Does Kirchhoff's Law Hold? Disagreeing with a Master

[bsfeechannel]

Right. Be prepared to become enlightened.

Since you rejected my baby-stepped method for guiding you to enlightenment, I'll be forced to reveal the shocking truth to you. The conservation of energy holds for when Kirchhoff fails because the energy the resistor is dissipating comes from the fuh...., the fuh-fieh..., the fie... No, I can't. I can't put you through this emotional sacrifice. I have scruples.

[ogden]

Right. Be prepared to become enlightened.

Since you rejected my baby-stepped method for guiding you to enlightenment, I'll be forced to reveal the shocking truth to you. The conservation of energy holds for when Kirchhoff fails because the energy the resistor is dissipating comes from the fuh...., the fuh-fieh..., the fie... No, I can't. I can't put you through this emotional sacrifice. I have scruples.

Again you show that you can't even read 

I did not ask to tell where energy comes from. I ask you to show law of conservation of electrical energy using Maxwell's equations. Apparently you are afraid of what comes next after you do it.

[bsfeechannel]

Again you show that you can't even read 

I did not ask to tell where energy comes from. I ask you to show law of conservation of electrical energy using Maxwell's equations. Apparently you are afraid of what comes next after you do it.

Yes. I'm afraid you won't understand. Since you don't want to know where the energy comes from, it'll be impossible for you to understand it using Maxwell's equations, or whatever.

[ogden]

Since you don't want to know where the energy comes from, it'll be impossible for you to understand it using Maxwell's equations, or whatever.

Do not confuse public forum with private chat, tell for those who you think will understand.

To cut the crap: KVL is based on conservation of the charge which is based on law of conservation of energy. As soon as you write energy_generated_inthe_loop = energy_dissipated_inthe_resistor equation, KVL can be derived from it. Seems, you know it well and seems I know what abbreviation "BSFEE" means.

[Berni]

This was exactly my point. It doesn't make sense to talk about a voltage source as purely being an impedance.

A voltage source is NOT an impedance, much less "purely". Read Feynman lectures volume II chapter 22.
...
What determining the equivalent circuit of a battery has to do with measuring an impedance in an AC circuit under a varying magnetic field?
...
So what causes the change in their behavior is the _ _ _ _ _.

Yes exactly my point that a voltage source is not an impedance.

In that chapter 22 that you mention it clearly shows that induced voltage acts like a voltage source. So including the induced voltage when calculating impedance of a component is just as nonsense as directly calculating the impedance of a voltage source using the voltage across its terminals.

So putting it all together:
2 terminal components can't have multiple impedance at the same moment in time.
2 terminal components can't have multiple different currents running trough it at the same moment in time.
Since impedance relates current to voltage this also means the before mentioned impedance can only have one well defined voltage across it. But this also defines the path of the voltage as being trough this impedance, hence why it doesn't go against Maxwell. The induced voltage didn't disappear, but the component it self doesn't care about it. Its only the circuit around it that sees the voltage (Since the loop needs to be closed) as this voltage adds on to whatever voltage is presented on the terminals. Much like the equivalent model of a voltage source looks on its terminals.

is there any reason why you replaced the world field with underscores? Its not exactly a secret that magnetic fields are what makes inductors work.

...
As you confirm, not only the secondary doesn't behave like an inductor (there's no 90 degree phase shift), but also it is not even an impedance: because the voltage on the secondary is a function of something external to itself, which is in fact the _ _ _ _ _ generated by the current in the primary.
...
How can this be, once the primary is connected to a voltage source?
...
So now not even the primary can be identified as an inductor anymore.
...
Forbidden? Why? It perfectly demonstrates what I said before: if you don't understand the underlying physics of electromagnetism you'll be limited in your ability to design and analyze circuits.
...
If you read your own words again you'll see that you've already answered your question.

Exactly it doesn't behave like an inductor anymore, but instead behaves like a coupled inductor.

