#562 – Electroboom!

[jesuscf]

I would be a little concerned with my probing if I measured V1 something else than 0V across a 0 ohm wire [when |V2 + V3| > 0].

Don't forget that not all voltage differences are ohmic.

There's batteries, capacitors, solar cells, peltier junctions, and yes, the ever popular inductive transformer.

All of those things can have voltages across them which would appear to violate ohms law if we assume that all voltage differences are strictly ohmic.

not all voltage differences are purely ohmic.

And one of those that is not strictly ohmic is the winding of a transformer.

According to team Lewin the induced EMF due to Faraday's law is 'special' (like themselves) because something-something and can not be treated just like any other EMF despite that all of them are measured in volts...

[Sredni]

Did you get the voltage V_AD yet?  Do you need more help?

I have got plenty of  V_AD voltages. One for every path I can think of.
Including one of the paths that gives the answer you like.

[jesuscf]

This is Lewin's ring: two resistors in a single loop that goes around a circular region (let's consider it of the same size as the loop, so you can see there is no 'room to twist' the wires) of variable magnetic field. The resistors are required to be on the opposite sides of the variable magnetic field region.


link https://i.postimg.cc/pLmfyHxZ/Lewin-ring-is-unlumpable.jpg

Here, I fixed your drawing.  Can you compute V_AD now?

[Kalvin]

Check the attached pdf from Electromagnetics by Notaros, pages 279-280, example 6.6.

Notaros seems to be modeling a similar circuit so that the EMF inducing the current is shown as two lumped voltage sources in the circuit, instead of computing the induced current in the distributed circuit due to the EMF. I kind of understand Notaros wanting to model the EMF into the circuit, but doing so Notaros is actually converting a non-conservative circuit into a conservative one. To me that looks like an illegal chess move (converting a non-conservative circuit into a conservative circuit).

[jesuscf]

Check the attached pdf from Electromagnetics by Notaros, pages 279-280, example 6.6.

Notaros seems to be modeling a similar circuit so that the EMF inducing the current is shown as two lumped voltage sources in the circuit, instead of computing the induced current in the distributed circuit due to the EMF. I kind of understand Notaros wanting to model the EMF into the circuit, but doing so Notaros is actually converting a non-conservative circuit into a conservative one. To me that looks like an illegal chess move (converting a non-conservative circuit into a conservative circuit).

Ok, tell me why you think the circuit is non-conservative.

[Kalvin]

Check the attached pdf from Electromagnetics by Notaros, pages 279-280, example 6.6.

Notaros seems to be modeling a similar circuit so that the EMF inducing the current is shown as two lumped voltage sources in the circuit, instead of computing the induced current in the distributed circuit due to the EMF. I kind of understand Notaros wanting to model the EMF into the circuit, but doing so Notaros is actually converting a non-conservative circuit into a conservative one. To me that looks like an illegal chess move (converting a non-conservative circuit into a conservative circuit).

Here is the problem with Notaros and a counter-example: Where would you put those voltage sources modeling the EMF so that you can measure the correct voltages across two neighboring resistors ie. V(Ra,Rb), V(Rb,Rc), V(Rc, Rf), V(Rf, Re), V(Re, Rd), V(Rd, Ra).

[jesuscf]

Check the attached pdf from Electromagnetics by Notaros, pages 279-280, example 6.6.

Notaros seems to be modeling a similar circuit so that the EMF inducing the current is shown as two lumped voltage sources in the circuit, instead of computing the induced current in the distributed circuit due to the EMF. I kind of understand Notaros wanting to model the EMF into the circuit, but doing so Notaros is actually converting a non-conservative circuit into a conservative one. To me that looks like an illegal chess move (converting a non-conservative circuit into a conservative circuit).

Here is the problem with Notaros and a counter-example: Where would you put those voltage sources modeling the EMF so that you can measure the correct voltages across two neighboring resistors ie. V(Ra,Rb), V(Rb,Rc), V(Rc, Rf), V(Rf, Re), V(Re, Rd), V(Rd, Ra).

That is a very good question that has been answered in this forum many, many times: each resistor in the loop behaves both as voltage source a resistor in series.  Check this post:

https://www.eevblog.com/forum/amphour/562-electroboom!/msg3830852/#msg3830852

[thinkfat]

That was my challenge to you, the task was to find the voltages across the resistors and the wires:


And that's what you came up with:


Which of course brings up the question why you found it necessary to add a "transformer secondary" to find the voltage across "2R".

