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

[Phrak]

I think, DaleSpam has lent clarity to all this, and he would be worth re-reading. Apply Faraday's law with Maxwell's correction and you should have a classically indisputable form of Kirchhoff's voltage law.

Now, I don't know what situation you are referring to. There are a lot of posts!

Take an inductor with a small number of turns like one turn around a high permeability material, to make things evident. How many rounds your meter probes make through the core determines the voltage measured.

 

[sarumonkee]

I think, DaleSpam has lent clarity to all this, and he would be worth re-reading. Apply Faraday's law with Maxwell's correction and you should have a classically indisputable form of Kirchhoff's laws.

Now, I don't know what situation you are referring to. There are a lot of posts!

Take an inductor with a small number of turns like one turn around a high permeability material, to make things evident. How many rounds your meter probes make through the core determines the voltage measured.

Are you referring to a current measurement? The point of Prof. Lewin's experiment was not about voltmeter measuring errors, it was to supposedly show measuring across different points of two "nodes" can give you different voltages. I don't think they were actually "nodes" as inductance was not included.

 

[atyy]

Are you referring to a current measurement? The point of Prof. Lewin's experiment was not about voltmeter measuring errors, it was to supposedly show measuring across different points of two "nodes" can give you different voltages. I don't think they were actually "nodes" as inductance was not included.

So you want to know if the voltmeters were connected at exactly the same two points?

 

[sarumonkee]

@atyy: Yes, that's what I want to know. He didn't really go into detail about his setup, and from the look of the video, the probes were separated by about 4" on both sides of the circuit of wire and resistors. From my experience, that kind of layout can lead to some inductances that matter in switching situations.

If the probes were actually touching each other, I rescind all my previous comments, and will probably go read an E&M book from cover to cover.

 

[stevenb]

So you want to know if the voltmeters were connected at exactly the same two points?

I hope that is not the point of his confusion because it's clear that the scopes are effectively tied to the same point, and such a small inductance is irrelevant on these time scales. You can take the same voltmeter or scope, pick it up, move it to the other side and the reading will change. You could swap the meters and their reading would also swap.

If the OP is in doubt of this, then he needs to do his own experiments and re-study Faraday's Law. This is all straightforward stuff. The meter probes themselves form an additional loop that is closed through the meter's internal resistance. The fact that the resistance is very high and the current in the probe wires is low has no affect on Faraday's Law. When the meter is moved, the loops change their encirclements of the internal flux change.

This is exactly the thing that makes the experiment non-intuitive to the uneducated and the educated alike.

 

[stevenb]

If the probes were actually touching each other, I rescind all my previous comments, and will probably go read an E&M book from cover to cover.

OK, this is the issue then. Definitely restudy Faraday's Law, but more importantly do your own experiments. You need to see it to believe it. These experiments are really fun actually. You don't really need to do his exact experiment to get a feel for Faraday's law. You can wire up a large coil and drive it with triangle waves of current. Then make loops and take measurements.

The funny thing is that you can do these experiments and show them to your friends, and many will still think it's a trick of some type.

 

[atyy]

@sarumonkee: I see. Lewin's experiment was just for a lecture, not to convince a skeptic, so yes, his experiment was not done totally properly. However, if his errors were significant, his results should be different from what his calculations predict using Faraday's law in the big loop as the major effect (he predicts that the ratio of the voltmeter readings should be related to the ratio of the resistances). I haven't watched enough to know whether he got what he predicted.

Anyway, I agree with stevenb - go and do the experiment yourself - unless some kind soul or Lewin himself would be so kind as to redo it and post it here.

 

[hikaru1221]

I look at the wire as a Voltage source induced by the magnetic field. If you consider the voltage source in the loop, KVL held.

I'm not arguing with you about KVL. It's about what you are trying to say, that his experiment & his explanation are all a fraud. Would you kindly show me quantitatively that the transformer effect has that gravity to refute Prof. Lewin's explanation?

If I hold a PP3 battery in my hand there is EMF, but no magnetic flux and therefore Faraday's Law is not applicable.

There is, of course, no circuit at this stage either.

If I now connect two identical batteries ( or carefully adjusted power supplies) in opposition in a circuit, perhaps including resistance, there is still no magnetic flux as there is no current.
Kirchoff's law can be applied to this situation as we can sum the opposing EMFs meaningfully.

Sorry, I didn't see your post when I posted.
When Faraday deduced his empirical law, he did experiments with closed loops. The Faraday's law we have referred to so far is also in his integral form. This is why we cannot apply Faraday's law for an open circuit, because the law only applies to closed circuit. But KVL is also not applicable.
Now for your example of 2 oppositely-connected batteries, both Faraday's law and KVL apply:
_ KVL: - e + e + e_{B}= IR where e_B is the emf due to the magnetic flux change, which is zero.
_ Faraday's law: - e + e + IR = \oint Edl = -d\phi/dt = 0

Hey Hikaru, I think the wire is important as if we look at the impedance of an inductor (which totally exists, (at least Yungman and I know exists), we have s*L. The s is proportional to frequency, and a step function (switch turning on), has some high frequency components in it. This means the inductance of the line could act like a pretty big impedance at higher frequencies.

I want Prof. Lewin to show two more volt meters, one going from both probes of the first two meters on the "D" "node" and another between the "A" "node" points. I put "node" in quotes because I believe his circuit model is flawed, as Yungman has stated (missing inductance).

This is why I asked for a qualitative explanation. Inductance exists everywhere. It's just that whether it's significant enough.

 

[yungman]

How much voltage you measure across an inductor depends upon how you route the probe wires. Does this help confuse things?

There is always a way, without thinking deeply, one can run a second set of wire closely tie to the original wire loop and serve as the loop to pickup what ever voltage generated by the magnetic field and do a common cancellation. Yes it would involve some thinking, but it is absolutely doable. I am less interested in making the experiment than to challenge the experiment. Point is there is a way to cancel the magnetic effect on the probe that hook onto the two end of the wire and I am sure it is not hard, nothing more than breadboard a differential amp or play with the meter connections.

 

[yungman]

Well, it doesn't actually apply in this situation, I think. Maybe specify a little more if I missed you point please. The voltmeter (an O-scope in this case) has a huge resistance, probably in the range of 10MΩ), so the current in the voltmeter probe wires will be small. This means the volt meter probe wires hopefully won't pick up too much EMI compared to his circuit of wire and resistors.

If you have the two probs of the meter connect one onto one end of the wire loop, you form a secondary loop which is from say probe E to one end of the wire, then to probe F which connect to the meter and back to probe E through whatever internal resistance of the meter. That can pickup the magnetic field from the setup. It become a one turn transformer also!

As I say, using the technique of common mode cancellation would be an easy to solve this problem.

Another simpler way that might or might not be good enough, use a twist pair to connect the meter. One side of the twisted pair solder to one end of the wire loop in the setup, the other wire twist onto the wire from where the first twisted wire solder on, follow the wire of the setup to the other end before soldering on the the wire loop. What I am doing is to minimumize the loop area of the probe. The smaller the loop area, the less magnetic flux pass through, the error might be small enough to be acceptable. But the common mode cancellation is the way to go if you want accurate measurement.

 

[yungman]

I'm not arguing with you about KVL. It's about what you are trying to say, that his experiment & his explanation are all a fraud. Would you kindly show me quantitatively that the transformer effect has that gravity to refute Prof. Lewin's explanation?

I don't know what quantitively to show, it is a simple one turn secondary winding transformer! Say he generate the magnetic field with a source ( solenoid or what not), the one turn loop just pickup the magnetic field to generate the current. The professor did say he just monitor the voltage across the resistors and adjust the strength of the mag field to get the right voltage across the resistors. All you have to do is to consider the secondary winding of the transformer ( in this case is the wire loop that connect the two resistors ). In this case, I think the secondary ( loop wire ) generate exactly 1V to drive 1mA through the two resistors and the result observation shown in his experiment.

Concept is nothing more than a simple transformer. I cannot do any math here because I don't know his setup, which govern the coupling between the primary ( magnetic field generator ) and the secondary ( the wire with resistors).

As I said, in transformer, we can get about 6V per turn, get 1V on the wire loop in his setup is not even close to pushing anything.