But it doesn't mean its inductance simply disappeared. The same magnetizing current is still needed to hold up the field, but because the two inductors are sharing the same flux means they can also share the magnetizing current. Since the resistor on the secondary can't provide a source of reactive current means that all the magnetizing current comes from the voltage source on the primary. The resistive load does however cause a in phase current that makes a opposing field in the secondary that affects the field in the primary, where it induces voltage according to Faradays law. Since there is a voltage source forcing a well defined voltage across the primary, this instead draws extra current to correct this field. This extra  in phase current is what drags the total current back away from lagging 90 degrees. As for the secondary, it has no need for out of phase current, because all of its magnetizing current is provided by the primary.

So the inductance didn't go anywhere. The effect of inductance is simply buried under the other currents.

So yeah, sorry i still don't see the exact circumstance when a piece of wire stops being an inductor. Or does becoming a coupled inductor not count as being inductive? If so please explain why.

At what point is my inductance explanation inconsistent with physics?

[bsfeechannel]

Today at 08:42:17 am » Insert Quote
You are ignoring this user.

It seems that you can't ignore me. Thank you. No wonder. I am managing to destroy mercilessly and systematically the myths you always held dear. But cheer up, dude. You'll be empowered by your new disbelief.

Do not confuse public forum with private chat, tell for those who you think will understand.

I've already done it. But you rejected it unceremoniously.

To cut the crap: KVL is based on conservation of the charge which is based on law of conservation of energy.

Charge conservation and energy conservation are two separate principles. Both can be derived for electromagnetism from Maxwell's equations.

Let's start with charge conservation, which is easier for a circuit-head guy like you to understand. You can find it demonstrated here.

In the picture below you can see how KCL fails, but charge conservation holds.



The sum of currents going in and coming out of the volume represented by the closed dashed line to the left is different from zero, violating KCL. But conservation of charge holds because the excess charge is being stored in the body inside the volume. On the volume to the right KCL holds, because no charge is being stored in the volume, so all the currents must add up to zero.

As soon as you write energy_generated_inthe_loop = energy_dissipated_inthe_resistor equation, KVL can be derived from it.

Energy conservation in electromagnetism is a little bit more complicated, and can be derived, as in the case of conservation of charge, from the modified (by Maxwell) Ampère's law, however you need to understand that the energy that's powering the resistor is not coming from a component in the circuit. While you don't accept this you'll be looking in vain around the wire for an EMF that will balance the voltage drop, and smashing your head against the wall.

And as in the case of charge conservation, we can also have KVL failing while energy conservation holds.

The difficulty Mehdi expressed in his first video comes exactly from not understanding this. For him, KVL can never fail, because that would represent a violation of energy conservation.

Nothing could be further than the truth.

EDIT: corrected the charge conservation equation in the attached picture (had forgot the minus sign).

[ogden]

Energy conservation in electromagnetism is a little bit more complicated, and can be derived, as in the case of conservation of charge, from the modified (by Maxwell) Ampère's law, however you need to understand that the energy that's powering the resistor is not coming from a component in the circuit.

Energy is delivered by the component of the circuit - wire loop. Most sources of electrical energy are energy conversion devices - so what? Instead of talking about law of electrical energy conservation, you play games around meaning of the word "generator". I can rewrite equation that needs to be filled-in with your wizdom if you are so picky about words I use: energy_delivered_bythe_wire_loop = energy_dissipated_inthe_resistor.

[ogden]

Let's start with charge conservation, which is easier for a circuit-head guy like you to understand. You can find it demonstrated here.

In the picture below you can see how KCL fails, but charge conservation holds.



The sum of currents going in and coming out of the volume represented by the closed dashed line to the left is different from zero, violating KCL. But conservation of charge holds because the excess charge is being stored in the body inside the volume.

It's just next fallacy of yours. Those two round objects on the left together form charged capacitor and wire between them - load where energy that is stored in the capacitor, dissipates. KCL holds.