You call it an "added secondary" but it MEASURES AND MODELS the exact same as if the right hand volt meter was instead on the left. Doesn't matter where it is. It doesn't loop through the core, which means it's not another winding.

Remember, KVL requires two-terminal elements. If we're not using a two-terminal element, OF COURSE kvl isn't even applicable.

You want me to run a volt meter lead through the core which effectively adds another secondary winding, making it into a 3 terminal element, and as such, it's no longer applicable for KVL.

Before I go further into the details of why I think your explanation is rubbish, let me expand on "observable reality": What is observed is not reality until you've asked "Why is it so?" often enough to rule out all possible reasons but one. The idea of it being enough to just observe and not ask the "Why is it so?" question has directly lead to the creation of divine beings, or gods, to explain phenomena of nature in ancient cultures. People observed weather and the changing of seasons and as they were not able to explain and thus gods were created.

You, instead of asking the right questions, just try to confirm your beliefs. Instead of asking why the volt meters in Lewins experiment show different voltages you say "He's just a fool, he made a mistake, it's bad probing". When asked about the mechanism that induces voltage in a transformer winding you say "It's Nature".

I feel now that I did injustice to the flatearthers by likening you to them. Because, as the Physicist Sabine Hossenfelder said about them, their science is wrong, but not stupid.

Anyway, thank you for answering my question about which of the loops in my diagram you consider a "transformer secondary" and which are not. I knew the answer beforehand of course, but I needed you to confirm it with your own words so that there will be no wiggling out of it later.

[Jesse Gordon]

Dude, that's Trevor Kearney. If Jesse hadn't flown away to another galaxy to avoid answering my question on the circuit path for Lewin's ring, he would tell you Trevor is "Armchair Physics Nobel Prize" number one. He's probably one of the most active people on YouTube trying to debunk Mehdi and the other KVLers. 

Isn't it hilarious that KVLers be so obtuse that they can't even recognize when a video was made to debunk their claims, due to their absolute lack of understanding of what is being discussed?

Congratulations, Mehdi Sadaghdar! Look what you've done! You've spawned a whole bunch of brain-damaged mock engineers like yourself.

Mehdi didn't start this, Lewin did. I'd made my videos in rebuttal to Lewin before I even know anybody else had.

[Jesse Gordon]

I didn't fly away,

Oh, good. So you can answer my question, since I have answered yours.

No, you didn't answer MY question, you asked a question of your own choosing.

I told you I unequivocally proved that Team Lewin absoutely refused to answer basic questions - EVERY SINGLE (then active) MEMBER of Team Lewin absolutely refused to answer my question. What's else to discuss when Team Lewin denies observable reality?

Maybe we did answer the question, and you are not able to accept the answer so you keep asking it over and over hoping to receive the answer you want?

No, you answered a question of YOUR CHOOSING, thus refusing to answer mine.

He too refused to answer numerous questions which I asked him, and also made false predictions about reality - in fact, when I told him that KVL would hold with a loop made from two transformer secondary windings and two resistors, he didn't believe me, so that's why I made the "KVL Holds with an iron core" video.

He too refused to answer my simple question that you all refused to answer - If it measures like it's working, why is it not working? is it a technicality?

As I repeated about a dozen times, if a circuit is lumpABLE and you choose the circuit path in such a way that it does not include a variable magnetic field, then you can consider all voltages between any two points on that circuit path as if they were path independent. The circuit can be considered lumpED and KVL works.

IF the circuit is lumpABLE.

See? You didn't answer my question with a yes or no, you answered with an IF, and then you refused to tell me whether my circuit met your IF.

So I ask again. I've provided a very clear unambiguous test circuit. I've specified even the points which are considered the terminals of the lumped elements.

By the way, you talk about lumpable circuits, but you seem awfully silent on which of my elements are not lumpable. According to your own trusted source, your Pratt & Whitney of textbooks, "Lumped circuts are obtained by connecting lumped elements. Typical lumped elements are resistors, capacitors, inductors, and transformers."

When you can answer MY question as described directly below, then we can talk. Until then, you're denying observable reality. Or you simply don't know what reality is in this case.

Question: In the following diagram, in a real life physical lab test performed with real (time synchronized) volt meters with a real transformer and real resistors CONNECTED AS SHOWN, will the readings of all the volt meters sum to zero, within the accuracy and resolution limitations of the volt meters? YES or NO.

