where we bring in the version of KVL you are stressing - the modern circuit version. So, in that post I try to express the main difference between the 3 versions by stating them in an order that clarifies the assumptions.

As to why it took so long to bring in this version to the thread, I'll give my opinion. Essentially, Lewin is not discussing circuit theory at all. You really need to watch his entire course and understand the level of students in the class to understand his point of view. These students (although extremely bright and talented) are freshman level students - most of whom are not heading to be physicist and electrical engineers. This is the general class that all students take along with basic mechanics. So Lewin is not discussing circuit theory, but field theory. His definition of KVL (although I also don't like it) is a field definition. It says that the line integral of electric field is zero. Classical circuit theory is not implied in his discussion. We may not like this, but we should respect the substance of what he is saying, even if we want to point out a criticism of the definition and foundation he applies.

As I mentioned a few times in this thread, personally I have no interest in debating semantics, and I won't go any further down this road than than this. So, my position is that if we accept his definitions and previous classwork in full context, he is essentially correct.

The real point of this thread, in my mind, is the issues the OP raised. He objected to the Prof's assertions and made his own prediction that the Prof was not measuring the voltages the way he said he was (basically an accusation of fraud, or at least extreme incompetence). He also made his own predictions of what a proper measurement would yield. He then did an experiment (improperly, mind you) that supporting his conclusions. Then he left thinking he was right. Later, once given enough time, I did the measurements and analysis and posted a full report on the proper way to do the measurements, the causes of error and a clear indication of the mistakes the OP made. I stand by all of this, and am quite confident in what I've put forward, with the motivation of helping others.

Are you referring me as the OP? I never admit I was wrong, I just loss interest when I saw what we are arguing is just the definition of path dependent. I alway asserted that there are additional elements like the distributed emf generator along the loop of wires and resistors. I showed very clearly how I get different reading by making the ground of the probe traveling at different path. You said this is path dependent.

What your report said was only one way of your mearsurement, you show nothing of the different position of the ground leads that cause different reading. I had a very detail experiment and detail explanation of my observation. I thought you agree to my finding and you call that path dependent, so I did not argue any further. It was what it was. The result showed.

Now Antiphon talked about his opinion that I totally agree. That what the professor drawn is a too simplistic of a drawing. Even if it is hard to measure the voltage correctly, it ABSOLUTELY don't imply the voltage sources are not there. So don't say I saw I was wrong.

I think you should speak for yourself to proof Antiphon is wrong on his assertion first.

 

[stevenb]

Are you referring me as the OP?

No, you are not the OP. OP is basically the original post or poster.

 

[stevenb]

.

I think you should speak for yourself to proof Antiphon is wrong on his assertion first.

I am speaking for myself. I'm not trying to prove anyone wrong. There are too many shades of grey and side issues for me to have any motivation for that. I'm just putting my opinion forward.

 

[cabraham]

I believe that the questions presented have all been answered. There seems to be disagreement regarding how to define voltage across 2 points in a non-conservative E field, like that encountered w/ induction. The voltage from a to b is unambiguous when the field is conservative, as it is independent of path of measurement. Voltage is a quantity defined as the work done per unit charge transporting said charge from a to b, along a specific path for a non-conservative E field, & independent of path for conservative E fields.

In the non-conservative case, the voltage from a to b can be defined & have valid meaning if a path is specified. Otherwise it's ambiguous. Prof. Lewin was only pointing that out, which he did do correctly. Of course his measurement techniques could have introduced error. But he was emphasizing that one cannot assume that KVL holds. Two circuit elements in parallel do not necessarily have the same voltage across them when the E field is non-conservative.

I believe it has been affirmed that Prof. Lewin is correct in his teachings, but most on this forum feel he did not explain it as well as it could be explained. I certainly explain it a little differently than Prof. Lewin, but he is spot on technically. As far as a voltage source is concerned, it could be added to the equivalent circuit, so that KVL would then apply. But Prof. Lewin has to inform the students that this equivalent independent voltage source does not show up in measurements directly. Rather, the non-zero sum of voltages around the loop are the value of said voltage source.

That has to be known & he explained it. Is there anything in Prof. Lewin's lecture that is technically wrong? I have not found it, but feel free to say so if you are still at odds w/ him technically. BR.

Claude

 

[yungman]

I just watch the two part video of the Levin and I have to reconfirm...I meant everything I said about him other than the mis use of the "Fraud", it should be "flawed".

After weeks on this subject and did the whole experiment myself and did all the ground lead placement and recording the observation. AND listen the part 1 of the video from 4:20 to the end 5 times and noting down what he said. HE IS FULL OF IT AND FULL OF HIMSELF.

1) He mentioned Lens Law at 4:30 that induce I, he drew the magnetic source and consequence generated 1v emf. But he never put the equivanlent voltage source into the circuit. If he acknowledge there is an induced emf according to Lens Law, why he fail to put in the equivalent voltage source?

2) In part 2, he recognize that the area of the loop consists of the two resistors is $10cm^2$. So he obviously know that what he draw is not just a circuit model. Then he fail to put the emf source into the drawing in part 1.

3) I gave it more thoughts, just because you cannot easily measure the voltage because of the loop created by the measuring probe don't imply the voltage source is not there. Path dependent voltage don't imply anything about how you can measure it. IF YOU CAN MEASURE VOLTAGE ACROSS THE RESISTORS, THEN YOU HAVE TO HAVE A VOLTAGE SOURCE SOMEWHERE IN THE LOOP. Or else where is the voltage come from?