[Berni]

I dont see how charge is conserved inside the dotted circle. Curent is charge divided by time anyway.

But yeah i can see what the point is, an example of KVL not holding. We KNOW that KVL is not a law of physics. It holds in most cases but not all, it only always holds in lumped circuit meshes. Hence why it cant be directly slapped onto any physical circuit, much like the rest of circuit analysis math. Go ahed and try to find a quote of me claiming it always holds in physical circuits in any of this thread

[ogden]

I dont see how charge is conserved inside the dotted circle. Curent is charge divided by time anyway.

He most likely did mean that charge is distributed evenly between two round objects. Yes, it is so - if there is separate point of reference (ground?) to measure voltages/charges of both round objects. In such case we have two capacitor paradox which again agrees with KVL.

[bsfeechannel]

I dont see how charge is conserved inside the dotted circle.

Charge conservation is just a matter of bookkeeping (as a matter of fact all conservation principles are). The dollar you spend has to be discounted from your account balance. That sort of thing.

∇·J = - ∂ρ/∂t means that the charges you see going away for good have to be discounted from the charges you hoard inside your closed surface (represented by the dashed line).

Or a little more rigorously, the total amount of charge you lose per unit area, per unit time, to the exterior of a close volume (∇·J) is equal to the rate of change over time of a decrease (hence the minus sign) on the amount of charge per unit volume (- ∂ρ/∂t).

Curent is charge divided by time anyway.

Precisely. Current is the rate of charges crossing an area per unit time.

So choose a closed region of space. Count the amount of charge you have in that volume. Say 10 coulombs. If you measure a current of 1 A, i.e. 1 coulomb per second, going out of that volume (and you see no other current), in one second you'll have 9 coulombs, because 1 coulomb will be gone.

If you have this current, plus another with a 2 amp intensity going in the volume, you will end up with 11 coulombs after one second.

You can have a situation in which the amount coulombs stored in the volume must be kept constant. In that case all that comes in per unit time has to go out. In other words, all currents must add up to zero. And that's KCL.

But yeah i can see what the point is, an example of KVL not holding. We KNOW that KVL is not a law of physics.

Kirchhoff studied carefully the behavior of currents and voltages in circuits and published the results of his findings in the "Annals of Physics". Then he derived his theorems, as he called them, from those empirical data. His discovery was a major breakthrough.

So KVL and KCL ARE laws of physics. But a law of physics has not to work under whatever condition. As important as it is to understand KVL and KCL it is to know when they hold and when they fail.

It holds in most cases but not all,

I would say that KVL and KCL do NOT hold most of the times. Where can you find a place on earth where you don't have varying electromagnetic fields? The thing is that we PRETEND that KVL and KCL hold by approximation. We stash fields inside capacitors and inductors, we create ground planes, employ shielded conductors, we decouple lines, inductors, capacitances, all to avoid having to deal with fields. And when we have to deal with them, we employ rules of thumb and equivalent approximate models.

And what we cannot tame and make to conform to KVL/KCL we call "parasitics".

This creates the illusion that KVL and KCL hold "in most cases". But it's only an illusion. Not that we will abandon this illusion all of a sudden. We need to know what it means, and not to try to linger to it if it clearly shows that we will be limited in our ability to interpret the phenomena around us.

[Berni]

But yeah i can see what the point is, an example of KVL not holding. We KNOW that KVL is not a law of physics.

Kirchhoff studied carefully the behavior of currents and voltages in circuits and published the results of his findings in the "Annals of Physics". Then he derived his theorems, as he called them, from those empirical data. His discovery was a major breakthrough.

So KVL and KCL ARE laws of physics. But a law of physics has not to work under whatever condition. As important as it is to understand KVL and KCL it is to know when they hold and when they fail.