BTW, after I think more about it, the inductance effect is not that important, I actually did a calculation with 24 gauge wire and calculate the inductance, it amount to only a few ohms at 1 giga hz. It is really the transformer effect that when a magnetic field pass through the loop, current generated, but it is consider as a voltage source. The professor just adjust the mag field the get 1V out of the loop to show the class. Below is the calculation of the inductance and the impedence:

I did some digging. say the wire is 24 gauge, the diameter is 2.032X10ee-4 m. Assume is copper \sigma=64.516X10^6\Omega^{-1}m^{-1}.

L= \frac {l}{\sigma \pi r^2} \frac{r}{4\pi f}\sqrt{\pi f \mu_0 \sigma}

\Rightarrow Z_L= j 2\pi f L \;=\; \frac {l}{2\sigma \pi r^2} \sqrt{\pi f \mu_0 \sigma} \;=\; \frac{l\sqrt{\mu_0} \sqrt{f}} {2r\sqrt{\pi\sigma}}

For 1 meter:

Z_L\;=\; \frac{\sqrt{4\pi X 10^{-7}} \sqrt{f}} {2X2.032X10^{-4} \sqrt{3.14X 64.516X10^6}} \;=\; 1.94X10^{-4} \sqrt f

So you see the impedence at reasonable freq is very low to be a factor in this experiment.

 

[Studiot]

Hikaru, thank you for being the only respondant to have the courage to post and answer to my question.


So did Farady state his law in 'Integral Form'


I think that what is happening here is that a non original form of Faraday's Law is being compared with a non original form of KVL. By non original I mean extended in the light of more modern knowledge.

 

[stevenb]

But the common mode cancellation is the way to go if you want accurate measurement.

This experiment has little to do with needing to make accurate measurements. The voltage readings from each meter are different by almost a factor of ten. You don't need much accuracy to show that there is a difference in the readings.

You are complaining about the routing of the meter leads, but this is exactly the point of the experiment. With nonconservative fields, voltage can't be defined without reference to a defined path. The meter placement and clearly shown lead paths define the measurement.

You're basically missing the whole point and making accusations needlessly.

 

[sarumonkee]

I hope that is not the point of his confusion because it's clear that the scopes are effectively tied to the same point, and such a small inductance is irrelevant on these time scales. You can take the same voltmeter or scope, pick it up, move it to the other side and the reading will change. You could swap the meters and their reading would also swap.

@ stevenb: look at the video part 2 at around 5:23. Freeze the video and look at his setup. The probes are NOT "effectively" connected to the same point. There is about 4-6" of wire on the secondary loop with the resistors on it. That means inductance to me. Your claim of moving the scope to the other side befuddles me, because the ENTIRE point of prof. Lewins lecture is not about the how to measure this system, but that across each resistor, a different voltage occurs, which I agree with.

Think of it this way: If 1mA amp is induced in the system, OF COURSE (as he puts it) there will be a -0.1V drop on the 100 Ω res, and 0.9V drop on the 900 Ω res. Now, if we simplify the system by saying "node A" is actually "effectively" the same point, we know have 1 V drop across "node D", a supposedly 0 Ω line (by Lewin's model). That means Lewin also denies that Ohm's Law applies in this situation, because that would mean infinite energy.

Ohm's law is hard to dispute, because this is more of a definition than a theory. Therefore, I contend we have a breakdown of his model.

Conversely, since you (stevenb) seem to be very sure of your answer (I am not 100% sure of mine, that's why I asked the question, and would like to learn), can you tell me how the energy got into the system from the main coil to his resistor circuit? Does it not involve inductance? I don't know of any case where you can couple energy like this without some kind of coupled inductor setup.

 

[atyy]

Does it not involve inductance? I don't know of any case where you can couple energy like this without some kind of coupled inductor setup.

Yes, it involves inductance, of the central big loop. That is the point.

But the same point is that that inductance will cause the voltmeters to read differently, even if they are connected to exactly the same two points.

There is some error due to the voltmeters not connected to exactly the same two points, and those little bits of resistance and inductance in principle count - but they are much smaller that the inductance of the central big loop.

 

[stevenb]

The probes are NOT "effectively" connected to the same point. There is about 4-6" of wire on the secondary loop with the resistors on it. That means inductance to me.

My point is that this 4-6 inch length of wire has such small resistance and inductance that the probes ARE effectively connected to the same point. That was the intent of my inserting the word "effectively". As you know, we often take different positions along a wire to imply the same nodal point. You are correct to point out that this can sometimes lead to erroneous measurements. I'm sure that if you do a careful enough measurement you could identify the effects of both resistance and inductance of the wire. But, in physics and engineering we try to develop the art of estimating orders of magnitude and understanding what effects are significant and which are not. The Prof. has set up an experiment that creates such a large disparity (0.1 V versus 0.9 V) that the gross behavior he wants to identify won't be masked out by these smaller effects.

Your claim of moving the scope to the other side befuddles me, because the ENTIRE point of prof. Lewins lecture is not about the how to measure this system, but that across each resistor, a different voltage occurs, which I agree with.

I didn't mean to create confusion. My main motive in mentioning the moving of the meter (how's that for an unintended alliteration! ) is to stress the point that the connection point of the meter at the nodes is not critical in this experiment. What matters is the location of the meter and the routing of the leads.

I think his point is that the voltage across each resistor is not well defined without a simultaneous definition of path for the measurement. It's clear that current times resistance (potential) is different on both resistors. However, if you try to measure that potential, you will get different readings of voltage depending on the path. The measurement that actually correctly indicates the potential is the one where the leads and meter do not encircle the flux change. Imagine if you were doing an experiment and did not know the flux change was there. You would start pulling your hair out because the voltage reading would change drastically when you move the leads. Of course, this can happen (and often does happen) in real modern circuit measurements, particularly when designing and testing switching power supplies.

Think of it this way: If 1mA amp is induced in the system, OF COURSE (as he puts it) there will be a -0.1V drop on the 100 Ω res, and 0.9V drop on the 900 Ω res. Now, if we simplify the system by saying "node A" is actually "effectively" the same point, we know have 1 V drop across "node D", a supposedly 0 Ω line (by Lewin's model). That means Lewin also denies that Ohm's Law applies in this situation, because that would mean infinite energy.

I'm not sure I'm understanding you here, but it seems to me that you are not grasping the concept of nonconservative fields, and the fact that both resistors can tie to the same nodes with different potentials. This seems counter-intuitive because we are trained to expect the potential across two nodes to be the same, but in this case they are not the same. The model of a 0 ohm connection, even if unrealistic, is perfectly acceptable as an approximation in this case. It helps reveal the physics, just as we often ignore friction to help teach physics principles in mechanics problems.

Ohm's law is hard to dispute, because this is more of a definition than a theory. Therefore, I contend we have a breakdown of his model.

Anyone can break down anyone else's model because no model is perfect. The only question is whether his model is good enough. I believe that it is because when I check his detailed analysis and explanation it agrees with his scope readings. I'm also giving him and his helpers the benefit of any doubt and assuming they are smart enough to check out all these things you are worried about. This is all stuff that is well known by people with experience. I don't see any red flags or smoking guns and the end result makes sense once you think about it.

Conversely, since you (stevenb) seem to be very sure of your answer (I am not 100% sure of mine, that's why I asked the question, and would like to learn), can you tell me how the energy got into the system from the main coil to his resistor circuit? Does it not involve inductance? I don't know of any case where you can couple energy like this without some kind of coupled inductor setup.

The energy conversion is through induction, as described by Faraday's Law. Whether you think of this as an inductor, a transformer or a generator is not the main issue. But, this inductance effect (if you like to call it that) is unrelated to the parasitic inductance of the wire itself. The small inductance and resistance of the wire just don't enter into the physics in a significant way, in this experiment and analysis. For this reason you can swap the locations where the two scopes tie into the nodes. You can also move the connection points anywhere along this few inch length you are concerned about. You can also physically pick up one meter and move it to the other meter's location and then both meters would read about the same.

 

[atyy]

Impressive.

Want to try assonance next?

 

[yungman]

This experiment has little to do with needing to make accurate measurements. The voltage readings from each meter are different by almost a factor of ten. You don't need much accuracy to show that there is a difference in the readings.

You are complaining about the routing of the meter leads, but this is exactly the point of the experiment. With nonconservative fields, voltage can't be defined without reference to a defined path. The meter placement and clearly shown lead paths define the measurement.