4) If Levine miss the voltage source in the drawing of the loop, what is the point of even talking about conservative and non conservative and path dependent.



Please stop arguing about the definition of the KVL, let's concentrate on the totality of the experiment and the lecture. Watch the lecture again and please read post #224 and #227. Tell me where is the voltage source?

As I specified, I am not arguing about what he claimed KVL don't hold in certain case. I just determine the whole lecture and experiment he did was flawed and don't mean anything about KVL and conservative path dependent.

 

[yungman]

I believe that the questions presented have all been answered. There seems to be disagreement regarding how to define voltage across 2 points in a non-conservative E field, like that encountered w/ induction. The voltage from a to b is unambiguous when the field is conservative, as it is independent of path of measurement. Voltage is a quantity defined as the work done per unit charge transporting said charge from a to b, along a specific path for a non-conservative E field, & independent of path for conservative E fields.

In the non-conservative case, the voltage from a to b can be defined & have valid meaning if a path is specified. Otherwise it's ambiguous. Prof. Lewin was only pointing that out, which he did do correctly. Of course his measurement techniques could have introduced error. But he was emphasizing that one cannot assume that KVL holds. Two circuit elements in parallel do not necessarily have the same voltage across them when the E field is non-conservative.
Can you show me a case of two parallel circuits do not have the same voltage across it. Please put in the equvalent voltage source also.

I believe it has been affirmed that Prof. Lewin is correct in his teachings, but most on this forum feel he did not explain it as well as it could be explained. I certainly explain it a little differently than Prof. Lewin, but he is spot on technically. As far as a voltage source is concerned, it could be added to the equivalent circuit, so that KVL would then apply. But Prof. Lewin has to inform the students that this equivalent independent voltage source does not show up in measurements directly. Rather, the non-zero sum of voltages around the loop are the value of said voltage source.
No, he did not inform anything to the student. I watched the part 1 5 times. He mentioned about the Lens law induce current and mentioned the induced emf. But he fail to incoporate into the drawing and went right into telling the student the magic of his finding. Of cause if you include the voltage source, then I won't be complaining. The next question would be where do you measure the voltage as the emf source is distributed along the wire? That proofed to be the tricky part of the experiment.

That has to be known & he explained it. Is there anything in Prof. Lewin's lecture that is technically wrong? I have not found it, but feel free to say so if you are still at odds w/ him technically. BR.

Claude

Watch the video over and listen to him again.

You've been gone before me and StevenB did the experiment and wrote the detail write up. Please look at #224 and #227 with the attachments.

 

[vanhees71]

In the meantime I browsed through this thread in a bit more detail. Here are some quotes from a textbook by Antiphon which are plain wrong, and Prof. Lewin's explanation is way better. I think all this has been answered already in the first few postings of this thread, but let's summarize it again.

"6.10 The Concept of Voltage and Kirchoff's Laws
[...] Kirchoff's voltage law states that the sum of the branch voltages along any closed path in the circuit (measured in the same direction) must be equal to zero.

That's plain wrong according to Faraday's Law. Kirchoff's Laws are strictly valid only for DC circuits. As soon as you have time-dependent magnetic fields they do not hold anymore. Faraday's Law says (in its local form)

$$\vec{\nabla} \times \vec{E}=-\partial_t \vec{B},$$

i.e., es soon as you have a time-varying magnetic field the electric field is not conserved anymore, and the "sum of the voltages" along the circuit is not 0. Of course "sum of the voltages" here means the integral along the closed circuit, and this value is according to the above equation the negative time derivative of the magnetic flux through any surface with the boundary given by this loop.

To make things easy, and I think that's also the case discussed in this thread, let's only discuss circuits without moving parts, i.e., in the following all surfaces and their boundaries are assumed to be at rest.

Now suppose, we have the most simple case of one resistor in a closed loop, and a volt meter measuring the voltage drop across that resistor. What we have then are effectively two loops, namely the resistor loop and the volt-meter loop of this parallel circuit. I assume a simple volt meter which I can treat as another resistor (of high resistance). Then we can use Faraday's Law for these two loops. Let's start with the resistor loop and integrate Faraday's Law over an arbitrary surface with a boundary given by this loop. The left-hand side can be taken as path integral along that path, using Stoke's Law. This gives

$$U_1=R i_1=-\dot{\Phi}_1$$,

where $$\Phi_1$$ is the magnetic flux through the surface. The integral is independent of the particular choice of this surface due to Faraday's Law. So there's no ambiguity here.

Now by the same argument we can integrate Faraday's Law across the area with the boundary given by the volt-meter loop, giving

$$-R i_1+R_V i_2=\dot{\Phi}_1+U_V=-\dot{\Phi}_2$$,

where $$R_V$$ is the resistance of the volt meter and $$U_V$$ the corresponding voltage. Thus, what you measure is

$$U_V=-\dot{\Phi}_1-\dot{\Phi}_2$$,

and of course the voltage, measured by the volt meter, depends on both fluxes, i.e., the volt-meter reading will change when the volt-meter loop is changed. [This result you can of course also get, if you integrate along the outer loop, containing only the volt meter as a resistance. The total magnetic flux is of course the sum of the fluxes through the resistor and the volt-meter loops.] If you want to measure the magnetic flux through the resistor loop alone, you not only have to make the resistance of the volt meter, $$R_{V} \gg R$$ (as would be sufficient for DC circuits) but also make sure that the magnetic flux through the volt-meter loop can be neglected (by either arranging it to be outside the relevant time-varying magnetic field or making it as small as possible).