It holds in most cases but not all,

I would say that KVL and KCL do NOT hold most of the times. Where can you find a place on earth where you don't have varying electromagnetic fields? The thing is that we PRETEND that KVL and KCL hold by approximation. We stash fields inside capacitors and inductors, we create ground planes, employ shielded conductors, we decouple lines, inductors, capacitances, all to avoid having to deal with fields. And when we have to deal with them, we employ rules of thumb and equivalent approximate models.

And what we cannot tame and make to conform to KVL/KCL we call "parasitics".

This creates the illusion that KVL and KCL hold "in most cases". But it's only an illusion. Not that we will abandon this illusion all of a sudden. We need to know what it means, and not to try to linger to it if it clearly shows that we will be limited in our ability to interpret the phenomena around us.

Yes for a time Kirchhoffs circuit laws ware the best explanation of electricity we had, but this was back in the mid 1800s. At that time we had no idea what an atom is made out of, we didn't even know electrons existed, radio waves have yet to be used to transmit information, mathematicians ware still discovering methods for working with complex numbers and some parts of calculus ware still being figured out.

Just like our understanding of what matter is made up of went from alchemy to Mendeleevs periodic table to atoms, to explaining atoms are made of some stuff in the middle, to figuring out its actually protons and neutrons in there, saying that are fundamental particles, but then later on managing to split them apart and finding quarks inside of them.

In the same way Maxwell did the next big step by explaining how electricity works in better more accurate detail that Kirchhoff could. At that point Kirchhoffs laws ware no longer considered laws of physics, its even in the name, they are called "Kirchoffs Cirucit Laws" since its circuits they apply to, not the theory of electricity itself, Maxwell has that now. But it didn't stop there, science kept on going and upon closer inspection found out that actually Maxwells explanation is still not quite the whole story, so the theory of Quantum electrodynamics was put together and it now carries the crown for the best theory of electricity (To this date that is, who knows for how long, there might be a even more fundamental one we haven't figured out yet).

So why do we still use Maxwells equations if they are wrong according to Quantum electrodynamics?  Its much like the reason why we still use Kirchhoffs circuit laws despite being wrong according to Maxwell. On a macroscopic level and under certain conditions these laws still work just fine, while being much more convenient to work with when you want to actually calculate them with actual numbers. The 3 sets of laws are basically just different abstraction layers for electricity. Just chose the desired abstraction level and be aware of its known limitations.

Tho to be honest there is very very little reason to go any deeper than Maxwells level of abstraction for engineering use.

[ogden]

As important as it is to understand KVL and KCL it is to know when they hold and when they fail.

Sure. Even more important is to understand when you do not apply KVL and KCL (Kirchoff's Circuit Law). You can't draw construct which is not even circuit - that has no return path for current, try to convince that current is flowing into nowhere, then happily conclude that KCL does not hold. It's not even laughable.

I would say that KVL and KCL do NOT hold most of the times. Where can you find a place on earth where you don't have varying electromagnetic fields? The thing is that we PRETEND that KVL and KCL hold by approximation. We stash fields inside capacitors and inductors, we create ground planes, employ shielded conductors, we decouple lines, inductors, capacitances, all to avoid having to deal with fields. And when we have to deal with them, we employ rules of thumb and equivalent approximate models.

And what we cannot tame and make to conform to KVL/KCL we call "parasitics".

Wow. With such rhetoric one can invalidate nearly every law of physics.

P.S. Nice video regarding electromagnetics

[SparkyFX]

As I said before, scientific populism is going to be a big problem a few yeas ahead.

Opinion based decisions are surely a problem (and i am guilty of making them myself), but anyway, science teaches to check your results, so "scientific populism" is an oxymoron - "pseudoscience" would be the word. Science also teaches that the observation of a process might interfere with the result (and therefore needs taken care of).

One usually does not need to understand astrophysics or biology (or have an opinion about them) to pick a fruit from a tree and eat it -> results count, the fruit exists, the process therefore works. It starts to matter once you want to know why and how the fruit grew, manipulate the process or want to make predictions about it.