(Or if you believe SOMETIMES is the answer, then explain one scenario for a YES condition and one scenario for a NO condition WITH THE VOLT METERS CONNECTED AS SHOWN - Running additional conductors through the transformer core is not allowed - nor is removing existing conductors from through the transformer core!)

There are in our universe, circuits that are not lumpable: I call them UNlumpable circuits.
They are circuits where you cannot find a circuit path that does not encloses the variable flux region.
Lewin's ring IS such a circuit because it REQUIRES the two resistors to be on the opposite sides of a variable magnetic flux region.
You think Lewin's ring is lumpABLE?

Well, PROVE IT.

This is Lewin's ring: two resistors in a single loop that goes around a circular region (let's consider it of the same size as the loop, so you can see there is no 'room to twist' the wires) of variable magnetic field. The resistors are required to be on the opposite sides of the variable magnetic field region.


link https://i.postimg.cc/pLmfyHxZ/Lewin-ring-is-unlumpable.jpg

Please, show everybody you can draw a circuit path (make it green, meaning it's 'flux-free') that joins the resistors' terminal to the "lumped transformer secondary" terminals and DOES NOT INCLUDE the variable magnetic field region in its interior. Like I did for the lumpABLE circuit I decided to see as lumpED (in my post "Lumpable (lumped and not lumped) and not lumpable circuits for dummies").

In addition, you can also show everybody you can draw the path inside your "lumped transformer secondary" that DOES INCLUDE the variable magnetic field region (make it orange) but IS NOT part of the green circuit path.
I will show you that if you can do that you will run into contradiction.

Like I said, answer the question I ASKED and then we can talk.

[Kalvin]

Check the attached pdf from Electromagnetics by Notaros, pages 279-280, example 6.6.

Notaros seems to be modeling a similar circuit so that the EMF inducing the current is shown as two lumped voltage sources in the circuit, instead of computing the induced current in the distributed circuit due to the EMF. I kind of understand Notaros wanting to model the EMF into the circuit, but doing so Notaros is actually converting a non-conservative circuit into a conservative one. To me that looks like an illegal chess move (converting a non-conservative circuit into a conservative circuit).

Here is the problem with Notaros and a counter-example: Where would you put those voltage sources modeling the EMF so that you can measure the correct voltages across two neighboring resistors ie. V(Ra,Rb), V(Rb,Rc), V(Rc, Rf), V(Rf, Re), V(Re, Rd), V(Rd, Ra).

That is a very good question that has been answered in this forum many, many times: each resistor in the loop behaves both as voltage source a resistor in series.  Check this post:

https://www.eevblog.com/forum/amphour/562-electroboom!/msg3830852/#msg3830852

Fair enough, but my circuit has only six resistors. Where would you put those voltage sources modeling the EMF in the circuit so that it will be possible to measure correct voltages a) across each individual resistor, and b) across two consecutive resistors?

[Jesse Gordon]

That was my challenge to you, the task was to find the voltages across the resistors and the wires:


And that's what you came up with:


Which of course brings up the question why you found it necessary to add a "transformer secondary" to find the voltage across "2R".

You call it an "added secondary" but it MEASURES AND MODELS the exact same as if the right hand volt meter was instead on the left. Doesn't matter where it is. It doesn't loop through the core, which means it's not another winding.

Remember, KVL requires two-terminal elements. If we're not using a two-terminal element, OF COURSE kvl isn't even applicable.

You want me to run a volt meter lead through the core which effectively adds another secondary winding, making it into a 3 terminal element, and as such, it's no longer applicable for KVL.

Before I go further into the details of why I think your explanation is rubbish, let me expand on "observable reality":

What is observed is not reality

That figures.

until you've asked "Why is it so?" often enough to rule out all possible reasons but one. The idea of it being enough to just observe and not ask the "Why is it so?" question has directly lead to the creation of divine beings, or gods, to explain phenomena of nature in ancient cultures. People observed weather and the changing of seasons and as they were not able to explain and thus gods were created.

You, instead of asking the right questions, just try to confirm your beliefs. Instead of asking why the volt meters in Lewins experiment show different voltages you say "He's just a fool, he made a mistake, it's bad probing". When asked about the mechanism that induces voltage in a transformer winding you say "It's Nature".

I feel now that I did injustice to the flatearthers by likening you to them.

