Author Topic: Does Kirchhoff's Law Hold? Disagreeing with a Master  (Read 60454 times)

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Offline rfeecs

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #175 on: November 18, 2018, 05:23:57 am »
For shielding, I was thinking more like coaxial shields around the test leads.

Just put whole experiment into transformer core like this:



Yes, put the current loop where the "windings" are, and route the wires connected to points A and B outside and measure.  Now you can move the meter from one side to the other and measure the same value.  Or two meters, one on each side, both connected to A and B would both measure the same.
 

Online GeorgeOfTheJungle

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #176 on: November 18, 2018, 07:57:33 am »
Dr. Lewin just uploaded another video.



He's got the current wrong :-)
« Last Edit: November 18, 2018, 09:21:31 am by GeorgeOfTheJungle »
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Offline Berni

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #177 on: November 18, 2018, 09:41:11 am »
Ah yeah i did think that current was pretty high for 140 Ohms but never went to check it. Yeah the decimal place is in the wrong spot and should be 0.064 A. Ah well can happen to anyone.
 

Online GeorgeOfTheJungle

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #178 on: November 18, 2018, 11:57:33 am »
In the last video 1) He's totally avoiding the crux of the matter with electroboom: that the voltmeter wires are part of the circuit, and when considered properly, explain the (seemingly bizarre) results he gets.

And 2) Kirchoff's KVL says "the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop", he leaves the induced EMF of the loop out of the equation to prove that KVL is wrong? Well, yeah, right.
« Last Edit: November 18, 2018, 04:36:49 pm by GeorgeOfTheJungle »
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Offline EEVblog

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #179 on: November 18, 2018, 12:39:23 pm »
Okay our voltmeters suck... so really what is the problem?
The experiment is never explained how the voltmeter 'selects' what voltage it can see. There is no mention given to the importance of the path that the voltmeters probe wires take and why they are routed in that exact way. It just leaves you head scratching how is it possible to see two different voltages at the same point. It demolishes your intuitive notion of voltage in circuits. Many electronics engineers after university are likely still confused as to how it works.

Most simply don't care  ;D
 

Offline Arznei

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #180 on: November 18, 2018, 05:18:07 pm »
Okay our voltmeters suck... so really what is the problem?
The experiment is never explained how the voltmeter 'selects' what voltage it can see. There is no mention given to the importance of the path that the voltmeters probe wires take and why they are routed in that exact way. It just leaves you head scratching how is it possible to see two different voltages at the same point. It demolishes your intuitive notion of voltage in circuits. Many electronics engineers after university are likely still confused as to how it works.

Most simply don't care  ;D

But they should to be honest. I mean, you should at least *know whats going on* and why voltage as a concept can break down in the presence of an induced EMF. You may practicaly never encounter it or have ways do deal with it, which surely is the case for most. But at least know the basic physics of your job and know the limits of the models you use in your daily work. I mean, you people have gone through university and have a masters degree, at least show some respect to your field of education.

You behave like a general practitioner not knowing how to perform a tracheotomy or what it even is. Yeah, he may never have to do one. But when he does, I want him to have at least a general idea of how to go on.
« Last Edit: November 18, 2018, 05:52:43 pm by Arznei »
 

Offline Berni

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #181 on: November 18, 2018, 05:37:41 pm »
Okay our voltmeters suck... so really what is the problem?
The experiment is never explained how the voltmeter 'selects' what voltage it can see. There is no mention given to the importance of the path that the voltmeters probe wires take and why they are routed in that exact way. It just leaves you head scratching how is it possible to see two different voltages at the same point. It demolishes your intuitive notion of voltage in circuits. Many electronics engineers after university are likely still confused as to how it works.

Most simply don't care  ;D

Well to be honest i wouldn't be surprised. Most people in university just memorise things to pass the test and are not even interested in understanding it.

It takes lots of enthusiasm for electronics to really get yourself to understand the field.
 

Offline Arznei

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #182 on: November 18, 2018, 05:56:52 pm »

Well to be honest i wouldn't be surprised. Most people in university just memorise things to pass the test and are not even interested in understanding it.

It takes lots of enthusiasm for electronics to really get yourself to understand the field.