I think it is a bit on the troll side to find two different perspectives on the same subject and try to push a wedge between the two, although both are able to produce the same result -> describe the same process. I reckon it is a good conversation starter and helped students to understand the differences between abstractions, simplifications (wiring diagrams do usually not contain dimensions, equivalent circuits) and physical reality, but if you start thinking in "camps" or "sides", insult others, the cause is somehow lost.

Coming from a practical approach you measure voltages, not fields - and field sensors will usually output an equivalent voltage. So the proof seems complicated without KVL. Trying to measure fields using the force exerted on an object takes the object (and eddy currents in it) into the equations, making it as complicated to calculate as a wiring diagram with all equivalent components (parasitic inductance, capacitance) in place. So both suffer from the same problem, even if one is proven with "all fields are considered" and the other is disproven using "observation influenced the result".

[bsfeechannel]

It's just next fallacy of yours. Those two round objects on the left together form charged capacitor and wire between them - load where energy that is stored in the capacitor, dissipates. KCL holds.

Let's examine KCL in the words of Kirchhoff himself:

Wird ein System von Dräten, die auf eine ganz beliebige Weise mit einander verbunden sind, von galvanischen Strömen durchflossen, so ist:

1) wenn die Drähte 1, 2, ...µ in einem Punkte zusammenstoßen,

I₁ + I₂ + ...+I_µ = 0,

wo, I₁, I₂, ... die Intensitäten der Ströme bezeichnen, die jene Drähte durchfließen, alle nach dem Berührungspunkte zu als positiv gerechnet;

Translation

Let a system of wires, which are connnected with each other in an entirely arbitrary way, be traversed by galvanic currents [i.e. DC], then:

1) if the wires 1, 2, ...µ meet at one point,

                                I₁ + I₂ + ...+I_µ = 0,

where, I₁, I₂, ... designate the intensities of the currents, which flow through each wire, all calculated as positive in the direction of the point of contact;

We have just one wire, with just one current. This problem is analogous to the KVL problem: we have just one voltage, and no other to balance it that can be directly measured in the circuit.

[bsfeechannel]

So why do we still use Maxwells equations if they are wrong according to Quantum electrodynamics?  Its much like the reason why we still use Kirchhoffs circuit laws despite being wrong according to Maxwell.

Kirchhoff's laws are not wrong according to Maxwell. Maxwell's equations do not only confirm that KVL and KCL are right, but also state in WHAT CONDITION they are right.

The source of the errors is elsewhere.

On a macroscopic level and under certain conditions these laws still work just fine, while being much more convenient to work with when you want to actually calculate them with actual numbers. The 3 sets of laws are basically just different abstraction layers for electricity. Just chose the desired abstraction level and be aware of its known limitations.

A cat is a special case of mammal, and the description of a mammal is an abstraction of a cat (and every other mammal, as a matter of fact).

QED is an abstraction of Maxwell's equations, as Maxwell's equations are abstractions of KVL/KCL.

KVL/KCL are a special case of Maxwell's equations, as Maxwell's equations are special cases of QED.

KVL/KCL are NOT abstractions of Maxwell's equations by the simple fact that they don't work for all the cases for which Maxwell's equations do.

This is another illusion. Because we ram KVL/KCL down the throats of our circuits and close our eyes to the errors due to this approximation (and we manage to get away with it in many cases) we have the impression that KVL/KCL are just simplified (hence abstracted) cases of Maxwell's equations. But this mindset will bite you in the butt sooner or later. You need to be always aware of the limitations of KCL/KVL and, if the error due to approximating Maxwell to Kirchhoff is gross enough, resort to what will give you the most accurate prediction.

Tho to be honest there is very very little reason to go any deeper than Maxwells level of abstraction for engineering use.

I think the inventors of the transistor would not agree with you, but anyway...

[bsfeechannel]

I dont see how charge is conserved inside the dotted circle. Curent is charge divided by time anyway.