This law is the equivalent of Maxwell's first equation, i.e. of Faraday's induction law. This equivalence, however, is not as directly evident as the relation between Kirchoff's current law and the conservation of charge. Indeed, the voltage law depends on how the branch voltages are defined in herms of the electromagnetic field. Although the concept of voltage has already been discussed in Sec. 6.8 in connection with inductive fields, it deserves some further, careful consideration in view of its key role in circuit theory.
To obtain a better feeling for what is involved in in the circuit concept of voltage, it is helpful to consider its definition from an experimental point of view. A little thought will make it obvious that all voltmeters are designed to measure the line intrgral of the electric field along the path formed by the connecting leads. This is evident in the case of electrostatic voltmeters whose operation depends directly on the forces exerted by the electric field. Other more common insturments measure actually the current through a resistor of known value; the current desnity in any such resistor is proportional, by Ohm's law, to the elctric field and, therefore the total current is proportional to the line integral of the electric field between the terminals of the resistor. On the other hand, there are implicit limitations on the use of voltmeters. For instance, nobody in his right mind would wrap the leads of a voltmeter around the core of a transformer in determining the voltage between two points in a circuit. Furthermore, it is understood that the leads of a voltmeter should be kept reasonably short and that little meaning should be attached to an indications which depends on the exact position of the leads. [YOUNGMAN, THIS IS YOUR EXPERIMENT]

This is the same thing with words as I derived for this most simple example above, but it's wrong to call this "voltage". A voltage is a difference of an electric potential. In the case of time-dependent fields, there is no electric potential. In this case, one must use not only a scalar but also a vector potential to describe the electromagnetic field, i.e.,

$$\vec{E}=-\vec{\nabla} \Phi-\frac{\partial}{\partial t} \vec{A}, \quad \vec{B}=\vec{\nabla} \times \vec{A}.$$

For a given electromagnetic field the electromagnetic potentials (relativistically the four-vector potential) is not unique but only determined up to a gauge transformation and have not a clear physical meaning except of giving the fields in a way such that the homogeneous Maxwell equations (i.e. Farday's Law and the absence of magnetic monopoles) is fulfilled, but that's not the point here.

In any case, if you have a time varying magnetic field, $$\vec{E}$$ is not a conserved vector field, which however is already clear from Faraday's Law in terms of the electromagnetic field itself, without using the potentials. "Voltage" thus doesn't make sense here. Of course sometimes, one calls $$L \frac{\mathrm{d} i}{\mathrm{d} t}$$ a "voltage", but that's at least misleading and precisely the reason for unnecessary confusion as in this thread. Prof. Lewin is right to stress this point as in http://ocw.mit.edu/courses/physics/...netism-spring-2002/lecture-notes/lecsup41.pdf (which has already been quoted in #9 of this thread).

These limitations on the use of voltmeters indicate that the voltage between two points has meaning only wjen the line integral of the electric field between two points is closely independent of the path of integration for all reasonably short paths. In mathematical terms, this amounts to saying that a voltage can be defined only between between points of a region in which there exists a scalar potential whose negative gradient is closely euqal to the electric field [VIOLATED BY PROFESSOR LEWIN'S EXPERIMENT]. Thus the concept of voltage in the presence of of time-varying currents is strictly an extension of the concept of voltage as defined in electrostatic systems; this extension is valid only when the path of integration used in the computation of the voltage is contained in a region of space in which the electric field behaves approximately as an electrostatic field."[THIS IS WHY A CIRCUIT HAS TO BE OF INFINITESIMAL SIZE;]

No, it's simply a wrong statement, as explained in detail above and in much more detail in the above quoted lecture note by Prof. Lewin. Volt meters simply have to be used in the right way to measure the very quantity you are interested in. Circuit theory can be used for any circuit as long as the quasistationary limit is applicable (i.e. as long as the typical wave length of the em. fields under consideration are much larger than the size of the circuit and thus Maxwell's displacement current can be neglected) and as long as all emf's from time-varying magnetic fluxes are taken into account properly.

 

[yungman]

Tell me whether I am wrong:

Sounds like a lot of physicist only talk about circuit that is physically there. It seems they really don't get the idea about using equivalent circuits. Equivalent circuit in this case is the induced emf in the loop can be represented by a voltage source or better yet, a differential voltage source ei. mini voltage source per unit length.

If people cannot comprehend this concept, they really have no place to talk circuit. They are going to bang their head on the wall when they deal with any physical circuits in microwave frequency.

People should really take a class in RF circuit design which is an extention of EM. I study both and I can tell you that the electrodynamics in physics class miss the whole thing on transmission lines where we deal with equivalent circuits. That a little section of transmission line can be made to behave like a capacitor or an inductor depend on the length of the section. That we can design all sort of filter network, impedance matching by just using sections of lines of different width and length that to physicist is only a line or worst yet only a note like Levine called point "A" and "D".

If this is how the physicist look at thing, I don't think they should even talk about this problem here. They need to study a few books in EM for engineering like "field and Wave Electromagnetic" by Cheng. There are detail theory about equivalent circuits.


A wire in microwave is equivalent to a series of inductors and capacitors. Induced voltage become a voltage source. Without these kind of knowledge, you really cannot talk about circuits. Sorry that circuits has to work in AC, not just DC. Don't tell me physicist sweep all these into "non conservative"! that would be really discouraging for me. I was planning to pursue advanced electrodynamics, but if this is what end up to be, I think I'd change my mind!