You realize the feeling is mutual, right?

Because, as the Physicist Sabine Hossenfelder said about them, their science is wrong, but not stupid.

Anyway, thank you for answering my question about which of the loops in my diagram you consider a "transformer secondary" and which are not. I knew the answer beforehand of course, but I needed you to confirm it with your own words so that there will be no wiggling out of it later.

Which I'm sure you will quote out of context, conveniently forgetting that I said that it's how IT MODELS AND MEASURES. Don't forget that part when you quote me, ya know?

What I can't understand is your (and all of Team Lewin's) refusal to answer my question. It's not even about Lewin's exact circuit. What's the harm in conceding that KVL at the very least appears to hold in the following circuit?

[Jesse Gordon]

Well folks that better be my two days for this week.

I don't understand why Team Lewin cannot see that a two-terminal toroidal transformer secondary makes a perfectly lumped element for use in a KVL loop.

Even the Rolls Royce of textbooks says that transformers are common lumped elements for a KVL loop. Dude.

Lumped circuits are obtained by connecting lumped elements. Typical
lumped elements are resistors, capacitors, inductors, and transformers.

PM me if anyone actually answers my question, but I suspect they won't.

I've asked it enough times to enough Team Lewin members I suspect nobody is going to.

If there's any newcomers, here's the question again.

Question: In the following diagram, in a real life physical lab test performed with real (time synchronized) volt meters with a real transformer and real resistors CONNECTED AS SHOWN, will the readings of all the volt meters sum to zero, within the accuracy and resolution limitations of the volt meters? YES or NO.

(Or if you believe SOMETIMES is the answer, then explain one scenario for a YES condition and one scenario for a NO condition WITH THE VOLT METERS CONNECTED AS SHOWN - Running additional conductors through the transformer core is not allowed - nor is removing existing conductors from through the transformer core!)

[Kalvin]

Here is the problem with Notaros and a counter-example: Where would you put those voltage sources modeling the EMF so that you can measure the correct voltages across two neighboring resistors ie. V(Ra,Rb), V(Rb,Rc), V(Rc, Rf), V(Rf, Re), V(Re, Rd), V(Rd, Ra).
<removed the image>

That is a very good question that has been answered in this forum many, many times: each resistor in the loop behaves both as voltage source a resistor in series.  Check this post:

https://www.eevblog.com/forum/amphour/562-electroboom!/msg3830852/#msg3830852

Let's say that someone is asking you: "We all know that a magnet has two poles N and S, and it can clearly be seen that the magnetic field starts at N and ends in S. But when there is a current flowing in a wire, a magnetic field will be created around the wire. Where does this magnetic field start and end?".

Would you explain this phenomenon something like this: "Well, you can think this situation as there are lots of very small magnets around the wire forming a closed loop, and that is why it is not possible to determine the start and end of the magnetic field". And the next question from that person will be: "Ok, and where do those little magnets come from?".

Or, would you explain it like this: "The current flowing in a wire is inducing a magnetic field around the wire, forming a closed loop, and it is not really possible to find the start and end of the magnetic field". Then that person is insisting: "How is it possible that there is a magnetic field without magnets. Your explanation is totally wrong! There has to be magnets somewhere, and every kid knows that magnets are creating a magnetic field, and magnetic field start at N and end in S."

[Kalvin]

Check the attached pdf from Electromagnetics by Notaros, pages 279-280, example 6.6.

Notaros seems to be modeling a similar circuit so that the EMF inducing the current is shown as two lumped voltage sources in the circuit, instead of computing the induced current in the distributed circuit due to the EMF. I kind of understand Notaros wanting to model the EMF into the circuit, but doing so Notaros is actually converting a non-conservative circuit into a conservative one. To me that looks like an illegal chess move (converting a non-conservative circuit into a conservative circuit).

Ok, tell me why you think the circuit is non-conservative.

I am not a physicist, so I am explaining it as follows:

1. When there is a constant current flowing in a wire, a magnetic field with a constant strength will be induced around this current carrying wire. The strength of the induced magnetic field is proportional to the current in the wire.

2. But this is not true another way around: When there is a constant magnetic field around the wire, there will not be a current induced in the wire. Only a changing magnetic field will induce a current in a wire. The magnitude of the current induced into the wire is proportional to the rate of change of the magnetic field. In order to maintain a constant current in a wire, the strength of the magnetic field shall be increasing at a constant rate.