He most likely did mean that charge is distributed evenly between two round objects. Yes, it is so - if there is separate point of reference (ground?) to measure voltages/charges of both round objects. In such case we have two capacitor paradox which again agrees with KVL.

Nope. The two capacitor paradox is about energy conservation not charge conservation. In the paradox, you have two wires. Here we have just one. In the paradox the wires are ideal. Here the wire can have resistance, inductance, and nonzero length.

[ogden]

We have just one wire, with just one current.

In case you insist that there is just one wire and just one current meaning no path for return current - then I say that you don't even have circuit, thus Kirchoff's Circuit Law do not apply. There is huge difference between "do not apply" and "do not hold".

This problem is analogous to the KVL problem: we have just one voltage, and no other to balance it that can be directly measured in the circuit.

You just mentioned voltage. Very nice. Charge was mentioned before - so those two round objects together indeed is capacitor, C=q/V. Here's your circuit - capacitor with load in form of wire. I already said so you just do not listen:

It's just next fallacy of yours. Those two round objects on the left together form charged capacitor and wire between them - load where energy that is stored in the capacitor, dissipates. KCL holds.

[bsfeechannel]

In case you insist that there is just one wire and just one current meaning no path for return current - then I say that you don't even have circuit, thus Kirchoff's Circuit Law do not apply. There is huge difference between "do not apply" and "do not hold".

Nope. Kirchhoff says clearly that the wires can be connected in an entirely arbitrary way. So there is no requirement for them to form a circuit or to provide a path for a return current.

so those two round objects together indeed is capacitor, C=q/V.

Not inside the dashed line. There is only one wire providing charges to (or removing from) that area.

[seagreh]

And I always thought, the EMF is defined as the tangential force per unit charge in the wire integrated over length, once around the complete circuit/loop! But not at all, it was hiding in the resistor and my voltmeter!

You clearly thought wrong, I regret. EMFs will never "hide" inside (static) wires (considered as ideal, that is).

Sorry, my wording was wrong, I should have said ‘I always believed, the EMF...’.!
Because the clearly wrong ‘thought’ is from Feynman Volume II chapter 16 Induced Currents.
As you say, electromag is so unintuitive, so much bullshit around.... you can’t even trust books anymore.

[seagreh]

Let's examine KCL in the words of Kirchhoff himself:

Wird ein System von Dräten, die auf eine ganz beliebige Weise mit einander verbunden sind, von galvanischen Strömen durchflossen, so ist:

1) wenn die Drähte 1, 2, ...µ in einem Punkte zusammenstoßen,

I₁ + I₂ + ...+I_µ = 0,

wo, I₁, I₂, ... die Intensitäten der Ströme bezeichnen, die jene Drähte durchfließen, alle nach dem Berührungspunkte zu als positiv gerechnet;

Translation

Let a system of wires, which are connnected with each other in an entirely arbitrary way, be traversed by galvanic currents [i.e. DC], then:

1) if the wires 1, 2, ...µ meet at one point,

                                I₁ + I₂ + ...+I_µ = 0,

where, I₁, I₂, ... designate the intensities of the currents, which flow through each wire, all calculated as positive in the direction of the point of contact;

We have just one wire, with just one current. This problem is analogous to the KVL problem: we have just one voltage, and no other to balance it that can be directly measured in the circuit.

This phenomena is well known in literature as the ‘One-Wire-Single Current-Sophism”.
For sure, can only be solved with Maxwell equations   
Maybe you missed the point, the ‘connection point’ (Berührungspunkt)?
Hence, a single wire hitting the connection point is a dead end, hence I1 = 0 .

[bsfeechannel]

And I always thought, the EMF is defined as the tangential force per unit charge in the wire integrated over length, once around the complete circuit/loop! But not at all, it was hiding in the resistor and my voltmeter!

You clearly thought wrong, I regret. EMFs will never "hide" inside (static) wires (considered as ideal, that is).