You're basically missing the whole point and making accusations needlessly.

I think you are missing the point of the transformer effect and I hope you see from the professor's drawing the wires and the two resistors form a loop. I never challenge the measurement of the two resistors, I challenge the fact he ignore the measurement of the wires. There is voltage develop across the two end of the wire due to the transformer effect because it is a loop. I hope you understand transformer even if it is a single turn loop like in this case. If you have a way to measure the voltage across the wires that connect the two resistors, you will find you voltage.

I have no easy way to draw a schematic here, maybe it is too confusing to describe in words. I claim the wires that connect the two resistors serve as the secondary winding of a transformer and generate 1V that create the 0.1 and 0.9V on those two resistors. And that is what the professor missed.

There is nothing wrong with his non conservative stuff, he just miss the voltage source from the transformer. You read through my long description about how we can generate about 6V per single turn of the transformer? Measuring at different points of the 4" to 6" wire like you described is like tapping at different position of the transformer winding!

 

[yungman]

My point is that this 4-6 inch length of wire has such small resistance and inductance that the probes ARE effectively connected to the same point. That was the intent of my inserting the work "effectively". As you know, we often take different positions along a wire to imply the same nodal point. You are correct to point out that this can sometimes lead to erroneous measurements. I'm sure that if you do a careful enough measurement you could identify the effects of both resistance and inductance of the wire. But, in physics and engineering we try to develop the art of estimating orders of magnitude and understanding what effects are significant and which are not. The Prof. has set up an experiment that creates such a large disparity (0.1 V versus 0.9 V) that the gross behavior he wants to identify won't be masked out by these smaller effects.
Inductance is very small, but the transformer effect is big. You ever seen transformer that have two output taps only half turn apart on the winding? I did, I worked in a company called Aydin Energy Div. in 1979 that wind huge custom transformers for enectrical companies, the winder was joking and told what is this about two taps within half a turn and showed me.

4 to 6" of line is not short, if it is on a mini transformer, 6" is 5 to 6 turns on the winding, that is a lot of volts! You look at the turn, not the length.


I didn't mean to create confusion. My main motive in mentioning the moving of the meter (how's that for an unintended alliteration! ) is to stress the point that the connection point of the meter at the nodes is not critical in this experiment. What matters is the location of the meter and the routing of the leads.

I think his point is that the voltage across each resistor is not well defined without a simultaneous definition of path for the measurement. It's clear that current times resistance (potential) is different on both resistors. However, if you try to measure that potential, you will get different readings of voltage depending on the path. The measurement that actually correctly indicates the potential is the one where the leads and meter do not encircle the flux change. Imagine if you were doing an experiment and did not know the flux change was there. You would start pulling your hair out because the voltage reading would change drastically when you move the leads. Of course, this can happen (and often does happen) in real modern circuit measurements, particularly when designing and testing switching power supplies.



I'm not sure I'm understanding you here, but it seems to me that you are not grasping the concept of nonconservative fields, and the fact that both resistors can tie to the same nodes with different potentials. This seems counter-intuitive because we are trained to expect the potential across two nodes to be the same, but in this case they are not the same. The model of a 0 ohm connection, even if unrealistic, is perfectly acceptable as an approximation in this case. It helps reveal the physics, just as we often ignore friction to help teach physics principles in mechanics problems.



Anyone can break down anyone else's model because no model is perfect. The only question is whether his model is good enough. I believe that it is because when I check his detailed analysis and explanation it agrees with his scope readings. I'm also giving him and his helpers the benefit of any doubt and assuming they are smart enough to check out all these things you are worried about. This is all stuff that is well known by people with experience. I don't see any red flags or smoking guns and the end result makes sense once you think about it.



The energy conversion is through induction, as described by Faraday's Law. Whether you think of this as an inductor, a transformer or a generator is not the main issue. But, this inductance effect (if you like to call it that) is unrelated to the parasitic inductance of the wire itself. The small inductance and resistance of the wire just don't enter into the physics in a significant way, in this experiment and analysis. For this reason you can swap the locations where the two scopes tie into the nodes. You can also move the connection points anywhere along this few inch length you are concerned about. You can also physically pick up one meter and move it to the other meter's location and then both meters would read about the same.

......

 

[stevenb]

I think you are missing the point of the transformer effect ...

... I claim the wires that connect the two resistors serve as the secondary winding of a transformer and generate 1V that create the 0.1 and 0.9V on those two resistors. And that is what the professor missed ... he just miss the voltage source from the transformer.

... You read through my long description about how we can generate about 6V per single turn of the transformer? Measuring at different points of the 4" to 6" wire like you described is like tapping at different position of the transformer winding!

I'm not sure why you would say that I and the Professor have missed the "transformer effect". This effect is the source of the EMF that drives current in the loop. The main difference between this situation and a real transformer is that one does not usually put two large resistors in the loop winding of a transformer. Certainly the transformers you took measurements on were not built like this. But, this is a side issue.

The professor goes through a process of setting up the problem. First he describes the case with a 1 V battery in the loop, and then he erases the battery cell and uses changing flux in the center of the loop to replace the 1 V EMF. How can you say "he just miss the voltage source of the transformer"? He didn't miss it at all.

Faraday's Law in integral form just tells you that the 1V EMF exists somewhere in the loop. It doesn't specify where it is in the loop. Typically, a transformer is tapped to change the number of loops is the circuit, not to somehow tap a section of one loop. The details of what happens when tapping one loop need to be considered more carefully, as has been done in the provided analysis. In this case we know where the potential drops are (we can measure them with a meter that does not encircle the flux change) and we see that it adds up to 1V around the main loop. There is very little potential drop across the wires themselves. The transformer EMF in the main loop is 1V, so all is well with Faraday's Law. Also, all is well with the classical definition of KVL (given by Maxwell). Obviously, the version KVL that says the sum of potential drops is zero is violated, which makes the professor jump up and down and denounce his physics books for spouting bad physics.

In doing the proper measurement for potential on each resistor, you trace a path (through the meter and the resistor) that does not encircle the flux change and this tells you which resistor potential you are actually measuring. FL and KVL (both versions of KVL, mind you) work here. The Professor also reveals that if you consider the path through the other resistor, you see an apparent contradiction. You end up tracing a loop through the other resistor that encircles the flux change and you are not really measuring the potential on that resistor. Faraday's Law still works through that other path, and the classical definition of KVL also works, but the other definition of KVL fails yet again.

Since the professor is not actually acknowledging the classical definition of KVL, we can just ignore that aspect, and conclude that everything he is saying is correct. The results do not depend (other than small parasitic changes) on where you tap the node along the wire, but they do depend on how you route the leads of the meter. If we had the experiment in front of us, there would be a very simple way to prove this. Simply move the exact point where you tie into the nodes and see if the measurements change. It is my contention that they will not change very significantly. Anyone who doubts this should just do the experiment and convince themselves. Do you really think the people who set up this experiment would go through all this trouble, and then not verify this straightforward thing? You really think MIT people can miss a factor of ten in this way? That's hardly proof, but experiments are proof. I've done similar experiments in the past as part of my work. I can't ask anyone to accept my word, and if others don't want to accept the professor's capability, then just do the experiment.

 

[atyy]

You really think MIT people can miss a factor of ten in this way?

I do. (It's only MIT, not Caltech.) But they didn't in this case.

 

[stevenb]

I do. (It's only MIT, not Caltech.) But they didn't in this case.

Good one!

Of course appeal to authority is not a good argument, but it's important to look at qualifications and evidence of due dilligence, as part of a debate like this. There seems to be enough horse power behind the experiment, and analysis to suggest that claims of fraud should be backed by a detailed analysis and/or a documented experiment, rather than vague hand-waving type arguments about parasitic inductance and transformer tapping.

 

[cabraham]

@ stevenb: look at the video part 2 at around 5:23. Freeze the video and look at his setup. The probes are NOT "effectively" connected to the same point. There is about 4-6" of wire on the secondary loop with the resistors on it. That means inductance to me. Your claim of moving the scope to the other side befuddles me, because the ENTIRE point of prof. Lewins lecture is not about the how to measure this system, but that across each resistor, a different voltage occurs, which I agree with.