Yeah, and those are probably the ones jerking off the most about how they are STEM educated and making fun of any non-STEM students during university. Which is funny, because if you just leave all the complicated stuff out of EE you can break it down to get pretty simple in practice.
 

Offline Vtile

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #183 on: November 19, 2018, 05:29:08 pm »

Well to be honest i wouldn't be surprised. Most people in university just memorise things to pass the test and are not even interested in understanding it.

It takes lots of enthusiasm for electronics to really get yourself to understand the field.

Yeah, and those are probably the ones jerking off the most about how they are STEM educated and making fun of any non-STEM students during university. Which is funny, because if you just leave all the complicated stuff out of EE you can break it down to get pretty simple in practice.
...And then they become walkers searching lost beans in some corporation, ruining everyones work with their idiocy.
 

Offline SiliconWizard

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #184 on: November 19, 2018, 05:37:16 pm »
I still don't think Lewin uses the right way to make his point nor quite the right examples, but I must admit he at least opened our eyes on something we tend to use without actually really *caring* about all the underlying theory, as Dave said. When we do our work properly, it still doesn't change anything much, but now we know we don't use KVL the way it was intended, and that our definition of "voltage" is in all aspects more practical than theoretical.

 

Offline rfeecs

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #185 on: November 20, 2018, 06:05:23 pm »
Yet another short video.  He mentions Electroboom this time.

https://youtu.be/d_XqrZo5_7Y
 

Offline KL27x

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #186 on: November 20, 2018, 08:44:37 pm »
Summary:
1. Title is "my sincere apologies"
2. 90% of video is arguing against the nonexistent strawman who is apparently suggesting that Farady's law is incorrect, and Kirchoffs is always correct. Take great glee in squashing this strawman by repeating the same thing he has stated like a broken record for the past week.
3. State that anyone with a masters in electronics who suggests that the different readings are only* due to placement of the probing leads is an idiot.
4. Clarifies that the "sincere apology" is for being too blunt in laying out his 100% correct argument against the fairy tale strawman while completely brushing off the actual point of contention.

*but let's forget that I was the one to apply real oscilloscpes and their readings to a real test circuit. If we applied these real oscilloscopes to my theoretical model, we would apparently learn that [start broken record]

Super shorter summary:
"I can see the sailboat, and you can't."

Next up:
"Newton's laws are just a special case of relativity. It's a crime that we call these things laws, when it is really Newton's Loopholes."
« Last Edit: November 20, 2018, 09:11:18 pm by KL27x »
 
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Offline Sredni

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #187 on: November 20, 2018, 11:33:14 pm »
Take two square clocks and put them side by side so that they have a common side. Paint it red to make it stand out.
Do you find it suprising that that same red side is seeing the hand of the left clock going down and the hand of the right clock going up?

Would you call that a measurement error? Or bad glancing?
All instruments lie. Usually on the bench.
 

Offline HackedFridgeMagnet

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #188 on: November 21, 2018, 04:56:23 am »
Maybe a bad analogy?
 

Offline free_electron

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #189 on: November 21, 2018, 12:52:18 pm »
Professional Electron Wrangler.
Any comments, or points of view expressed, are my own and not endorsed , induced or compensated by my employer(s).
 

Offline EEVblog

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #190 on: November 21, 2018, 01:33:17 pm »
I still don't think Lewin uses the right way to make his point nor quite the right examples

I think the same. Lewin's not wrong, but his experiment to explain his point is poor IMO.
Because he's not a practical engineer, I think he's incapable of seeing it from that aspect. He lives in the world of physical theory and knows it so intimately it's all he can see. And there is nothing wrong with that of course, it's important stuff in it's own right, and he's right to point it out.

Quote
, but I must admit he at least opened our eyes on something we tend to use without actually really *caring* about all the underlying theory, as Dave said. When we do our work properly, it still doesn't change anything much, but now we know we don't use KVL the way it was intended, and that our definition of "voltage" is in all aspects more practical than theoretical.

How many of us have ever really thought about it? I doubt there is a single one of us. KVL is a practical theory that works and holds for all but the most obscure aspects of the entire EE field.

It's like trying to argue that Newtons laws are "for the birds" and are just a special case of general relativity. You aren't wrong by saying that, but geeze, try going into NASA and telling all the space probe engineers that Newtons laws are "for the birds", you'd get laughed out of the room.
 
