Does Kirchhoff's Law Hold? Disagreeing with a Master

[Berni]

]

By the way. Here is the real thing without the lumping box, in case someone still has some doubts.

Yep that's what it would show without the box.

Notice that the inner voltmeters still show 0.1V and 0.9V? Care to explain why they didn't change regardless of the shielding box being there while others did change?

I can't see where we are disproving ourselves. We are not claiming anything. We're consistently showing that the claim that Kirchhoff always hold is nothing but quackery.

It always holds in circuit meshes, not elsewhere. Typical word twisting as usual.

I wonder when you realize that those guys do not have word "agree" in their vocabulary They are ready to disprove their own words - if it is you who is speaking

Yeah this has turned into a Maxwell versus Kirchhoff pissing contest 15 pages ago. But so far i have yet to see a good explanation why the two can't be both used provided you know how to use them rather than just slapping formulas on things without knowing what they actually do.

[ogden]

We're consistently showing that the claim that Kirchhoff always hold is nothing but quackery.

You have serious issues. Nobody claims that Kirchhoff always hold.

[bsfeechannel]

By the way. Here is the real thing without the lumping box, in case someone still has some doubts.

Yep that's what it would show without the box.

Notice that the inner voltmeters still show 0.1V and 0.9V? Care to explain why they didn't change regardless of the shielding box being there while others did change?

Of course. Because the line integral along the path that includes them and the wires is exactly the same. In other words, the varying magnetic field that the meters and the wires are encircling is exactly the same. The magnetic field outside the closed path doesn't affect the EMF.

This is what Faraday discovered and Maxwell described mathematically. As simple as that. That's the way nature works. There's nothing we can do to change that. You have to accept it. Not because I'm tell you, but because every time you try to repeat this experiment, it will always work that way.

There is, of course, an explanation for the underlying phenomenon of induction, but it is not the topic of this thread.

I can't see where we are disproving ourselves. We are not claiming anything. We're consistently showing that the claim that Kirchhoff always hold is nothing but quackery.

It always holds in circuit meshes, not elsewhere. Typical word twisting as usual.

NOOOOOOOOOO. Kirchhoff doesn't always hold even for circuit meshes. The inductor itself is a proof of that.

If Kirchhoff always held you couldn't even have inductors, as the voltage inside an inductor, i.e. along the path of the wire, is zero and outside it is different from zero. How can that be?



You don't understand it because you didn't read Feynman carefully as I recommended you to. This explanation is there.

It's because Kirchhoff fails that we have inductors, generators, transformers, antennas, etc.

Thanks to your favorite deity, or the lack thereof, that Kirchhoff fails. The failure of Kirchhoff is the best thing that could happen to humankind. Every time Kirchhoff fails, the world smiles. (I think I'll create a t-shirt with those words.)

I wonder when you realize that those guys do not have word "agree" in their vocabulary They are ready to disprove their own words - if it is you who is speaking

Yeah this has turned into a Maxwell versus Kirchhoff pissing contest 15 pages ago. But so far i have yet to see a good explanation why the two can't be both used provided you know how to use them rather than just slapping formulas on things without knowing what they actually do.

This is not a pissing contest between Maxwell and Kirchhoff. As Kirchhoff is a special case of Maxwell, the only thing we are trying to show you is exactly that.

[bsfeechannel]

We're consistently showing that the claim that Kirchhoff always hold is nothing but quackery.

You have serious issues. Nobody claims that Kirchhoff always hold.

Ogden said that Mehdi is nobody. Duly noted.

[ogden]

We're consistently showing that the claim that Kirchhoff always hold is nothing but quackery.

You have serious issues. Nobody claims that Kirchhoff always hold.

Ogden said that Mehdi is nobody. Duly noted.

I did not say anything about Mehdi. Your perception is very strange to say it politely.
You shall provide proof of your claim - show where Mehdi say "Kirchhoff always hold".

[bsfeechannel]

Look up the word sarcasm in the dictionary.

[ogden]

Look up the word sarcasm in the dictionary.

There's no need to telegraph every new word you just learned.