Think of it this way: If 1mA amp is induced in the system, OF COURSE (as he puts it) there will be a -0.1V drop on the 100 Ω res, and 0.9V drop on the 900 Ω res. Now, if we simplify the system by saying "node A" is actually "effectively" the same point, we know have 1 V drop across "node D", a supposedly 0 Ω line (by Lewin's model). That means Lewin also denies that Ohm's Law applies in this situation, because that would mean infinite energy.
Ohm's law is hard to dispute, because this is more of a definition than a theory. Therefore, I contend we have a breakdown of his model.

Conversely, since you (stevenb) seem to be very sure of your answer (I am not 100% sure of mine, that's why I asked the question, and would like to learn), can you tell me how the energy got into the system from the main coil to his resistor circuit? Does it not involve inductance? I don't know of any case where you can couple energy like this without some kind of coupled inductor setup.

Honestly, I don't know where to begin. Ohm's law is in effect, & Dr. Lewin has not denied Ohm at all. You keep wanting to account for that extra volt of missing potential. If 2 points are connected by a short, then there is 0 volts if measured through the wire. If the wire loop is superconducting, then J = sigma*E, or E = rho*J. For rho=0, J= finite, then E=0. But v = integral E*dl, so v=0.

Of course, along differing paths outside the interior of the wire, results may vary. The potential from A to D is undefined unless a specific path is chosen. Vad is -0.1V along one path, & it is +0.9V along another path. The law of energy conservation always holds. If we compute the I^2*R loss converted to heat, it will never exceed the power in the mag field.

The product of the induced current & voltage is power. This induced power is less than or equal to the incident power on the loop in the mag field. If R is reduced power cannot increase w/o limit. A smaller R results in more induced current, which results in a larger mag field due to self inductance of the loop. The induced current has an associated mag field around the wire which opposes the external mag fiels per the law of Lenz.

Thus the induced I & V are subject to the laws of Lenz, Ohm, Faraday, Ampere, & conservation of energy. No paradox is present at all. Dr. Lewin's methods of demonstration differ from mine. I would explain it a bit differently. I understand his point & agree with him, as he is spot on re science. I would however, refrain from calling KVL "a joke". KVL, like all other laws, is defined under limited conditions, not universal conditions.

Since KVL is not taught as universal, I would reiterate KVL for what it is. It is valid w/ conservative fields. With non-con fields, it does not always hold, but can under specific conditions. Dr. Lewin has no contradictions w/ science. I would only offer him constructive criticism on the way he presents the material.

I've worked w/ magnetics for decades, & I understand what Dr. Lewin is saying, but I can see how an e/m novice could get blind sided by said material. Comments are welcome.

Claude

 

[yungman]

I'm not sure why you would say that I and the Professor have missed the "transformer effect". This effect is the source of the EMF that drives current in the loop. The main difference between this situation and a real transformer is that one does not usually put two large resistors in the loop winding of a transformer. Certainly the transformers you took measurements on were not built like this. But, this is a side issue.

The professor goes through a process of setting up the problem. First he describes the case with a 1 V battery in the loop, and then he erases the battery cell and uses changing flux in the center of the loop to replace the 1 V EMF. How can you say "he just miss the voltage source of the transformer"? He didn't miss it at all.

Faraday's Law in integral form just tells you that the 1V EMF exists somewhere in the loop. It doesn't specify where it is in the loop. Typically, a transformer is tapped to change the number of loops is the circuit, not to somehow tap a section of one loop. The details of what happens when tapping one loop need to be considered more carefully, as has been done in the provided analysis. In this case we know where the potential drops are (we can measure them with a meter that does not encircle the flux change) and we see that it adds up to 1V around the main loop. There is very little potential drop across the wires themselves. The transformer EMF in the main loop is 1V, so all is well with Faraday's Law. Also, all is well with the classical definition of KVL (given by Maxwell). Obviously, the version KVL that says the sum of potential drops is zero is violated, which makes the professor jump up and down and denounce his physics books for spouting bad physics.

In doing the proper measurement for potential on each resistor, you trace a path (through the meter and the resistor) that does not encircle the flux change and this tells you which resistor potential you are actually measuring. FL and KVL (both versions of KVL, mind you) work here. The Professor also reveals that if you consider the path through the other resistor, you see an apparent contradiction. You end up tracing a loop through the other resistor that encircles the flux change and you are not really measuring the potential on that resistor. Faraday's Law still works through that other path, and the classical definition of KVL also works, but the other definition of KVL fails yet again.

Since the professor is not actually acknowledging the classical definition of KVL, we can just ignore that aspect, and conclude that everything he is saying is correct. The results do not depend (other than small parasitic changes) on where you tap the node along the wire, but they do depend on how you route the leads of the meter. If we had the experiment in front of us, there would be a very simple way to prove this. Simply move the exact point where you tie into the nodes and see if the measurements change. It is my contention that they will not change very significantly. Anyone who doubts this should just do the experiment and convince themselves. Do you really think the people who set up this experiment would go through all this trouble, and then not verify this straightforward thing? You really think MIT people can miss a factor of ten in this way? That's hardly proof, but experiments are proof. I've done similar experiments in the past as part of my work. I can't ask anyone to accept my word, and if others don't want to accept the professor's capability, then just do the experiment.

I think we are talking in circles. Just look at the circuits as the secondary of the transformer with two resistors connect in series between the two end of the secondary. Then adjust the voltage at the primary to get EXACTLY 1V across the two resistor, you get what the professor was doing. Nothing more. YOu measure the 100ohm, you get 0.1V and 900ohm you get 0.9V. Problem is you miss the whole secondary of the transformer that generate the 1V to drive the 1V across the resistor.

Do you understand that if you connect the two resistors like what the professor draw, you form a loop EXACTLY like the secondary of the transformer with two resistors in series connected at the two end of the secondary? The length of the wire is not an issue here, it is the loop that create the transformer...that create a voltage when a varying magnetic field pass through the area enclosed by the loop. The professor has to draw in the voltage generator in his two resistor loop, with that, KVL hold.

You work with transformer before? You ever seen voltage created in just one or even half a loop of wire? If you don't believe me, just wind a 10 turn on a bobbin of some non magnetic material, then wind one turn on top as a secondary. You can even put the same two resistor in series. Hook up a scope onto the two end of the secondary. Use a 1.5 volt battery on the primary with a switch. Open and close the switch and see the meter needle jump, see how high ( voltage) it just! You will see that one little loop with only 1" or less can produce voltage.

 

[yungman]

Good one!

Of course appeal to authority is not a good argument, but it's important to look at qualifications and evidence of due dilligence, as part of a debate like this. There seems to be enough horse power behind the experiment, and analysis to suggest that claims of fraud should be backed by a detailed analysis and/or a documented experiment, rather than vague hand-waving type arguments about parasitic inductance and transformer tapping.

You mean you don't accept the idea of generating voltage of wire of less than 1" or 2" long forming a one turn loop? And you don't accept a 4" wire with two resistors connect at two ends is a loop? You think the 4" wire connecting the resistors to form the loop is insignificant? You really want me to go through the trouble to type out a simple transformer equation here?

If you ever design transformer for switching power supply, you will have no difficulty understanding what I have been talking. As switching frequency goes up, efficiency goes up, less turn is needed. That is the reason why the switching power supply is so so much smaller because less turn is needed, size of the core can be drastically reduced because core is lot more efficient at higher frequency. For a working engineer, I don't think it is hard to even get the idea of this. This is really simple!

I pretty much tell you how to reproduce the experiment in the other post, just wind the wire onto a Big ball point pen and you can do the experiment. Just be careful and wear rubber groves to avoid shock because when you open the switch, the coil can momentary generate very high voltage...Like ignition coil.

I can tell you, I designed high speed pulsing circuits with transformer driving MOSFETS. Because the design is 5KV switching, I had to stack 8 MOSFET in series to take the voltage. The driving circuit of each MOSFET has to be able to float. The transformer is the best approach. I actually design the transformer onto the PC board as trace. I only used 3 turns on the secondary to generate 15V to drive the gate of the MOSFET. 3 turns for 15V! The whole length of the secondary is less than 3". I hope you stop and think a little on this, this is real products been produced in the 90s. I am not a switching supply engineer, I was the manager and I came up with all the ideas on low turns, fast switching DC to DC converters that made our products exceptional at the time. I had my engineer did the detail calculation to get the turn number but the idea absolutely sound and was implemented on successful products.