THis sum up my observation. Seem like We are talking in different languages and I think this seems to be the problem right here. That might be the reason why some people find it so hard to comprehend the induced voltage concept here. People that work in high speed microwave electronics look at this as cake walk! The non existing induced emf source really deliver power, those non existing capacitor really behaving like a cap that filter out high frequency and the non existing inductors really work as inductors. And these are all swept under " non conservative" behaviors?

 

[cabraham]

Tell me whether I am wrong:

Sounds like a lot of physicist only talk about circuit that is physically there. It seems they really don't get the idea about using equivalent circuits. Equivalent circuit in this case is the induced emf in the loop can be represented by a voltage source or better yet, a differential voltage source ei. mini voltage source per unit length.

If people cannot comprehend this concept, they really have no place to talk circuit. They are going to bang their head on the wall when they deal with any physical circuits in microwave frequency.People should really take a class in RF circuit design which is an extention of EM. I study both and I can tell you that the electrodynamics in physics class miss the whole thing on transmission lines where we deal with equivalent circuits. That a little section of transmission line can be made to behave like a capacitor or an inductor depend on the length of the section. That we can design all sort of filter network, impedance matching by just using sections of lines of different width and length that to physicist is only a line or worst yet only a note like Levine called point "A" and "D".If this is how the physicist look at thing, I don't think they should even talk about this problem here. They need to study a few books in EM for engineering like "field and Wave Electromagnetic" by Cheng. There are detail theory about equivalent circuits.


A wire in microwave is equivalent to a series of inductors and capacitors. Induced voltage become a voltage source. Without these kind of knowledge, you really cannot talk about circuits. Sorry that circuits has to work in AC, not just DC. Don't tell me physicist sweep all these into "non conservative"! that would be really discouraging for me. I was planning to pursue advanced electrodynamics, but if this is what end up to be, I think I'd change my mind!


THis sum up my observation. Seem like We are talking in different languages and I think this seems to be the problem right here. That might be the reason why some people find it so hard to comprehend the induced voltage concept here. People that work in high speed microwave electronics look at this as cake walk! The non existing induced emf source really deliver power, those non existing capacitor really behaving like a cap that filter out high frequency and the non existing inductors really work as inductors. And these are all swept under " non conservative" behaviors?

But this lecture by Dr. Lewin is from an undergraduate physics class. Transmission lines have not been covered at that point. So an undergrad probing a circuit where induction is happeneing will notice that the voltage summation around a loop does not always equal zero. Dr. Lewin is informing the students that it is perfectly normal to get a non-zero loop voltage summation when induction is taking place.

Regarding the equivalent circuit approach, I've already covered it. You may add the measured loop summation voltage to the equiv circuit as an independent voltage source. Then KVL holds. As far as "distributed emf sources" go, this is already covered in the Lorentz force law. The source that is giving rise to the non-zero loop emf is the external circuit generating the time varying fields. A portion of, or nearly all of the magnetic flux generated by the primary circuit links the secondary circuit. A transformer can serve as an example.

We can model the xfmr referring to either the primary or secondary. In this case we are viewing the secondary equiv circuit. The primary power source which drives the primary circuit generating the magnetic field, gets reflected to the secondary in accordance w/ the turns ratio & coupling coefficient. The secondary circuit undergoes induction, i.e. "non-conservative" E field, & a measurement of the loop emf summation will result in non-zero value.

But the equiv circuit ref secondary includes a voltage source which is really a reflection of the one driving the primary. As far as RF goes, & "distributed parameters", that is EE course material for junior & senior EE majors. An undergraduate physics class does not have the time to delve into RF/T-lines & distributed parameters. Dr. Lewin is correct that a loop voltage summation measurement will not be zero-valued when induction happens.

But distributed parameters like L, C, R, equiv emf sources, etc., is beyond the scope of said course. Dr. Lewin's lecture is not all encompassing, he is dealing w/ undergrads in elementary physics, many of them sophomores. Most will not major in EE, but ME, CE, ChE, physics, etc. Dr. Lewin gave them good info. Those majoring in EE will later learn about distributed parameters & t-line concepts.

The critics of Dr. Lewin are making too much ado over nothing. His thesis is correct. But now the focus has moved to RF & t-lines, which are too advanced & specialized for an undergrad general physics class. For such topics, the 2nd semester or third quarter of e/m fields is a good place to learn. Yungman, you are taking the view that a wire being an inductance, resistance, & capacitance, distributed per unit length, is some earth-shattering revelation nobody but you is aware of.

I learned that in e/m fields in the 70's & it was ancient news then! Sir Oliver Heaviside pretty much summed up t-lines in the 1870's, also the same decade Maxwell published his cornerstone equations. It is too well known to be giving us lectures.

Anything else that needs to be clarified?

Claude

 

[vanhees71]

It may well be that there are powerfull analyses techniques in EE to treat such problems for practical purposes. Physics is not about such techniques but about fundamental properties of nature, and there are Maxwell's equations for the fields and the Lorentz-force Law for the forces of em. fields on charged particles (let alone the self-force problem at this point, which makes things more complicated). I think the here considered experiments can be well explained and understood using only the very basic principles, i.e., Maxwell's equations. One doesn't need more advanced calculational tools of EE, which do not add to the understanding of the basic principles but are practical tools for more complicated problems. They are for sure not part of an introductory (or even advanced) EM lecture for physicists but for more specialized engineers.