This fact that "this is not true another way around" when a magnetic field is inducing current in a wire makes this circuit non-conservative.

[bsfeechannel]

Check the attached pdf from Electromagnetics by Notaros, pages 279-280, example 6.6.

Notaros seems to be modeling a similar circuit so that the EMF inducing the current is shown as two lumped voltage sources in the circuit, instead of computing the induced current in the distributed circuit due to the EMF. I kind of understand Notaros wanting to model the EMF into the circuit, but doing so Notaros is actually converting a non-conservative circuit into a conservative one. To me that looks like an illegal chess move (converting a non-conservative circuit into a conservative circuit).

What Notaros did was a math trick, very common in textbooks, but that unfortunately confuses KVLers. They think that if you model some circuit with an equivalent circuit, the components of that equivalent circuit will be found in the modeled circuit.

For instance, this is a very simplified model of a transistor for small signals at low frequencies.



KVLers think that if they open a transistor up they'll find a resistor connected in parallel with a voltage-controlled current source. Well, no. That's just a mathematical trick to help you solve the circuit. A lot of assumptions are implicit in this model. Some of them are in the model name. Signals must be small and frequencies, low, among other things (like, for example, ambient temperature, biasing, etc.)

Notaros modeling gives the same result if he decided to use Faraday's law, however there are a lot of assumptions that he doesn't mention, just as in the transistor model. One of them is that there's no real battery or generator in the path of the circuit.

KVLers can't understand that the battery they are looking for is not in the resistors or the wires. Their explanations always contradict each other. For example. When the loop with two dimensionally small resistors are connected with wires, they say that the voltage is generated in the wires, but not in the resistors. When we eliminate the wires, or when the wires are the resistors themselves, they say that itsy bitsy teeny tiny little batteries suddenly migrate inside the resistors.

What they don't tell you is when exactly these itsy bitsy teeny tiny little batteries migrate from the wires to the resistors. There's no theory to predict that. Search and you'll not find anywhere in the literature about electromagnetism.

Notaros, for example, contradicts the itsy bitsy teeny tiny little battery model, as he put two lumped generators in series with the resistors, although his loop is comprised of two resistive wires and nothing else.

[bsfeechannel]

According to team Lewin the induced EMF due to Faraday's law is 'special'

Precisely. That's what Michael Faraday himself discovered on 28 October 1831.

(like themselves)

Nah. We are just regular people who decided to not give ears to charlatubers but set out to study electromagnetism like real men.

because something-something and can not be treated just like any other EMF despite that all of them are measured in volts...

You're right again. You're starting to see the light. Hang out with us and soon you'll understand the "something-something" and how being a KVLer really sucks.

[Kalvin]

Check the attached pdf from Electromagnetics by Notaros, pages 279-280, example 6.6.

Notaros seems to be modeling a similar circuit so that the EMF inducing the current is shown as two lumped voltage sources in the circuit, instead of computing the induced current in the distributed circuit due to the EMF. I kind of understand Notaros wanting to model the EMF into the circuit, but doing so Notaros is actually converting a non-conservative circuit into a conservative one. To me that looks like an illegal chess move (converting a non-conservative circuit into a conservative circuit).

What Notaros did was a math trick, very common in textbooks, but that unfortunately confuses KVLers. They think that if you model some circuit with an equivalent circuit, the components of that equivalent circuit will be found in the modeled circuit.

I do not really care who is KVLer and who is not. I am just trying to understand how Dr. Lewin's circuit needs to be analyzed. So far my understanding can be summarized as follows:

1. The circuit is residing inside a magnetic field, so it should not be modeled with lumped sources.
2. Applying #1: The EMF induced by the magnetic field cannot really be modeled as lumped voltage source(s).
3. There is a current flowing in the circuit due to EMF induced by the magnetic field, and its magnitude is EMF/R_total.
4. Trying to incorporate the induced EMF into circuit model is an illegal chess move (see #2 and #3).
5. Although it may seem counterintuitive, but there can be a current flowing in the circuit without voltage sources in the circuit.
6. The magnetic field inducing this current is a non-conservative field, which means that KVL will not hold.
7. Consequence from #6: The voltage between two points in the circuit is path-dependent violating KVL, and there is no magic or probing error behind it.
8. Any attempt in modeling the voltage source(s) as lumped source(s), eg. transformer, will modify the original circuit in a fundamental way, and this new circuit is not identical to the original circuit anymore.
9. If it is found that KVL holds while analyzing this particular circuit, the model is probably ignoring one or more items from #1 - #8.