 

[stevenb]

I think we are talking in circles.

That's exactly what we are supposed to do when discussing Faraday's Law and Kirchoff's Voltage Law.

 

[cabraham]

You mean you don't accept the idea of generating voltage of wire of less than 1" or 2" long forming a one turn loop? And you don't accept a 4" wire with two resistors connect at two ends is a loop? You think the 4" wire connecting the resistors to form the loop is insignificant? You really want me to go through the trouble to type out a simple transformer equation here?

If you ever design transformer for switching power supply, you will have no difficulty understanding what I have been talking. As switching frequency goes up, efficiency goes up, less turn is needed. That is the reason why the switching power supply is so so much smaller because less turn is needed, size of the core can be drastically reduced because core is lot more efficient at higher frequency. For a working engineer, I don't think it is hard to even get the idea of this. This is really simple!

I pretty much tell you how to reproduce the experiment in the other post, just wind the wire onto a Big ball point pen and you can do the experiment. Just be careful and wear rubber groves to avoid shock because when you open the switch, the coil can momentary generate very high voltage...Like ignition coil.

I can tell you, I designed high speed pulsing circuits with transformer driving MOSFETS. Because the design is 5KV switching, I had to stack 8 MOSFET in series to take the voltage. The driving circuit of each MOSFET has to be able to float. The transformer is the best approach. I actually design the transformer onto the PC board as trace. I only used 3 turns on the secondary to generate 15V to drive the gate of the MOSFET. 3 turns for 15V! The whole length of the secondary is less than 3". I hope you stop and think a little on this, this is real products been produced in the 90s. I am not a switching supply engineer, I was the manager and I came up with all the ideas on low turns, fast switching DC to DC converters that made our products exceptional at the time. I had my engineer did the detail calculation to get the turn number but the idea absolutely sound and was implemented on successful products.

This is irrelevant. Number of turns vs. frequency is not the issue here. I know xfmrs very well. This discussion involves the non-con nature of induced fields. Since you love to view things in terms of xfmrs, I'll do just that as illustration.

The secondary of a xfmr has 120V rms open circuited, with a secondary winding resistance of 0.10 ohm. The leakage inductance is very small, & the frequency is very small, meaning the reactance is much smaller than the 0.10 ohm resistance, so we can ignore it. An 11.9 ohm load is connected across the xfmr secondary. The current is of course 10 amp rms.

The terminal voltage at the secondary measured with a DVM is 119V rms. Thus we can say that if the secondary terminals are marked "a" & "b", then "Vab" is 119V rms. This is fine as long as it is understood we are measuring Vab along a path outside the xfmr core, so that the core flux does not influence the DVM reading. But consider the voltage from "a to b" along a different path, namely inside the secondary winding. We start at terminal a, integrate the E field along the path through the secondary wire, ending at terminal b. Now, Vab = Isec*Rsec = 10A*0.10 ohm = 1.0V rms. Thus "Vab" is 119V outside the xfmr assembly, & it is 1.0V inside the copper wire from which the secondary is wound.

This is the issue being discussed here. The fact that higher frequencies allow for a smaller xfmr & higher volts per turn is well known. Nobody is disputing that. My example shows that with non-con E fields, "Vab", the value of voltage from a to b, is not unique. The value depends upon the path of integration.

So what is the "real" value of Vab? Is it 119V, or 1.0V? The answer is that you must specify a path. Along the secondary conductor path it is "really 1.0V". Along an outer path, away from the conductor & core, it is "really 119V".

Think of this. Voltage is merely the math ratio of work expended moving a charge from a to b, per unit charge. To move 1.0 coulomb of charge through a path outside the core & winding, requires 119 joules of energy. But to move that same 1.0 coulomb along the path inside the wire requires only 1.0 joule of energy.

If the 11.9 ohm load resistor is a heater, it is emitting (10A)^2*(11.9 ohm) = 1190 watts of heat. But the xfmr secondary winding copper conductor is dissipating heat equal to (10A)^2*(0.1 ohm) = 10 watts of heat.

The 11.9 ohm heating element & the 0.10 copper wire secondary winding emit 1190 watt & 10 watt resp. But they carry the same exact current, 10 amp rms. What is going on here? If they carry the same current, yet have unequal powers, then the voltages must be unequal. But they are in parallel! How can parallelled elements have differing voltages?

Because the notion that 2 elements in parallel must be at the same potential is valid only with conservative fields, not so with non-con fields. KVL is the basis for 2 elements in parallel being at equal potentials. Not so with non-con conditions.

Does this help. I'll clarify if necessary. BR.

Claude

 

[yungman]

Claude, I am glad you use your example and we can build on this. If you remember the professor original drawing of replacing the 1V battery with a short circuit and then sent a magnetic field to get 0.1V on the 100ohm and 0.9V on the 900ohm.

Use your example. We use 110ohm in series with 9ohm across the secondary. Then we pulse the primary to get 9V on the 9ohm and 110V on the 110ohm. As in the professor case, let A be the junction between two resistors which in this case has 0 length. Where is point D?


He obvious know that the setup he had, by replacing the 1V battery with a short wire result in a loop formed by the wire and the resistors. Then he said he measure 0.1V across 100ohm and 0.9V across 900 ohm. Then he claimed he measure say clockwise from one point is 0.1V and counter clockwise as 0.9ohm! So where is the transformer that gave him the induced voltage in the picture?

Back to your example, the wire is the secondary of your transformer, point D is not a point, it consist of the winding (wire) of your secondary winding.


Is there any way for me to post a simple drawing of just two resistors and the secondary of the transformer without have to using a PDF and then attach, then have to wait for a day for other people to see it? Let me try this.


Let us redo the presentation again:

1) Let's arrange the components in counter clockwise.

2) Start with the 900ohm, then 100ohm and call the point between the two resistor is point A. I call the open end of the 900ohm resistor point C.

3) Then we connect one end of 4" wire to the 100ohm resistor and call this junction B. Remember I am still going counter clockwise now.

4) Then the other side of the 4" wire connect back to the open end of the 900ohm resistor which I call point C in step 2.

With this, we form a closed loop starting from point A between the two resistor, travel counter clockwise through 100 ohm resistor, to point B to the wire, through the wire to point C that connect to the other side of the 900ohm resistor.

Then you inject a pulse of magnetic field, you measure 0.1V across the 100 ohm resistor, and 0.9V across the resistor. Just like the good professor did.

Lets call point C is +ve and call point B as -ve. Let's travel from point B counter clockwise through point C to point A, you get 1V-0.9V=0.1V. If you travel from point B clockwise this time to point A, you get 0.1V! Why are they the same now? Because the transformer effect, this time I include the transformer in the picture and voltage come together! IN this case, KVL works beautifully.

 

[yungman]

I know I sounded vey bull headed and one track mind. But I watched very carefully his presentation and the drawing on his first video. AND the way he go from point A to D in one direction and from D to A in the opposite direction and totally ignore the transformer effect. In this case, context is very important.

Until someone explain to me how he can just make a big statement with just the drawing on his video one, everything else in 4 pages here, all the forumlas, the non conservative, integrations just become bla bla bla to me. I don't even want to go any further until I can be convinced that his first presentation make sense. Without that, any conclusion derive out of his drawing means nothing.

 

[sarumonkee]

@Claude: I totally agree with your example. Thank you for agreeing with Yungman and myself. A standard model of the secondary of a transformer with sufficient frequencies being put through it (not too high, not too low) is a voltage source (or current source depending on your take on things). I am contending that KVL still applies, because the secondary of the transformer still exists, and is a voltage source that Prof Lewin left out, thus making his example suspect.

Also, @stevenb. If orientation of your scope probes matters that much, what happens if the oscilloscope is directly above the table? Is there some voltage between 0.9 and -0.1V? Or does it just suddenly change between the two when you cross some threshold degree? I just don't see it yet. I am not being facetious, I really do want to understand what you are saying. If physical orientation of a voltage probe matters, why isn't it taught in school? Physical placement is important, and also taught in school.

Also, everyone who keeps harping on the fact that the Prof got the factor about 10 (actually exactly 9) correct, I never said he wouldn't. A resistor that is 1/9 the size of another resistor with the same current WILL have 1/9 the voltage drop on it. That is not impressive.