Sorry, my wording was wrong, I should have said ‘I always believed, the EMF...’.!
Because the clearly wrong ‘thought’ is from Feynman Volume II chapter 16 Induced Currents.
As you say, electromag is so unintuitive, so much bullshit around.... you can’t even trust books anymore.

Thank you for bringing that up. This is the source of much confusion.

In chapter 16, Feynman is talking about REAL wires, that admit the presence of electric fields inside them. Lewin does the same in his famous Lecture 16 and also generates the same kind of confusion. In the middle of the lecture he talks about EMFs in the path of the wires.

Real wires behave just like a resistor. In fact they ARE resistors.

At the end of his lecture, Lewin uses real wires, but his setup allows the approximation to ideal wires because the resistance of the wires are much less than the resistors he uses (100 and 900 ohms). Since he doesn't make that explicitly clear, there are people up to this day looking for the missing EMF in the wires.

In chapter 22, Feynman treat the wires as ideal wires, that he calls "perfect conductor". The electric field inside those wires are ideally (duh!) zero. And that's the kind of wires we've been using in this discussion, unless noted differently.

So, to make it clear, I'll repeat: EMFs will never "hide" inside (static) wires (considered as ideal, that is).

[bsfeechannel]

This phenomena is well known in literature as the ‘One-Wire-Single Current-Sophism”.

Sophism or not there is only one wire there. That's all that counts for KCL.

For sure, can only be solved with Maxwell equations   

And I did it in from of your eyes: ∇·J = - ∂ρ/∂t

Maybe you missed the point, the ‘connection point’ (Berührungspunkt)?
Hence, a single wire hitting the connection point is a dead end, hence I1 = 0 .

Nope. If I is zero, then charge conservation is violated. The volume inside the dashed line is having a variation in the amount of charge, and there's no current crossing the border to account for this variation. It is like a bank account having its balance increasing or decreasing without money being deposited or withdrawn.

[bsfeechannel]

Yes exactly my point that a voltage source is not an impedance.

In that chapter 22 that you mention it clearly shows that induced voltage acts like a voltage source. So including the induced voltage when calculating impedance of a component is just as nonsense as directly calculating the impedance of a voltage source using the voltage across its terminals.

If the voltage source is NOT an impedance there's no sense in talking about direct or indirect calculation of its "impedance" or the inclusion or not of said "induced voltage". It is not an impedance, period.

2 terminal components can't have multiple impedance at the same moment in time.

For that to happen you have to comply to at least the following conditions: you can't have external varying fields; the field generated by the component has to be confined and away from its terminals.

is there any reason why you replaced the world field with underscores?

Because I wanted to check if you really understand that the answers to explain how circuits work are not always found in the path of circuits themselves.

Its not exactly a secret that magnetic fields are what makes inductors work.

Well, fields are what makes everything work in electronics, even when you are not thinking about them.

Exactly it doesn't behave like an inductor anymore, but instead behaves like a coupled inductor.

Coupled inductors cannot be considered 2 terminal components anymore.

But it doesn't mean its inductance simply disappeared. The same magnetizing current is still needed to hold up the field, but because the two inductors are sharing the same flux means they can also share the magnetizing current. Since the resistor on the secondary can't provide a source of reactive current means that all the magnetizing current comes from the voltage source on the primary. The resistive load does however cause a in phase current that makes a opposing field in the secondary that affects the field in the primary, where it induces voltage according to Faradays law. Since there is a voltage source forcing a well defined voltage across the primary, this instead draws extra current to correct this field. This extra  in phase current is what drags the total current back away from lagging 90 degrees. As for the secondary, it has no need for out of phase current, because all of its magnetizing current is provided by the primary.

So the inductance didn't go anywhere. The effect of inductance is simply buried under the other currents.