 

[yungman]

It may well be that there are powerfull analyses techniques in EE to treat such problems for practical purposes. Physics is not about such techniques but about fundamental properties of nature, and there are Maxwell's equations for the fields and the Lorentz-force Law for the forces of em. fields on charged particles (let alone the self-force problem at this point, which makes things more complicated). I think the here considered experiments can be well explained and understood using only the very basic principles, i.e., Maxwell's equations. One doesn't need more advanced calculational tools of EE, which do not add to the understanding of the basic principles but are practical tools for more complicated problems. They are for sure not part of an introductory (or even advanced) EM lecture for physicists but for more specialized engineers.

It is not, the physical property of what I described about capacitor inductors is absolutely based on EM wave behavior in the transmission line media. The analogy is light wave in optics, I had some very limited knowledge, something like avoiding reflection using coating of quater wave thickness and make the medium thickness into half wavelength and put into another medium and it literally disappeared and that wave length because of the transformation.

It is not a special technique. the voltage induced into the loop of Levine's experiment is REAL! Physics is about dealing with real things and behavior, you cannot just disregard and chuck into " non conservative". This seems to be a big gapping hole in electrodynamics compare to electromagnetics studied in EE.

This happened to be a very easy circuit. I am going to draw up a multi pole filter used in microwave design only make up of sections of copper lines on the pcb. If Levine look at it, it is only a wire from point A to point B...or better yet, just a point C...a note. But this circuit PHYSICALLY IS a real filter that as effective as the real circuit components...In fact even more because the real physical cap is not a cap in RF! It is physically not a cap at RF! BECAUSE Physically, there is parasitic components inside the cap, the conductance of the dielect, inductance of a straight wire, skin effect due to EM attenuation in a conductor...Every bit of it is Electrodynamics and every bit of it is physics.

The most power tool in RF design is using the Smith Chart, which is based on EM wave behavior when the wave encounter a boundary and have reflection trabelling backwards. It is all electromagnetics, not a technique. They should really put this part into the physics electrodynamic class for the graduate level.

 

[vanhees71]

What is wrong with explaining the issue with Farday's Law (one of Maxwell's equations)? What was, in your opinion, wrong with this very simple explanation, I've given this morning?

I have not considered any capacitors, but that's also not a big deal with the there explaned technique of directly applying simply Maxwell's equations to simple circuits. So what's the problem to explain simple things in the most simple way and not simpler?

 

[Studiot]

I wonder what post#1000 will say in this thread?

Perhaps Danger will have a view.

 

[Andrew Mason]

Prof. Lewin mentions Lenz's Law but does he take it into account in his analysis of the circuit? I don't see where he does. Or perhaps I am missing something. He seems to be treating it as negligible and I think that is a big mistake.

Let's consider the situation where Lenz' Law is not a factor: no induced current. Suppose a very small switch is inserted at the bottom of the circuit and opened. The voltmeter on the left measures the potential from the left side of the open switch to the middle top of the circuit - the 100 ohm side - and the voltmeter on the right measures the potential from the middle top to the right side of the switch - the 900 ohm side. What would the voltmeters read when the solenoid is powered up?

Applying Faraday's law, the changing flux from that large solenoid induces an emf around the path of the resistance and wires + the open switch such that $\oint E\cdot dl = - d\phi/dt$. What would the voltmeters read? I would think the left one would read the same as the right one because the paths are the same length and the E field would be symmetrical between the sides. I don't see why the value of the resistance would affect the induced voltage since there is no current (switch open). The potential depends on the path length, not the value of the resistance.

Now suppose that the switch is closed and the experiment repeated. As soon as the magnetic field of the solenoid starts building up, an emf is induced in the circuit such that $emf = \oint E\cdot dl = -d\phi/dt$. Now the induced emf starts current flowing in the circuit. Suppose at time t very shortly after the solenoid current begins that total induced emf is 1 volt. The rate of change of that current is quite high at the beginning so there is a high back-emf (Lenz' law) opposing that increase in current so, while the induced voltage from the solenoid field at time t is 1 volt, the current is not 1/1000 A. = 1 mA. It is much less. The two voltages measured on the voltmeters cannot add up to 1 volt.

AM

 

[yungman]

Levine's circuit is as simple as it gets. Try this one.

I design this kind of circuits all the time. Top is the circuit in inductors and capacitors. It is a 6 pole low pass filter that can be design say to cut at 2 GHz. At 4GHz, it can be design to attenuate the signal to 1/20.

The bottom part is what I design the same filter with just the copper clad pattern on a circuit boards. Look just like a pattern! It is every bit as real as the circuit on top. My guess when Levine look at it, he'll be saying it's only a wire connected from A to B. Or better yet, it is a note "C"!

This design is not just an application. It is design according to electromagnetic of guided structure with forward and backward EM wave. Design is making use of boundary condition at B and use the mismatch reflection to manipulate the impedance at each point of the line. Everything is Electromagnetic in the books!

So these all chuck to "non conservative" again? Path dependent again?

Back to Levine, The induced emf is every bit a REAL voltage source. Try to convince someone that put the fingers across the terminals and wet his/her pants if you induce a high enough voltage into it! Ask whether that is real or not! How do physicist justify this, non conservative?

the example I gave is just a very simple circuit that is made of pure passive components. try some with active components and you'll see. So most of the advanced electronics is just non conservative?