What IS impressive is calling a node a node even if it has supposedly two different voltages on it. I thought that the definition of a node is that it has one voltage on it.

 

[yungman]

@Claude: I totally agree with your example. Thank you for agreeing with Yungman and myself. A standard model of the secondary of a transformer with sufficient frequencies being put through it (not too high, not too low) is a voltage source (or current source depending on your take on things). I am contending that KVL still applies, because the secondary of the transformer still exists, and is a voltage source that Prof Lewin left out, thus making his example suspect.

Also, @stevenb. If orientation of your scope probes matters that much, what happens if the oscilloscope is directly above the table? Is there some voltage between 0.9 and -0.1V? Or does it just suddenly change between the two when you cross some threshold degree? I just don't see it yet. I am not being facetious, I really do want to understand what you are saying. If physical orientation of a voltage probe matters, why isn't it taught in school? Physical placement is important, and also taught in school.

Also, everyone who keeps harping on the fact that the Prof got the factor about 10 (actually exactly 9) correct, I never said he wouldn't. A resistor that is 1/9 the size of another resistor with the same current WILL have 1/9 the voltage drop on it. That is not impressive.

What IS impressive is calling a node a node even if it has supposedly two different voltages on it. I thought that the definition of a node is that it has one voltage on it.

I am actually approach Engineering from the opposite end. I never have an EE degree, my degree was organic chemistry, electronics was my hobby. I started as a technician and I studied on my own really hard. I got promoted to an engineer in two years and been a design engine and a manager of EE over 25 years. In the past 10 years, I decided to go back and study all the math including PDE, EM, RF design on my own.

That said, I am very glad I did this the other way around. A lot of the professor in EE never have a day of real engineering job. All the books never talked about the simple things like the ground connection, power supply V+ etc. In real life, these are the ones that give nightmare to engineers. Because in schematics, it is only one point like the good professor did with point A and point D. BUT in real life, it is a physical connection, a wire that can become a loop in this case, become inductance or resistance. Worst, the wire become an antenna and start picking up noise. The probe lead are part of the problem of the parasitic length that can form loop.

The circuits in the book really work! They just ignore the un-foresee stuffs like grounding and supply and the way to hook up your measuring equipment. In real life these "parasitic" are usually what kill the project. I have seen people from ivy league college cannot adapt to the real world and screw up on the job. The sad part is some have too much eagle to realize what they don't know. That is one thing I am impressed with a small university call U of Santa Clara. I actually contact with one professor call William Egan who wrote a very good phase lock loop textbook. He actually work over half the time in the private industry and teach part time. This is the kind of professor I want.

I always told my technicians, if they don't get the right measurement, 50% of time is the setup of the measurement is at fault. It goes higher as frequency goes up.

I have more books on RF, microwave and EM than the Stanford university book store, I was there buying books and gave up. I have one tall bookcase of books in these subjects and cauculus. I can tell you, only RF book talks a little about parasitic elements of components, nobody else does. Still none emphasis on power supply and grounding and NO BOOKS talk about the way to measure like what you are asking. This problem is getting worst when the speed of electronics getting higher. They actually have a special kind of engineer called "Signal Integrity" engineer to do nothing but to catch grounding, un-intention loop that pickup magnetic field, signal return path. In one of my contract with KLA Tencor, I worked on the signal integrity issue and help doing the pcb layout for their 3.3G bit CCD camera. That was in 2003. The un-foresee "parasitic" are the killer of a lot of electronics and you have to be very careful in the way you measure. A lot of times, we use a scope probe adapter that have very short ground lead and we solder it onto the circuit. Then we plug the probe into the adapter to measure the signal. This is to get rid of the ground loop caused by the ground lead hooking onto some distant ground point. It is all about grounding!

 

[stevenb]

Also, @stevenb. If orientation of your scope probes matters that much, what happens if the oscilloscope is directly above the table? Is there some voltage between 0.9 and -0.1V? Or does it just suddenly change between the two when you cross some threshold degree? I just don't see it yet. I am not being facetious, I really do want to understand what you are saying. If physical orientation of a voltage probe matters, why isn't it taught in school? Physical placement is important, and also taught in school.

I'm not taking your questions as facetious at all. I can see you are trying to come to grips with this difficult concept. The problem is that it hard for people to learn when they start off with lack of trust. You don't trust that the Prof is trying to teach you and is qualified to teach you. So, the learning process is going to be slower than it needs to be. Although your question to me is genuine, it also implies your lack of trust that I might know what I'm talking about too. Can't say I blame you since you don't know me at all, but it places me at a serious disadvantage in trying to help you. On top of that, this format is not terrible conducive to getting ones thought across clearly. As an example, I never said the orientation of the probes matter that much. What I said was that the path formed by the leads is the critical thing. So, I'm not hopeful that I can be of great help, and I think I've passed the frustration threshold for this thread in general.

The simplest answer I can give is that full understanding of Faraday's Law removes all mysteries here. Study FL thoroughly and when you feel that FL is telling you something that you just don't want to believe, then figure out how to do an experiment (yourself, since you don't trust others, no matter what their qualifications - not always a bad thing, by the way) to convince yourself of its truth. Your question about what happens if the meter is placed above the circuit is outstanding, and convinces me that you will understand this soon. Please explore the answer using FL. It's not difficult to answer, but the answer will help you come to grips with the concepts here.

 

[atyy]

What IS impressive is calling a node a node even if it has supposedly two different voltages on it. I thought that the definition of a node is that it has one voltage on it.

Yes, that is exactly what Lewin, stevenb, cabraham etc have all been saying - in the case of a time varying electric field, the electric field cannot be completely obtained from a scalar potential.

The part about 9:1 or whatever is just to show that in fact Lewin's results are consistent with his model, and not due to small factors he neglected, like the voltmeters not being connected at exactly the same points in his setup. If his model is wrong, then the voltmeter readings would be 1:1, and the small errors you have in mind would have to change this 1:1 to 9:1, basically the errors would have to be huge. The alternative is that the errors are small, and the 9:1 is the same 9:1 he predicts using his model.

 

[sarumonkee]

I'm not taking your questions as facetious at all. I can see you are trying to come to grips with this difficult concept. The problem is that it hard for people to learn when they start off with lack of trust. You don't trust that the Prof is trying to teach you and is qualified to teach you. So, the learning process is going to be slower than it needs to be. Although your question to me is genuine, it also implies your lack of trust that I might know what I'm talking about too. Can't say I blame you since you don't know me at all, but it places me at a serious disadvantage in trying to help you. On top of that, this format is not terrible conducive to getting ones thought across clearly. As an example, I never said the orientation of the probes matter that much. What I said was that the path formed by the leads is the critical thing. So, I'm not hopeful that I can be of great help, and I think I've passed the frustration threshold for this thread in general.

The simplest answer I can give is that full understanding of Faraday's Law removes all mysteries here. Study FL thoroughly and when you feel that FL is telling you something that you just don't want to believe, then figure out how to do an experiment (yourself, since you don't trust others, no matter what their qualifications - not always a bad thing, by the way) to convince yourself of its truth. Your question about what happens if the meter is placed above the circuit is outstanding, and convinces me that you will understand this soon. Please explore the answer using FL. It's not difficult to answer, but the answer will help you come to grips with the concepts here.

So after all that lead in, you don't answer my question about the scope above the table :)? If you know the answer, please tell me... Or at least hint at the direction I should look (but I think just hinting will make it look like you don't know the answer).

I still don't get what you mean by path. If a node is a node, the path to it, and through it are transparent. The two probes have the same path if connected to the same nodes. I just don't think these are actually nodes in this case.

Thanks.

 

[atyy]

So after all that lead in, you don't answer my question about the scope above the table :)? If you know the answer, please tell me... Or at least hint at the direction I should look (but I think just hinting will make it look like you don't know the answer).

I still don't get what you mean by path. If a node is a node, the path to it, and through it are transparent. The two probes have the same path if connected to the same nodes. I just don't think these are actually nodes in this case.

Thanks.

Hint:
integral(E.dl)~d(B.A)/dt
A is a vector perpendicular to the area in question.
There is a dot product, so there will be a cosine of some angle.
That angle is related to the angle in your question.