The secondary is a generator, not an inductor. Although what is going on between the wires is the phenomenon of induction, for the circuit connected to the terminals of those wires they are not. Always remember that lumped components are only seen at their terminals. So if a piece of wire looks like a generator and smells like a generator at its terminals it is because it is a generator. The primary acts as an impedance that can change depending on the load connected to the secondary.

So yeah, sorry i still don't see the exact circumstance when a piece of wire stops being an inductor. Or does becoming a coupled inductor not count as being inductive? If so please explain why.

I think it is clear to you now that a piece of wire can be many things, an inductor, a generator, or whatever impedance depending on whether or not it's under a varying magnetic field.

If you consider it always an inductor, this will lead you to try to write things like L(di/dt) - R*I = 0, when you should have written R*I = -d/dt (∬_ΣB·dS).

[Berni]

So why do we still use Maxwells equations if they are wrong according to Quantum electrodynamics?  Its much like the reason why we still use Kirchhoffs circuit laws despite being wrong according to Maxwell.

Kirchhoff's laws are not wrong according to Maxwell. Maxwell's equations do not only confirm that KVL and KCL are right, but also state in WHAT CONDITION they are right.

The source of the errors is elsewhere.

Yes the source of the error is people like Dr. Lewin applying it directly to a circuit without consideration if its applicable in those CONDITIONS. Fix those conditions by properly modeling the thing as a circuit mesh, if not then forget about Kirchhoffs circuit laws and stick to Maxwell.

On a macroscopic level and under certain conditions these laws still work just fine, while being much more convenient to work with when you want to actually calculate them with actual numbers. The 3 sets of laws are basically just different abstraction layers for electricity. Just chose the desired abstraction level and be aware of its known limitations.

A cat is a special case of mammal, and the description of a mammal is an abstraction of a cat (and every other mammal, as a matter of fact).

QED is an abstraction of Maxwell's equations, as Maxwell's equations are abstractions of KVL/KCL.

KVL/KCL are a special case of Maxwell's equations, as Maxwell's equations are special cases of QED.

KVL/KCL are NOT abstractions of Maxwell's equations by the simple fact that they don't work for all the cases for which Maxwell's equations do.

This is another illusion. Because we ram KVL/KCL down the throats of our circuits and close our eyes to the errors due to this approximation (and we manage to get away with it in many cases) we have the impression that KVL/KCL are just simplified (hence abstracted) cases of Maxwell's equations. But this mindset will bite you in the butt sooner or later. You need to be always aware of the limitations of KCL/KVL and, if the error due to approximating Maxwell to Kirchhoff is gross enough, resort to what will give you the most accurate prediction.

Okay yes i was using more the software engineering definition of abstraction layers rather than the mathematics definition of abstraction. With the mathematics definition it is indeed the other way around.

And i fully agree, all of the levels of explaining electricity work fine as long as you use them within those limitations. Hence why i never really had any problems applying KVL to Dr. Lewins experimental circuit from his lecture. Any paradox between KVL and Maxwell with that circuit is simply down to using them wrong.

Tho to be honest there is very very little reason to go any deeper than Maxwells level of abstraction for engineering use.

I think the inventors of the transistor would not agree with you, but anyway...

I'm pretty sure QED had nothing to do with the development of the first transistors.

There are patents for field effect transistors from before QED was a thing, tho nobody tried to make them at that point. Then the first working BJT device popped up by accident from a bunch of people trying to build a better solid state RF mixer.

The usual transistors can still be explained rather well with Maxwells fields pushing charged particles around. Mostly just a case of controlling where the charge carriers are rather than making use of any quantum mechanical effect. Tho the worlds finest lithography processes used for digital chips are now getting to making transistors small enough for quantum effects to start becoming a problem.

I'm pretty sure very few forum members here work in a semiconductor fab, let alone one that works with such fine feature capabilities or work on building quantum computers. Hence why very very few engineers would have a good reason to dig deeper than Maxwell, heck for 95% of cases even Kirchhoff is close enough(As long as you know about the other 5%).