I understand Lavine taught a beginer's class, but when he involked challenging professors in EE, he cross the line. He must have grapped the professor in DSP, AI ( artificial intel). those that don't know $#%t about RF design. matter of fact, a lot don't even know analog design!


You have to take into account of all the components, physical and equivlent! Or else, you really get stuck.

 

[stevenb]

Prof. Lewin mentions Lenz's Law but does he take it into account in his analysis of the circuit? I don't see where he does. Or perhaps I am missing something. He seems to be treating it as negligible and I think that is a big mistake.

Why would you say this without first doing an order of magnitude estimate to see if you are right? Assuming I'm interpreting your concern correctly, I think if you run the numbers, you'll see that it is not a big mistake to neglect this effect. There are probably about a 6 orders of magnitude buffer here.

For example, in the experiment I did and documented well, I estimate a loop self-inductance to be of the order of 0.1 microHenries. With this inductance value and a 1 V loop emf, the current change will initially be 10 megaAmps per second. So, how long does it take to get to 1 mA? It's on the order of 100 picoseconds. Now consider the circuit time constant (L/R) which is of the order of 100 picoseconds. So round this up to a nanosecond (1 GHz frequencies) and consider that the MIT old lab scopes are probably 10 MHz or maybe 100 MHz scopes. Will the scope even pick this up? And, even if it did, who cares since it's practically instantaneous for our purposes? The interesting effects are happening on the order of milliseconds, as clearly mentioned by Lewin in the video. With 6 orders of magnitude faster response time, we should be safe neglecting the effect.

 

[cabraham]

Can you show me a case of two parallel circuits do not have the same voltage across it. Please put in the equvalent voltage source also.

The transformer is such a case. A power source, ac constant voltage amplitude & frequency, sine wave, excites the primary of a xfmr. The secondary is connected to a heater load. The secondary output is 120V rms, & 10A rms. The secondary winding resistance is 0.1 ohm. At a full load of 10 amp, the voltage drop in the sec winding is Iload*Rsecwdg = 10A*0.1 ohm = 1.0V.

So if we place a voltmeter across the sec terminals, we read 119V rms. But what is the voltage across the same 2 points if the path is the copper secondary winding. Answer: 1.0V. So if we measure the sec terminal voltage outside the sec winding it is 119V rms, but inside the copper sec it is 1.0V rms.

Of course when analyzing in terms of equiv circuit, we can add the source. THe source is 120V rms, & 1.0V rms is dropped across the sec winding resistance, leaving 119V rms, which is what a VM connected across the sec terminals displays. KVL is aok when the source is added to the equiv circuit. I've said that 100 times.

But the voltage from a to b along the copper path is still 1.0V. By definition, J = sigma*E, & Vab = integral E*dl. The E field inside the conductor is very small, so that the line integral is also small, resulting in a small voltage. The 120V rms source is not present inside the copper. The sec winding insulation, however, is subjected to the full 120V stress divided by the number of turns.

Outside the sec copper winding, the 120V source is present, but not inside. Two parallel paths have differing potentials. Or look at it another way.

How is voltage defined? Is it not the work per unit charge transporting said charge from a to b? It is , of course. IF the external load resistor across the sec in 11.9 ohm, then transporting 10A (10 coulomb/second) through 11.9 ohms requires 119 joule/coulomb, which is 120V. But transporting the same 10A (the sec winding is in series w/ the load) through the 0.1 ohm sec winding requires 1.0 joule/coulomb = 1.0V rms.

It requires much more work per unit charge to transport said charge from a to b when the path is outside the sec copper winding, as opposed to inside. So here is a prime example of 2 paths in parallel w/ differing voltages.

Again, Dr. Lewin's style of teaching is not among my favorite. His methods of explaining things differ from mine. Hopefully you can understand what I've been explaining. BR.

Claude

 

[Studiot]

+3 Cabraham, very well put.

Which brings us nicely back to the point Maxwell clearly understood and made himself viz

The whole beauty of KVL, properly formulated, is that it allows us to completely sidestep the issue of what goes on inside a transformer, battery or indeed any source of EMF.

 

[yungman]

The transformer is such a case. A power source, ac constant voltage amplitude & frequency, sine wave, excites the primary of a xfmr. The secondary is connected to a heater load. The secondary output is 120V rms, & 10A rms. The secondary winding resistance is 0.1 ohm. At a full load of 10 amp, the voltage drop in the sec winding is Iload*Rsecwdg = 10A*0.1 ohm = 1.0V.

So if we place a voltmeter across the sec terminals, we read 119V rms. But what is the voltage across the same 2 points if the path is the copper secondary winding. Answer: 1.0V. So if we measure the sec terminal voltage outside the sec winding it is 119V rms, but inside the copper sec it is 1.0V rms.

Of course when analyzing in terms of equiv circuit, we can add the source. THe source is 120V rms, & 1.0V rms is dropped across the sec winding resistance, leaving 119V rms, which is what a VM connected across the sec terminals displays. KVL is aok when the source is added to the equiv circuit. I've said that 100 times.
That is not true, emf sources are distributed throughout the winding, say you have 120 turns in the secondary, each turn is only going to give you (1 - 1/120)V. Point is the voltage cannot be separated from the winding. You cannot measure as if 1V drop across the coil and 120 equivalent generator. That is the whole thing about distribution.
But the voltage from a to b along the copper path is still 1.0V. By definition, J = sigma*E, & Vab = integral E*dl. The E field inside the conductor is very small, so that the line integral is also small, resulting in a small voltage. The 120V rms source is not present inside the copper. The sec winding insulation, however, is subjected to the full 120V stress divided by the number of turns.