 

[yungman]

So after all that lead in, you don't answer my question about the scope above the table :)? If you know the answer, please tell me... Or at least hint at the direction I should look (but I think just hinting will make it look like you don't know the answer).

I still don't get what you mean by path. If a node is a node, the path to it, and through it are transparent. The two probes have the same path if connected to the same nodes. I just don't think these are actually nodes in this case.

Thanks.

The whole point is point D cannot be considered as a note. The wire IS a path. A note is a single point, no if and buts about it. The whole point of consider D as a note is not correct. The drawing that the professor should have at least 3 notes even if you solder the two resistor back to back. And if the other side of the two resistor at what so called point A is another short piece of wire, point A is actually a path with two notes in this one loop case, no if and buts about this. Some how, people here do not accept the idea the even that little piece of wire is part of the circuit and has to be accounted for. If you take the wire as a voltage source and work KVL around it, there is no mistake.

Path integration we are talking here is very simple, just integrate along the path. Just like the basic integration \int f(x)dx[/tex], this only mean that the integration is carry out on the path of the x-axis. In the \int_C \vec E \cdot d\vec l \hbox { is actually } \int_C \vec E \cdot \hat T dl it is nothing more than integration of E along the path of the loop. THis is very well covered in vector calculus ( part in 3rd semester multi variable calculus).<br /> <br /> In my post #78 in page 5, in step 2) and 3), points B and C are two notes with the wire in between which is part of the path of the closed loop. In the example, I made is simpler by soldering the two resistor back to back so the point A is truly a note with no wire length ( approximate only). So there are only 3 notes in that loop.

 

[kcdodd]

Any time a scalar potential is used to derive all the physics, it is being assumed that the electric field is conservative.

In situations where the electric field is not static, a scalar potential may still be useful if only approximate. This is the quasistatic approximation.

KVL uses a scalar potential, and is closely related to conservative fields.

My point is that in "normal" circuits, where KVL is applied, there are always non-conservative electric fields present. When applying the voltage law you get a -V on a resistor which represents an electric field pointing in the direction of current. However, the resistance itself is a non-conservative force and must be electric in nature. In an emf component you get a +V, which if we are consistent, represents an electric field opposing current. Of course this cannot be the whole story because for current to flow against the electric field there must be non-conservative forces present inside the emf too. Otherwise current would never flow anywhere in the circuit. And all of those forces are fundamentally electric in nature as well.

However, when dealing with KVL those non-conservative forces are "simply ignored", if for no other reason then they would be hard to calculate, and only the conservative part of the field is taken when calculating V. KVL in that sense basically just says that conservative forces are conservative, because it would always ignore non-conservative forces.

Why is this important? Because if one is consistent with "ignoring non-conservative forces" in this way for "normal" circuits, there is no reason to suddenly include them when you have a macroscopic non-conservative electric field which acts as an emf. If Lewin is to start including non-conservative forces in his loop integral then he should include all of them and not just pick and choose which ones to include. My guess is that in including all forces one would find the integral to in fact be zero.

 

[sarumonkee]

Hint:
integral(E.dl)~d(B.A)/dt
A is a vector perpendicular to the area in question.
There is a dot product, so there will be a cosine of some angle.
That angle is related to the angle in your question.

So you are saying pointing the "loop" of the voltage probe at a certain angle, I will get 0 Volts?

I actually rigged up this experiment, and sufficiently convinced myself that KVL is holding... I held the probes above, below, across, etc, and got the same numbers time and time again. I am seeing the inductance that yungman has been talking about, and a voltage drop across the wire, which definitely should not be a node. I think Lewin should have had at least a coupled inductor in his model (or two the way his experiment was setup).

 

[atyy]

So you are saying pointing the "loop" of the voltage probe at a certain angle, I will get 0 Volts?

I actually rigged up this experiment, and sufficiently convinced myself that KVL is holding... I held the probes above, below, across, etc, and got the same numbers time and time again. I am seeing the inductance that yungman has been talking about, and a voltage drop across the wire, which definitely should not be a node. I think Lewin should have had at least a coupled inductor in his model (or two the way his experiment was setup).

How did you ensure that the changing B field is confined to the central loop?

Also, what are the parameters of your setup?

 

[sarumonkee]

How did you ensure that the changing B field is confined to the central loop?

Also, what are the parameters of your setup?

I made my setup similar to what I think he did, except I made one connection from the 100Ω to 900Ω resistors very short. I then put ground of both probes between the two resistors on the short connection. The other sides of the resistors were connected with a 6" wire. I probed the resistors close to the actual resistor on the opposite side from the short "node".

The primary coil was about 40 turns of something like 14-16AWG wire, around a huge core I had laying around, with an effective core cross sectional area of probably just under 2 square inches. I then introduced a 10 V step onto the primary, while having the secondary (the resistors and wire) around the core, like Lewin's setup is presumably from 5:33 on part 2.

I observed a factor of about 1:9 as expected in the two voltages, since this was the ratio of the resistances. Now, the fun part. I connected the grounds of the probes to half way between the long wire, about 3" from both resistors, leaving the probe ends in the same location. Since this is a "node" in Lewin's analysis, I should not see any voltage across it if I make another step function on the primary.

Well, I introduced my step, and both probes read about the same magnitude (one was negative from the other, since it points the other way), and the sum of the two magnitudes (had to invert one because I wasn't using differential probes) equaled the sum of the previous points in standard KVL style, all adding to 0 if you do the loop. I was measuring a voltage across the 6" wire in two 3" segments.

I also held the probes above, across, and in many different orientations, and it still produced the same results. I plan on taking some pictures and maybe making a video this weekend if I have time.

Let me know if you have any measurements you would like me to make, or if you think my setup or analysis is flawed somehow... I'm here to learn.

 

[atyy]

Cool! So in the part where you got different readings of 9:1, did you connect the voltmeters to exactly the same two points?

 

[sarumonkee]

Cool! So in the part where you got different readings of 9:1, did you connect the voltmeters to exactly the same two points?

No, I just realized I need to show that one as well... I will next time I'm back in that lab. The time I got 1:9 ratio is when I had the probe leads as close as possible to the resistors, and the grounds on the short side (1 cm wire connection). The probe leads were separated by the 6" wire on one side direction around the loop, and the two resistors on the other.

I never actually connected the probes to the exact same point (probe on probe, and ground on ground). I will try to remember to do that next time, and spread the probes to opposite sides of the loop like I bet you will ask for.

I hope that paints the picture for you.

 

[yungman]

I made my setup similar to what I think he did, except I made one connection from the 100Ω to 900Ω resistors very short. I then put ground of both probes between the two resistors on the short connection. The other sides of the resistors were connected with a 6" wire. I probed the resistors close to the actual resistor on the opposite side from the short "node".

The primary coil was about 40 turns of something like 14-16AWG wire, around a huge core I had laying around, with an effective core cross sectional area of probably just under 2 square inches. I then introduced a 10 V step onto the primary, while having the secondary (the resistors and wire) around the core, like Lewin's setup is presumably from 5:33 on part 2.

I observed a factor of about 1:9 as expected in the two voltages, since this was the ratio of the resistances. Now, the fun part. I connected the grounds of the probes to half way between the long wire, about 3" from both resistors, leaving the probe ends in the same location. Since this is a "node" in Lewin's analysis, I should not see any voltage across it if I make another step function on the primary.

Well, I introduced my step, and both probes read about the same magnitude (one was negative from the other, since it points the other way), and the sum of the two magnitudes (had to invert one because I wasn't using differential probes) equaled the sum of the previous points in standard KVL style, all adding to 0 if you do the loop. I was measuring a voltage across the 6" wire in two 3" segments.

I also held the probes above, across, and in many different orientations, and it still produced the same results. I plan on taking some pictures and maybe making a video this weekend if I have time.

Let me know if you have any measurements you would like me to make, or if you think my setup or analysis is flawed somehow... I'm here to learn.

You are good man, you prove my point to the T! You grounded the probe in the middle of the wire 3" from each side and you keep the probe on the junction where you measure the voltage before and you get equal and opposite voltage. This is the transformer I am talking about and you prove my point from the post #2 on that the wire is the voltage source. The voltage source that the professor MISSED, and went on to trash others in such an arrogance manner. He need to go get a real job before he talked so loud.