[Berni]

Of course. Because the line integral along the path that includes them and the wires is exactly the same. In other words, the varying magnetic field that the meters and the wires are encircling is exactly the same. The magnetic field outside the closed path doesn't affect the EMF.

This is what Faraday discovered and Maxwell described mathematically. As simple as that. That's the way nature works. There's nothing we can do to change that. You have to accept it. Not because I'm tell you, but because every time you try to repeat this experiment, it will always work that way.

There is, of course, an explanation for the underlying phenomenon of induction, but it is not the topic of this thread.

Yes, so when you say they are exactly the same also means that you are saying this circuit exactly acts exactly the same as a ideal transformer. If not, can you show in what way does it behave differently?

I can't see where we are disproving ourselves. We are not claiming anything. We're consistently showing that the claim that Kirchhoff always hold is nothing but quackery.

It always holds in circuit meshes, not elsewhere. Typical word twisting as usual.

NOOOOOOOOOO. Kirchhoff doesn't always hold even for circuit meshes. The inductor itself is a proof of that.

If Kirchhoff always held you couldn't even have inductors, as the voltage inside an inductor, i.e. along the path of the wire, is zero and outside it is different from zero. How can that be?



You don't understand it because you didn't read Feynman carefully as I recommended you to. This explanation is there.

It's because Kirchhoff fails that we have inductors, generators, transformers, antennas, etc.

Thanks to your favorite deity, or the lack thereof, that Kirchhoff fails. The failure of Kirchhoff is the best thing that could happen to humankind. Every time Kirchhoff fails, the world smiles. (I think I'll create a t-shirt with those words.)

Have you ever did AC circuit analysis my hand? If you did then i would have assumed you would have less trouble understanding what an inductor is. Sometimes circuit modeling even uses inductors where there are no magnetic effects involved  (One such example is the common model of a quartz crystal). An inductor is simply U=L*di . If you want to have always zero voltage over it just give it 0H of inductance, but i don't think that's a particularly useful use case for an inductor model.

What exactly are you trying to prove with that diagram? We all know you can't just directly use Kirchhoffs circuit laws inside real world magnetic fields. Did anyone say you can?

This is not a pissing contest between Maxwell and Kirchhoff. As Kirchhoff is a special case of Maxwell, the only thing we are trying to show you is exactly that.

Well yeah its a special case where circuit meshes (Where KVL is meant to be used) without realistically modeled wires happen to behave the same as a real world circuit.

Both Maxwell and Kirchhoff work just fine when used correctly. So why is it a problem that there are two ways to go about calculating electrical circuit behavior?

[bsfeechannel]

Yes, so when you say they are exactly the same also means that you are saying this circuit exactly acts exactly the same as a ideal transformer.

No I'm not saying that.

If not, can you show in what way does it behave differently?

It behaves differently because you made the lines of the varying magnetic field return elsewhere. Now V₁ and V₂ are equal to V₃ and V₄, respectively. This means that the sum of the voltages around the inner loop is 1V, which rightfully violates Kirchhoff. So this is not an ideal transformer anymore. This is just a regular circuit subject to induction like simply all real circuits.

Have you ever did AC circuit analysis my hand? If you did then i would have assumed you would have less trouble understanding what an inductor is.

I do not have any trouble with inductors. I designed and built an isolation transformer and documented it on the Internet. Do you remember?

Sometimes circuit modeling even uses inductors where there are no magnetic effects involved  (One such example is the common model of a quartz crystal). An inductor is simply U=L*di . If you want to have always zero voltage over it just give it 0H of inductance, but i don't think that's a particularly useful use case for an inductor model.

I bet you read Feynman again and didn't understand what he says when he defines an inductor.

What exactly are you trying to prove with that diagram? We all know you can't just directly use Kirchhoffs circuit laws inside real world magnetic fields. Did anyone say you can?

The voltages are not measured inside the field. An inductor is the simplest circuit mesh possible. It's just a piece of wire connected to whatever. The voltage across the piece of wire is always zero. The voltage across whatever is different from zero. If you add them up you get something different from zero.