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Offline Sredni

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #191 on: November 21, 2018, 02:18:52 pm »
Maybe a bad analogy?

Do you really not see any relevance of the two clocks example with electromagnetism?
It exemplifies the convention used to define positive oriented areas in vector integral calculus.
The orientation of the path defines the orientation of the area.

Now, that is instrumental in computing the flux of a vector field. And the flux of a function of said field, like its time derivative.
Even the flux of the rotor of a vector field.

And what is the definition of rotor? Basically, it's the circulation around a tiny closed path around a point. So the flux of the rotor can be computed by summing, integrating, all those tiny contributions.
And what happens to the contours? Well, thanks to that 'bad' clock analogy they all cancel out except for those on the external border (look at figure 3.9 here http://www.feynmanlectures.caltech.edu/II_03.html). That's what Stokes theorem tells you: the surface integral of the rotor of a field on an oriented area is the circulation of that field along the closed contour encircling it, with the convention of the right hand rule. Like the hand of a clock.

Add in Faraday-Maxwell equation that tells you that the rotor of E is the time derivative of B (ok, there's a sign but that does not change anything since it's always the same) and you should now see the relevance of that analogy.

In fact, if you split a finite area in two parts with a common side, just like those two clocks, you will find that despite the orientation of the areas be the same, the orientation of the common path will come out reversed. Namely, if we assume the same flux configuration, you will get opposite contributes to the circulation along that path depending on which loop it is considered to be part of.
This 'reversal' of the integral of E dot dl (which in an electrostatic situation we would call "the" potential) is not because of bad probing or a measurement error, it is just a consequence of that inversion you see along the common side of two adjacent clocks.

I doubt anyone would find it surprising, just as they would find perfectly normal that the hand of the right clock is seen going up along the common side, while the hand of the left clock is seen as going down.

And there is no escape from this, no matter how small you choose the adjacent contours.
And when you consider finite contours, you can still divide them in two with a common side: the result is the same: if the same flux is intercepted by both partial areas (edit: actually this is not even required, what it counts is that the E field is the same along the common side and well, it has to be since it's the same set of points), the contribute to the emf on the common path will be reversed.
Would you call that measurement error, or probing error?
I would call that "that's just the way it is", Kronkite style.

This is the same inversion that comes out with Lewin's experiment when both resistor are the same.
Would you call that probing error?
To me, that's just how EM works. And the roots of this behavior go down to both that orientation behavior and the fact the circulation of one quantity is related to (a function of) the flux of another one.

No, I would not call that a bad analogy. But that's just me.

(of course, if you remove the link with the flux because the function of B is always zero you get a very special situation where this weird shit does not happen)

EDIT: changed "convention" with "behavior", because its the correlation between area orientation and path orientation that makes all this happen (clockwise-countclockwise vs up and down in this case)
EDIT: changed "infinitesimal" with "tiny" for not riling up mathematicians. Added link to picture. Corrected some minor typos.
EDIT: changed path with contour where relevant to avoid ambiguities.
« Last Edit: November 21, 2018, 06:42:33 pm by Sredni »
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Offline Sredni

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #192 on: November 21, 2018, 03:40:27 pm »

It's like trying to argue that Newtons laws are "for the birds" and are just a special case of general relativity. You aren't wrong by saying that, but geeze, try going into NASA and telling all the space probe engineers that Newtons laws are "for the birds", you'd get laughed out of the room.

I'm sorry Dave, but it's not like that.
Faraday's law is not a refinement of the theory used in the 'generalized KVL' engineers use to analyze circuits with inductances, transformers and motors. It is the very same theory.

The only reason the 'generalized KVL' works, giving 'single-valued potentials' is because we are not allowed to cut through the fluxes that make inductances, transformers and motors work. All the weird stuff happens inside, and since our physical circuit cannot repartition the area where the variable flux is linked in the device, nor can it go around it the other way (think of a toroidal transformer, you can go around it any way you want, but you cannot cut through the flux since it is all contained inside - same happens with normal iron core transformers, yes, there may be leakage, but you can't cut through the core) [edit]... we get single valued potentials, like when we measure Lewin circuit from one side OR from the other.
If we avoid that repartitioning and cutting through, we're fine. We can still delude ourselves into believing that our voltages are uniquely determined by endpoints only. But that's just an illusion that helps in making circuit analysis more streamlined. Nothing more than that.