Outside the sec copper winding, the 120V source is present, but not inside. Two parallel paths have differing potentials. Or look at it another way.
There is no two parallel path, it is one path with infinite micro voltage source per dl.
How is voltage defined? Is it not the work per unit charge transporting said charge from a to b? It is , of course. IF the external load resistor across the sec in 11.9 ohm, then transporting 10A (10 coulomb/second) through 11.9 ohms requires 119 joule/coulomb, which is 120V. But transporting the same 10A (the sec winding is in series w/ the load) through the 0.1 ohm sec winding requires 1.0 joule/coulomb = 1.0V rms.

It requires much more work per unit charge to transport said charge from a to b when the path is outside the sec copper winding, as opposed to inside. So here is a prime example of 2 paths in parallel w/ differing voltages.

Again, Dr. Lewin's style of teaching is not among my favorite. His methods of explaining things differ from mine. Hopefully you can understand what I've been explaining. BR.

Claude

......

 

[yungman]

+3 Cabraham, very well put.

Which brings us nicely back to the point Maxwell clearly understood and made himself viz

The whole beauty of KVL, properly formulated, is that it allows us to completely sidestep the issue of what goes on inside a transformer, battery or indeed any source of EMF.

No you cannot. Show me how.

 

[yungman]

Guys, it is becoming clearer and clearer the difference between my issue with this whole thread vs a lot of you guys in the electrodynamic side is the existing of the voltage source or emf source. Please feel free to disagree with me and adress this directly, you don't have to be diplomatic. If I am wrong, I'll learn. I just don't see how you can ignor the existence of the induced voltage source and go through hoops to justify the non existence of a REAL voltage source.

Yes Maxwell's eq. have no provision for induced voltage source. BUT Maxwell's equations to a big extend are formed by observation. Just like in time varying case of $$\nabla \times \vec H$$ where the $$\frac {\partial \vec D}{\partial t}$$ needed to be added because $$\nabla \cdot \vec J = \frac {\partial \vec \rho_v}{\partial t}$$.

The secondary voltage of the transformer case by Cabraham is even more obvious. With multiple turn secondary, you cannot even measure the two paths and show different voltages like in Levine's experiment. The 1V drop is a theractical voltage, and cannot be measure by any known means because the voltage sources are distributed throughout the entire secondary. Levine uses a single turn transformer, at least you can play some games to measure the voltage of the two separate paths like what I did because the probe ground is a single turn also.

All Electromagnetics textbooks use equivalent voltage and components. How can electrodynamic accomadate all the electronic theories which is a big part of RF and analog world and we actually have to have two branches of EM!

 

[cabraham]

From yungman: "That is not true, emf sources are distributed throughout the winding, say you have 120 turns in the secondary, each turn is only going to give you (1 - 1/120)V. Point is the voltage cannot be separated from the winding. You cannot measure as if 1V drop across the coil and 120 equivalent generator. That is the whole thing about distribution."

I don't think so. How can there be distributed voltage sources inside the copper? Ohm's law must be met, i.e. J = sigma*E. Also, Faraday's Law holds inside as well as outside the wire. FL states that curl E = -dB/dt. So the E field in the wire which gives rise to a "distributed source of emf", must have curl to do so. In order to have a curly E field inside the wire, there must be a "dB/dt" inside the wire as well. For a perfect superconductor, B does not enter the wire. For an ordinary conductor, there is a small B field entering the wire.

The reason there is very little emf source inside the copper is because there is very little B field inside the CU, & hence very little rotational (curly) E field, & hence very little emf "source".

I find it most helpful to look at this in terms of Lorentz force. The xfmr core B field is accompanied by an E field, both sinusoidal. The E & B fields exert a force on the free electrons in the secondary Cu winding & the resistive heater which is the external load. There is 120V rms of emf acting on the circuit loop. But a volt is just a joule/coulomb, so there is 120 joules of energy expended transporting one coulomb of charge around the loop one time. OK?

The Cu sec winding & the heater have resistance. Energy is converted to heat per P = I^2*R. The 10A through the sec Cu, Rsec=0.1 ohm, results in 1.0 joules lost for every coulomb. The 10A through the 11.9 ohm heater results in 119 joules per coulomb. Thus the 120V loop emf is divided as follows. The voltage across the terminals a & b along the Cu path is 1.0V, & along the external heater path is 119V.

When drawing an equivalent circuit for computational purposes, it is perfectly fine to use a lumped parameter representation. A 120V source in series with the 0.1 ohm Cu sec resistance in series w/ the 11.9 ohm heater load serve to facilitate analysis. The right answer is obtained w/ this approach.

An equivalent circuit is by definition, mathematically precise enough for computational purposes. It is not always a 1 to 1 replica of the true physical phenomena. I cannot accept the "distributed source of emf" because there is little B field inside the Cu. The distributed sources of emf, infinitessimal in length have to exist on the outside of the Cu.

If I've erred feel free to show me where. But what I've stated has been known through observation & reaffirmation for over a century. To claim otherwise means that over a century of the best scientific minds using instruments have missed something a modern critic has perceived intuitively. I don't think so. The case for distributed emf sources inside the Cu is pretty weak, actually more like non-existant.