Read Feynman once more and if you still don't understand, maybe we can help.

Well yeah its a special case where circuit meshes (Where KVL is meant to be used) without realistically modeled wires happen to behave the same as a real world circuit.

No. Stop this pseudo-scientific talk. KVL is a special case of Faraday when there's no varying magnetic field inside the circuit. Repeat until enlightened.

Both Maxwell and Kirchhoff work just fine when used correctly. So why is it a problem that there are two ways to go about calculating electrical circuit behavior?

There's ONLY ONE theory to explain electricity and magnetism: Maxwell, and Kirchhoff is just a special case of it. This is a tried and proven truth.

[Berni]

If not, can you show in what way does it behave differently?

It behaves differently because you made the lines of the varying magnetic field return elsewhere. Now V₁ and V₂ are equal to V₃ and V₄, respectively. This means that the sum of the voltages around the inner loop is 1V, which rightfully violates Kirchhoff. So this is not an ideal transformer anymore. This is just a regular circuit subject to induction like simply all real circuits.

So then if the voltages are different why do the voltmeters show the same values regardless of the circuit being represented with Maxwell or with a ideal transformer?

The last 3 voltmeters ware left out of the transformer model on purpose to show the difference. This is the reason why things don't work when Maxwell and ideal lumped circuit analysis is recklessly mixed together. If you stick to just one for the entire circuit then things work fine.

Have you ever did AC circuit analysis my hand? If you did then i would have assumed you would have less trouble understanding what an inductor is.

I do not have any trouble with inductors. I designed and built an isolation transformer and documented it on the Internet. Do you remember?

Then you also shouldn't have trouble understanding how to apply a transformer model to a real circuit.

What exactly are you trying to prove with that diagram? We all know you can't just directly use Kirchhoffs circuit laws inside real world magnetic fields. Did anyone say you can?

The voltages are not measured inside the field. An inductor is the simplest circuit mesh possible. It's just a piece of wire connected to whatever. The voltage across the piece of wire is always zero. The voltage across whatever is different from zero. If you add them up you get something different from zero.

Read Feynman once more and if you still don't understand, maybe we can help.

That's why i put the shielding box there, none of the voltages there are measured inside the field. What is the reason that the inside of the box could not be considered a transformer?

What part of Feynmans lecture did i understand wrong?

Well yeah its a special case where circuit meshes (Where KVL is meant to be used) without realistically modeled wires happen to behave the same as a real world circuit.

No. Stop this pseudo-scientific talk. KVL is a special case of Faraday when there's no varying magnetic field inside the circuit. Repeat until enlightened.

No thanks, that's called religion instead of engineering.

I believe something when its backed up by experimental data or a sensible explanation, not because someone told me to believe something without giving a reason to back it up. So far i still have not seen a explanation in what way circuit analysis is wrong about Dr. Lewins circuit (Even tho it reliably produces results that match the experimental results).

So far experimental results and explanations found on the topic show me that both are valid ways of evaluating the circuit and both produce identical results.

Both Maxwell and Kirchhoff work just fine when used correctly. So why is it a problem that there are two ways to go about calculating electrical circuit behavior?

There's ONLY ONE theory to explain electricity and magnetism: Maxwell, and Kirchhoff is just a special case of it. This is a tried and proven truth.

Exactly and Maxwell is explaining that one and is doing a great job. Kirhhoffs circuit laws instead explain how circuit meshes work, hence why they are not directly interchangeable.

Does this also mean we have to chose between Maxwell equations and Quantum electrodynamics to declare one of them being for the birds because they explain a similar area of science?

[bsfeechannel]

What part of Feynmans lecture did i understand wrong?

Alright. Since that's a broad question, let's investigate. Please, tell me what is the voltage (it does need to be a number) between points A and B in the picture below? We have a varying magnetic field.

[Berni]

Its undefined since you haven't specified a path.

[bsfeechannel]

Perfect. Now let's suppose that I define two paths: #1 from A to B and #2 from B to A. Let's suppose, then, that the voltages measured between these two points following these two different paths are different. If we start form point A via path #1 and return to it via path #2, and if we add up these two voltages, will we have zero volts?