My understanding is that trying forcefully to model the original circuit using lumped sources (eg. transformers etc.) so that KVL will still hold has lead into this debate.

[Sredni]

1. Almost. The circuit includes (or better, cuts) the variable magnetic flux. But the circuit itself (i.e. the components and the conductors joining them can be in a region of space where there is no magnetic field at all (excluding that generated by the flow of the current in it, but we consider that negligible in the case of Lewin's ring)
2. Correct.
3. Correct
4. Trying to incorporate the nonlocalized EMF on the ring with lumped sources will give you a voltage configuration around the ring that will not correspond to the actual physical system (there will be jumps in correspondence of the lumped sources); trying to distribute it along the ring will give you a distribution of voltage corresponding to the effects of the coloumbian field alone, as if the Eind component of the field had been removed leaving the charges (at a given instant of time) frozen where they were. In my next posts I will show how this is a 'partial' description of the system.
5. Yeah, I guess you can say so.
6. The magnetic field inducing this current is a non-conservative field, yes, but most importantly it is changing and is therefore associated with a non-conservative induced electric field Eind. It's this non-conservative component of the electric field that messes things up from the point of view of voltage (which is the path integral of the total electric field Etot = Eind + Ecoul). KVL will not hold if you consider paths that follow the curling electric field full circle - it is easier to see it in this way: KVL will not hold if your closed voltage loop is going around the changing flux region.
7. Correct. It is basically a consequence of the fact that by 'going around' you eliminate the possibility to 'compensate' the contributes of Etot to path integral going 'along the path' with contributes 'against the path'. See my answer on EE Stack Exchange for pictures.
8. Correct.
9. Correct.

[Kalvin]

@Sredni, thank you for adding the details and corrections. Highly appreciated. 

[jesuscf]

Check the attached pdf from Electromagnetics by Notaros, pages 279-280, example 6.6.

Notaros seems to be modeling a similar circuit so that the EMF inducing the current is shown as two lumped voltage sources in the circuit, instead of computing the induced current in the distributed circuit due to the EMF. I kind of understand Notaros wanting to model the EMF into the circuit, but doing so Notaros is actually converting a non-conservative circuit into a conservative one. To me that looks like an illegal chess move (converting a non-conservative circuit into a conservative circuit).

Here is the problem with Notaros and a counter-example: Where would you put those voltage sources modeling the EMF so that you can measure the correct voltages across two neighboring resistors ie. V(Ra,Rb), V(Rb,Rc), V(Rc, Rf), V(Rf, Re), V(Re, Rd), V(Rd, Ra).

That is a very good question that has been answered in this forum many, many times: each resistor in the loop behaves both as voltage source a resistor in series.  Check this post:

https://www.eevblog.com/forum/amphour/562-electroboom!/msg3830852/#msg3830852

Fair enough, but my circuit has only six resistors. Where would you put those voltage sources modeling the EMF in the circuit so that it will be possible to measure correct voltages a) across each individual resistor, and b) across two consecutive resistors?

That is exactly the problem: the resistors are both behaving as a voltage source and a resistor when in a loop exposed to a varying magnetic field.  But you only have access to the terminals of the resistor, so when you measure across the terminals you'll get the net voltage: the generated EMF minus the voltage drop due to ohms law.

[Kalvin]

That is exactly the problem: the resistors are both behaving as a voltage source and a resistor when in a loop exposed to a varying magnetic field.  But you only have access to the terminals of the resistor, so when you measure across the terminals you'll get the net voltage: the generated EMF minus the voltage drop due to ohms law.

Are you suggesting that if I have for example six resistors with identical resistance but with different physical lengths eg. 0402, 0603, 0805, 1206, and leaded (non-inductive) resistors, I should see different voltages across these resistors due to the different physical sizes because the longer resistors should have getting more EMF than the shorter ones?

Edit: For example if 1206 is three times the length of 0402, the 1206 should be getting three times the EMF?

[jesuscf]

Check the attached pdf from Electromagnetics by Notaros, pages 279-280, example 6.6.

Notaros seems to be modeling a similar circuit so that the EMF inducing the current is shown as two lumped voltage sources in the circuit, instead of computing the induced current in the distributed circuit due to the EMF. I kind of understand Notaros wanting to model the EMF into the circuit, but doing so Notaros is actually converting a non-conservative circuit into a conservative one. To me that looks like an illegal chess move (converting a non-conservative circuit into a conservative circuit).