Claude

 

[yungman]

From yungman: "That is not true, emf sources are distributed throughout the winding, say you have 120 turns in the secondary, each turn is only going to give you (1 - 1/120)V. Point is the voltage cannot be separated from the winding. You cannot measure as if 1V drop across the coil and 120 equivalent generator. That is the whole thing about distribution."

I don't think so. How can there be distributed voltage sources inside the copper? Ohm's law must be met, i.e. J = sigma*E. Also, Faraday's Law holds inside as well as outside the wire. FL states that curl E = -dB/dt. So the E field in the wire which gives rise to a "distributed source of emf", must have curl to do so. In order to have a curly E field inside the wire, there must be a "dB/dt" inside the wire as well. For a perfect superconductor, B does not enter the wire. For an ordinary conductor, there is a small B field entering the wire.

The reason there is very little emf source inside the copper is because there is very little B field inside the CU, & hence very little rotational (curly) E field, & hence very little emf "source".

I find it most helpful to look at this in terms of Lorentz force. The xfmr core B field is accompanied by an E field, both sinusoidal. The E & B fields exert a force on the free electrons in the secondary Cu winding & the resistive heater which is the external load. There is 120V rms of emf acting on the circuit loop. But a volt is just a joule/coulomb, so there is 120 joules of energy expended transporting one coulomb of charge around the loop one time. OK?

The Cu sec winding & the heater have resistance. Energy is converted to heat per P = I^2*R. The 10A through the sec Cu, Rsec=0.1 ohm, results in 1.0 joules lost for every coulomb. The 10A through the 11.9 ohm heater results in 119 joules per coulomb. Thus the 120V loop emf is divided as follows. The voltage across the terminals a & b along the Cu path is 1.0V, & along the external heater path is 119V.

When drawing an equivalent circuit for computational purposes, it is perfectly fine to use a lumped parameter representation. A 120V source in series with the 0.1 ohm Cu sec resistance in series w/ the 11.9 ohm heater load serve to facilitate analysis. The right answer is obtained w/ this approach.

An equivalent circuit is by definition, mathematically precise enough for computational purposes. It is not always a 1 to 1 replica of the true physical phenomena. I cannot accept the "distributed source of emf" because there is little B field inside the Cu. The distributed sources of emf, infinitessimal in length have to exist on the outside of the Cu.

If I've erred feel free to show me where. But what I've stated has been known through observation & reaffirmation for over a century. To claim otherwise means that over a century of the best scientific minds using instruments have missed something a modern critic has perceived intuitively. I don't think so. The case for distributed emf sources inside the Cu is pretty weak, actually more like non-existant.

Claude

Thanks for taking the time. I see your rationel on the voltage source cannot be inside because curl E is small inside the copper wire if $\frac{\partial \vec B}{\partial t}$is small in good conductor.

But where is the voltage come from? Len's law is not about current only, it is a physical voltage because of all the formulas on voltage ratio regardless of load. That is my whole thing about this whole thread. Where is the voltage come from? It is sure not at the end of the wire between the heater load and the secondary winding. The fact that you can physically meansure continuous incrememtal increase of voltage along the secondary winding, that has to show some voltage source along the wire. How does Maxwell's equation justify this voltage?

I think this is the bottom line my disaggrement with Levine and some of the people here. How do you account for the voltage? Took me a long time to even realize you guys don't do voltage! No wonder we are talking in different language! Levine only has one turn secondary that make measurement along the loop difficult as proofen from my experiment. The example you gave about the secondary of the transformer make it very very easy to physically measure the voltage along the winding. I actually have a Marklin train set that has a transformer supply and the speed is adjusted by physically sweeping on the surface of the secondary winding. That is also how the variac work.

It's is so clear that there is a voltage source in Levine's case and your transformer case and there is no way to take it out or ignor it. I truly don't care about the definition of KVL or conservative and all. It is the voltage! It would be nice it you can explain this to me.

Thanks

Alan

 

[Antiphon]

Folks, I'm trying my level best to stay out of this thread but like Michael Corleone in Godfather 3, I feel I am being pulled back in.

Let's clarify something right from the start. There is electromagnetics which has E, H and J (current density). This is physics.

Then there is a whole 'nother field of study called circuit analysis. In this discipline there are no electric and magnetic fields. There is electric current I and voltage V.

In this discipline KVL has been defined as the sum of potentials around a loop adding to zero. This is an axiomatic definition of KVL *in circuit theory*. It is NOT physics.

*Whenever* a field of any kind is discussed in relation to a circuit, it is a physics problem, not a problem in circuit theory.

EE professors do things that physicists do not do in order to arrive at self-consistent useful theories like circuit theory that are NOT physics.

Every day EEs design power supplies using ideal transformers shunted by inductors. No physicist would ever think to connect a battery to an ideal transformer and get stepped up DC to come out the secondary. But this is what a transformer *is* in circuit analysis. A EE shunts this DC-capable transformer with an inductor to arrive at a description of what a more realistic transformer does. This isn't even close to the correct physics but it's what you do to design a transformer.

When physicists in this forum talk about the obvious flaw of leaving out induction from the KVL, it simply means they aren't familiar with modern circuit theory as practiced by the circuit professionals, Electrical Engineers.

Now, professor Lewin: he invoked the KVL of circuit theory then switched over to physics to make a point with the students. His physics and teaching style are wonderful. It's just that there is an Electrical Engineering KVL which has no fields and no induction, and there is physics with induction and potententials.

That's all.