[Sredni]

Ah alright that's what is bothering you, alright fine il do some drawing too.

I wonder when you realize that those guys do not have word "agree" in their vocabulary

You should be grateful for that.
Had I agreed with you a month ago, you would still not know how a transformer works.

[Berni]

Perfect. Now let's suppose that I define two paths: #1 from A to B and #2 from B to A. Let's suppose, then, that the voltages measured between these two points following these two different paths are different. If we start form point A via path #1 and return to it via path #2, and if we add up these two voltages, will we have zero volts?

Nope

[bsfeechannel]

Thank you. So far so good. But we can already notice that there's something strange here. Because we are accustomed to talk about voltages between two different points. Normally we tend to think that the voltage from a point to itself should be zero. Just because we chose different paths to go and come back we have a voltage. Since this is weird, let's call this voltage EMF (Electromotive Force).

I don't know the length of those paths, nor the area they bound, but since I know you know how to calculate this EMF, given the magnetic field B and the area, let's skip that part and suppose that this EMF is 1V.

Now I'd like to introduce you to the wire. Wire is an interesting material. The electric field inside it is always zero. No matter what. It doesn't care about magnetic fields, varying or static. It also doesn't care about electric fields outside itself. Its "jurisdiction" is limited to its premises. There electric fields are banned. Let's have this properties very well understood in our minds for the next question.

If we connect points A and B with a piece of this wire, what will be the voltage between A and B?

[Berni]

Following the textbook definition of voltage
Path1: 0V
Path2: 866.6 mV

Following the circuit analysis definition of voltage:
Path1: 133.4mV
Path2: 133.4mV

[bsfeechannel]

Can  you please show how you reached those numbers?

[Berni]

Following the textbook definition of voltage
Path1: 0V (Because as you said there is a wire there that nulls out the sum of E fields)
Path2: No wire to null the field so the voltage is purely the EMF around that path, however the EMF was specified for the whole loop so Path1 has to be subtracted out
Total Area of loop: 35.295 cm2
Total EMF voltage around the loop: 1V
Loop area occupied by Path1: 4.71 cm2
Loop area ratio: 4.71 / 35.295 =  0.1334
Loop2 EMF: 1V * (1-0.1334) = 866.6 mV


Following the circuit analysis definition of voltage:
Path1: Amount of charge separation caused by the EMF in the wire
Loop1 EMF: 1V * 0.1334 = 133.4mV
Path2: Same two points so same voltage: 133.4 mV


If your results don't agree please also explain how you reached your numbers.

EDIT:
Sorry forgot about the electrostatic field created by the wire affecting the other path. See: https://www.eevblog.com/forum/chat/does-kirchhoffs-law-hold-disagreeing-with-a-master/msg2144605/#msg2144605

[Sredni]

Following the circuit analysis definition of voltage:
Path1: Amount of charge separation caused by the EMF in the wire
Loop1 EMF: 1V * 0.1334 = 133.4mV
Path2: Same two points so same voltage: 133.4 mV


If your results don't agree please also explain how you reached your numbers.

I do not want to spoil bsfeechannel's fun, so I will only pose a question.
To be clear, the unique, single-valued, 'circuit-analysis-defined' voltage across the physically tangible piece of wire has a value that depends on the area (or ratio thereof) that such wire defines with an arbitrary imaginary path?

I mean, if the imaginary 'path #2' had a vertical side  comprised between the symbols "2" and "B" inside the square, you would have found a different value for the unique circuit-analysis voltage? And another one, if it went way out on the left of the paper?

Edit: grammar and clarified where w and B are.

[bsfeechannel]

I do not want to spoil bsfeechannel's fun, so I will only pose a question.

No wuckers.