I am surprised though that the probe is so insensitive to position. It would be nice if you take a few pictures. Placement is everything in the real world. It is almost pointless to talk about this subject on paper drawing resistors and nodes like the professor did.

You really make my day. I spent the whole day today going back and forth trying to get this point across, make me missed the whole day in studying EM! I really need to get back to my studying. I better get back to the theoretical world!

 

[yungman]

No, I just realized I need to show that one as well... I will next time I'm back in that lab. The time I got 1:9 ratio is when I had the probe leads as close as possible to the resistors, and the grounds on the short side (1 cm wire connection). The probe leads were separated by the 6" wire on one side direction around the loop, and the two resistors on the other.

I never actually connected the probes to the exact same point (probe on probe, and ground on ground). I will try to remember to do that next time, and spread the probes to opposite sides of the loop like I bet you will ask for.

I hope that paints the picture for you.

You did get 9:1 read across the two resistor as the professor. As long as you move both grounds of the two probes to the middle of the wire and have the probes at the junction of the end of the wire to the resistor on both sides, you did the right thing. This is my understanding from your write up and that prove my point of the transformer effect. You should see 0.5V on each probe and add up to be 1V.

 

[hikaru1221]

Hikaru, thank you for being the only respondant to have the courage to post and answer to my question.


So did Farady state his law in 'Integral Form'


I think that what is happening here is that a non original form of Faraday's Law is being compared with a non original form of KVL. By non original I mean extended in the light of more modern knowledge.

Faraday's conclusion from his experiment was that a change in magnetic flux induces an induced current inside a closed circuit. The later speculation was that a change in magnetic flux induces an induced emf. Then Maxwell came in.
What I meant by "integral form" is that we consider a whole loop when applying Faraday's law. It is equivalent to the integral form of Maxwell-Faraday equation. Just the same as KVL. We write the equation for a loop, not a branch.
Please enlighten me with the modern knowledge you mentioned.

 

[Phrak]

Are you referring to a current measurement? The point of Prof. Lewin's experiment was not about voltmeter measuring errors, it was to supposedly show measuring across different points of two "nodes" can give you different voltages. I don't think they were actually "nodes" as inductance was not included.

I broke down and watched the first video. I found Lewin to be irritating. He seems to get too much delighted in generating confusion rather than clarity.

You can measure the same two physical points and get two different measurements because the leads of the measuring instrument enclose different regions of changing magnetic flux. It's really that simple.

The fact that this crazy thread has gone on so long is evidence of the guy's overwhelming success in creating confusion. Then he gets to be the genius-hero and rescue you from the confusion he, himself has so cleverly led you into. good grief.

Clear the indoctrination of this subversive screwball out of your head, learn about electromagnetic fields, then come back to it, and the confusion will have evaporated.

 

[sarumonkee]

Just to clarify, with my experimental setup, I was not getting a full 0.1V and 0.9V on the resistors. I don't think I have a large enough primary coil (read needs more turns), and I only did a 10V step, which was well away from the max current I could put through the thing. It was a quick first run, and I could do it with a stronger field next time.

The important thing still holds though, I got the right ratios, and the wires had voltages across them showing they weren't totally nodes as was originally contended.

 

[cabraham]

Claude, I am glad you use your example and we can build on this. If you remember the professor original drawing of replacing the 1V battery with a short circuit and then sent a magnetic field to get 0.1V on the 100ohm and 0.9V on the 900ohm.

Use your example. We use 110ohm in series with 9ohm across the secondary. Then we pulse the primary to get 9V on the 9ohm and 110V on the 110ohm. As in the professor case, let A be the junction between two resistors which in this case has 0 length. Where is point D?


He obvious know that the setup he had, by replacing the 1V battery with a short wire result in a loop formed by the wire and the resistors. Then he said he measure 0.1V across 100ohm and 0.9V across 900 ohm. Then he claimed he measure say clockwise from one point is 0.1V and counter clockwise as 0.9ohm! So where is the transformer that gave him the induced voltage in the picture?

Back to your example, the wire is the secondary of your transformer, point D is not a point, it consist of the winding (wire) of your secondary winding.


Is there any way for me to post a simple drawing of just two resistors and the secondary of the transformer without have to using a PDF and then attach, then have to wait for a day for other people to see it? Let me try this.


Let us redo the presentation again:

1) Let's arrange the components in counter clockwise.

2) Start with the 900ohm, then 100ohm and call the point between the two resistor is point A. I call the open end of the 900ohm resistor point C.

3) Then we connect one end of 4" wire to the 100ohm resistor and call this junction B. Remember I am still going counter clockwise now.

4) Then the other side of the 4" wire connect back to the open end of the 900ohm resistor which I call point C in step 2.

With this, we form a closed loop starting from point A between the two resistor, travel counter clockwise through 100 ohm resistor, to point B to the wire, through the wire to point C that connect to the other side of the 900ohm resistor.

Then you inject a pulse of magnetic field, you measure 0.1V across the 100 ohm resistor, and 0.9V across the resistor. Just like the good professor did.

Lets call point C is +ve and call point B as -ve. Let's travel from point B counter clockwise through point C to point A, you get 1V-0.9V=0.1V. If you travel from point B clockwise this time to point A, you get 0.1V! Why are they the same now? Because the transformer effect, this time I include the transformer in the picture and voltage come together! IN this case, KVL works beautifully.

Please provide a diagram. My xfmr example demonstrated that KVL does not always work. We are not in agreement here.

Claude

 

[sarumonkee]

Please provide a diagram. My xfmr example demonstrated that KVL does not always work. We are not in agreement here.

Claude

In my studies, the secondary resistance is modeled as a series resistance with the secondary inductance. It is the inductance that allows the energy transfer in a transformer, and is modeled as a voltage source when fed from the primary. I don't see a KVL error here.

Source: Fundamentals of Power Electronics 2nd ed., Erickson/Maksimovic

 

[Studiot]

Faraday’s and Kirchoff’s laws were developed for different circumstances and are therefore different.
Both sometimes apply to situations not covered by the other; neither is a special case of the other.

I am in general agreement with Prof Lewin in his statements, with the exception that I have no trouble applying the original form of Kirchoff’s law to his apparatus.

It is instructive to consider the original form of both laws to see where they overlap and where they differ. It should be remembered that in their time magnetism was treated in terms of ‘lines of force’.

This is Maxwell’s translation of Kirchoff

“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 currents in each conductor multiplied by the resistance of that conductor.”

They went on to state that this sum is known as the total EMF in a circuit (loop).


And this is Nightingale's record of Faraday

“Whenever a conductor cuts magnetic lines of force an EMF is generated. This EMF is proportional to the time rate at which the lines are cut.”

My understanding of Faraday's law is that it is in differential form as stated here. It is more far reaching than Kirchoff’s Law as it connects electric and magnetic effects. Kirchoff 's Law relates purely to electric effects. However the downside of this is that there must actually be magnetic flux to vary to yield the EMF.

Further differences are that Faraday does not require a closed loop, although he does not prohibit one either.
Kirchoff’s treatise concerned loops in meshes. He does not actually mention potential difference or drop and he does not distinguish between sources of EMF. They are all the same to him.

So to apply Kirchoff to Lewin proceed as follows:

The sum of the EMF's = The sum of the IR products

Used in this form it appears to me that the law is satisfied.

The total EMF in the circuit is 1 volt (the EMF induced by the coil) and the IR sum is 0.9 + 0.1 volt.

I believe it used to be phrased in this way to allow for just such a situation.

What has Lewin done then?

Well there is only one source of EMF in the loop and it is distributed around the whole loop. It is not lumped into any particular circuit element and cannot be applied at any particular point in the loop.

This brings out the difference between EMF (which is distributed around the circuit in this case) and Potential Difference or Potential Drop.

So Prof Lewin has demonstrated is that an EMF and a Potential Difference are not two names for the same thing. They are in fact different animals.

The give away clue is in his statement about conservative and non conservative fields.

For PD the line intergral \ointE.dl is zero around the loop.

For EMF it is not.

Another way to look at it is that an EMF is capable of introducing energy into the system, but PD is not.

A third way to look at it is to note that PD's result from the solution of Laplaces equation, EMF's result from the solution of Poissons equation, where there is a forcing function.