What Notaros did was a math trick, very common in textbooks, but that unfortunately confuses KVLers. They think that if you model some circuit with an equivalent circuit, the components of that equivalent circuit will be found in the modeled circuit.

For instance, this is a very simplified model of a transistor for small signals at low frequencies.



KVLers think that if they open a transistor up they'll find a resistor connected in parallel with a voltage-controlled current source. Well, no. That's just a mathematical trick to help you solve the circuit. A lot of assumptions are implicit in this model. Some of them are in the model name. Signals must be small and frequencies, low, among other things (like, for example, ambient temperature, biasing, etc.)

Notaros modeling gives the same result if he decided to use Faraday's law, however there are a lot of assumptions that he doesn't mention, just as in the transistor model. One of them is that there's no real battery or generator in the path of the circuit.

KVLers can't understand that the battery they are looking for is not in the resistors or the wires. Their explanations always contradict each other. For example. When the loop with two dimensionally small resistors are connected with wires, they say that the voltage is generated in the wires, but not in the resistors. When we eliminate the wires, or when the wires are the resistors themselves, they say that itsy bitsy teeny tiny little batteries suddenly migrate inside the resistors.

What they don't tell you is when exactly these itsy bitsy teeny tiny little batteries migrate from the wires to the resistors. There's no theory to predict that. Search and you'll not find anywhere in the literature about electromagnetism,

Notaros, for example, contradicts the itsy bitsy teeny tiny little battery model, as he put two lumped generators in series with the resistors, although his loop is comprised of two resistive wires and nothing else.

No dumdum, we know the MOSFET small signal equivalent circuit comes from this equation (for an enhancement N-MOSFET):

\$i_D  = \frac{1}{2}k_n^{'} \frac{W}{L}(v_{GS}  - V_t )^2 \left( {1 + \lambda v_{DS} } \right)\$

when v_GS is small and we apply superposition to get the AC component (did you understand all those word?).  What you call 'mathematical tricks' is a fundamental part of engineering which you seem to be unaware off.

A side note for team Lewin: calling that induced voltage a 'tiny battery' is incorrect.  It is not a battery, it is an induced EMF that we represented in the circuit with voltage source.

EDIT: by the way, I have said it many, many times, that the same apply to wires and resistors:  under a varying magnetic field, both wires and resistors behave like a voltage source in series with a resistor.
 

[jesuscf]

That is exactly the problem: the resistors are both behaving as a voltage source and a resistor when in a loop exposed to a varying magnetic field.  But you only have access to the terminals of the resistor, so when you measure across the terminals you'll get the net voltage: the generated EMF minus the voltage drop due to ohms law.

Are you suggesting that if I have for example six resistors with identical resistance but with different physical lengths eg. 0402, 0603, 0805, 1206, and leaded (non-inductive) resistors, I should see different voltages across these resistors due to the different physical sizes because the longer resistors should have getting more EMF than the shorter ones?

Edit: For example if 1206 is three times the length of 0402, the 1206 should be getting three times the EMF?

Yes, for the resistors placed in a circle as you put then in the figure, the induced voltage is proportional to the length of the resistor, but the voltage drop only depends on the resistance.

[Kalvin]

That is exactly the problem: the resistors are both behaving as a voltage source and a resistor when in a loop exposed to a varying magnetic field.  But you only have access to the terminals of the resistor, so when you measure across the terminals you'll get the net voltage: the generated EMF minus the voltage drop due to ohms law.

Are you suggesting that if I have for example six resistors with identical resistance but with different physical lengths eg. 0402, 0603, 0805, 1206, and leaded (non-inductive) resistors, I should see different voltages across these resistors due to the different physical sizes because the longer resistors should have getting more EMF than the shorter ones?

Edit: For example if 1206 is three times the length of 0402, the 1206 should be getting three times the EMF?

Yes, for the resistors placed in a circle as you put then in the figure, the induced voltage is proportional to the length of the resistor, but the voltage drop only depends on the resistance.

Just to make sure that I understand you correctly: You are saying that if I have six 100 ohm 0402 resistors and measure the voltages across these resistors one at a time, I should get different voltage values when I have six 100 ohm 1206 resistors and repeat the voltage measurement across each resistor?