[bsfeechannel]

Following the textbook definition of voltage
Path1: 0V (Because as you said there is a wire there that nulls out the sum of E fields)
Path2: No wire to null the field so the voltage is purely the EMF around that path, however the EMF was specified for the whole loop so Path1 has to be subtracted out
Total Area of loop: 35.295 cm2
Total EMF voltage around the loop: 1V
Loop area occupied by Path1: 4.71 cm2
Loop area ratio: 4.71 / 35.295 =  0.1334
Loop2 EMF: 1V * (1-0.1334) = 866.6 mV


Following the circuit analysis definition of voltage:
Path1: Amount of charge separation caused by the EMF in the wire
Loop1 EMF: 1V * 0.1334 = 133.4mV
Path2: Same two points so same voltage: 133.4 mV


If your results don't agree please also explain how you reached your numbers.

I think I owe you an apology. My drawing was not sufficiently clear. The magnetic field B should be spread uniformly all over the page. But that's OK, because the next step would be to make the magnetic field spread uniformly over the area like in the picture below. I.e., it is zero outside the loop formed by paths #1 and #2, and it is also zero for the blank portion of the same loop. B's intensity will be adjusted so that, together with that area (that you may consider square if you want), the EMF is still 1V.

I also forgot to say that the wire does not produce charge separation. It just "magically" nullifies any attempt at producing an electric field inside it. However you can keep on calculating your "circuit analysis definition of voltage" as if it were, if you want.

As for the voltage according to your "text definition of voltage", path #1 is OK, even with my unclear drawing. Path #2 I think would be a different value, but since my drawing is screwed, it is OK that at least you considered it different from zero.

So now, we're gonna use this ideal piece of wire to cover path #2 and we will leave path #1 free. We still need to know the voltage between points A and B. Let's see if our calculations will lead to the same value, shall we?

[Berni]

Following the circuit analysis definition of voltage:
Path1: Amount of charge separation caused by the EMF in the wire
Loop1 EMF: 1V * 0.1334 = 133.4mV
Path2: Same two points so same voltage: 133.4 mV


If your results don't agree please also explain how you reached your numbers.

I do not want to spoil bsfeechannel's fun, so I will only pose a question.
To be clear, the unique, single-valued, 'circuit-analysis-defined' voltage across the physically tangible piece of wire has a value that depends on the area (or ratio thereof) that such wire define with an arbitrary imaginary path?

I mean, if the imaginary 'path #2' had a vertical side  comprise between 2 and B, you would have found a different value for the unique circuit-analysis voltage? And another one, if it went way out on the left of the paper?

The dependence on Path2 comes from the fact that bsfeechannel defined the strength of the field being as strong to generate 1V of EMF for the entire loop. So given this being a uniform field means that a larger surface area always means more of the field is enclosed in the loop, this means the field has to be weaker to still produce 1V. Hence why making the loop area around Path2 larger causes the voltage on Path1 appear smaller because the field is still in the same spot but its weaker. It also changes if you move the field origin around, but does not change once a loop is a fully closed path.

[Berni]

I think I owe you an apology. My drawing was not sufficiently clear. The magnetic field B should be spread uniformly all over the page. But that's OK, because the next step would be to make the magnetic field spread uniformly over the area like in the picture below. I.e., it is zero outside the loop formed by paths #1 and #2, and it is also zero for the blank portion of the same loop. B's intensity will be adjusted so that, together with that area (that you may consider square if you want), the EMF is still 1V.

I also forgot to say that the wire does not produce charge separation. It just "magically" nullifies any attempt at producing an electric field inside it. However you can keep on calculating your "circuit analysis definition of voltage" as if it were, if you want.

As for the voltage according to your "text definition of voltage", path #1 is OK, even with my unclear drawing. Path #2 I think would be a different value, but since my drawing is screwed, it is OK that at least you considered it different from zero.

So now, we're gonna use this ideal piece of wire to cover path #2 and we will leave path #1 free. We still need to know the voltage between points A and B. Let's see if our calculations will lead to the same value, shall we?

Just missed your reply while writing my post.
Yes i assumed the field B to be uniform across the page since there was no confinement of the field mentioned.

Now that the wire is moved Path2 is 0V since the wire is nulling the sum E field along that path.

[bsfeechannel]

And what about path #1?