But if we are presented with a circuit that cuts through or allows for encircling with opposite orientation a varying flux region, then we can no longer indulge in that illusion and we must fall back to the reality of electromagnetism, where that linking between fluxes and circulations is deeply rooted down to the bone.
Saying that the multivalued potential we are witnessing can be ascribed to a 'probing error' is denying what Maxwell's equations and basic vector calculus are telling you.

Edit: added "and basic vector calculus".
Edit: added conclusion to sentence after very long parentheses. I had forgot to finish it.
I also wanted to add the voice of Hal saying "I'm sorry, Dave. I can't let you do that, Dave" but did not find a way to do that.

« Last Edit: November 21, 2018, 08:40:11 pm by Sredni »
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Offline Berni

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #193 on: November 21, 2018, 07:28:32 pm »
Calm down a bit. Nobody is claiming that Maxwell equations are wrong or that KVL describes the underlying physics.

Maxwells equations describe the underlying physics perfectly fine. And yes KVL is indeed in theory wrong.

But this does not mean that KVL is "for the birds" as these feathery creatures have no use for it, while in contrast engineers use it all the time, sometimes even daily. Try to find an engineer who claims to have used Maxwells equations in the last 12 months (And i don't mean use the idea behind it, but actually calculated something with it). So why are we all using the clearly inferior KVL when we could all be using proper Maxwells stuff? Well... turns out KVL is simply more useful for everyday use.

Maxwells equations involve fields and geometry that needs to know the exact dimensions and locations of everything in 3D space. This brings about a lot of extra complicated math that just slows you down when you are trying to get actual work done and drastically increases the potential for human error. The way engineering has solved this problem is to introduce an abstraction called circuit schematics. For the case of magnetic components we can simplify all of this geometry and fields down to a single inductance number in units of Henry. We have pre-baked equations (That do eventually involve Maxwell if you drill deep enough) that quickly turn common geometrical segments of wire into inductance values, or the same inductance value of a real life circuit can be measured quicker and more accurately than its geometry. This single number is then inserted in the equivalent inductor model and is used for all further calculation. An extra benefit of doing this is that it not only abstracts the magnetic effects but it even abstracts voltage in to a sort of "effective voltage" that always has 1 defined value. An even better bonus is that now KVL works for all cases, but as a consequence the voltage it operates with and gives as a result are these "effective voltages" rather than the real definition of voltage(Intergal of fields around a path). Getting a result of "the voltage here is 1.4 V" is more useful than the result being multiple values and you need to use the correct one depending on what you are doing with the voltage. In order to give a single number it is not simply throwing away the other values and cherry picking this one. The math deep down works out in a way where the positive and negative signs of all the numbers line up in a way that gives the same result regardless of the path. The results of these abstracted calculations can be verified with experiments and they match up with measured results. This is the same kind of thing as using Complex numbers in calculations, we could have 4+j3 Volts across two points. So when a voltmeter in real life shows 5V is it wrong? No its not, its just that our math was using imaginary numbers as an abstraction of phase to make math much easier, we still need to know how to interpret the abstraction.

KVL is not a special case of Faradays law even if it looks similar. Instead it is a tool used in analysis of abstracted schematic circuits. If you are to unravel all of these mathematical circuit modeling tools far enough you would eventually get to Maxwells equations, but its not as simple as sticking an extra voltage into KVL, you would end up with multiple pages of math before you get there. Our circuit schematics are the equivalent of "spherical cows in vacuum" in physics, its an abstraction that optimizes and simplifies the math for quick and easy computation. In physics the well known F=m*a equation(Often called Newtons 2nd law) is also wrong in certain cases (Rockets and mass–energy equivalence) and we still use it with its limitations in mind rather than saying its for the birds.

So is it bad probing? I think we need a definition of what that is first. Its hard to find a formal definition of it but lets say we use something like this:
Quote
Bad probing is the result of performing a measurement of a desired quantity in such a way that the resulting measured value differs from the actual value of the quantity by more than than our defined error margin allows for.

So by this definition Dr. Lewin is not doing bad probing since he is indeed measuring the voltage he is after within tolerances required by the particular demonstration. The one who is doing bad probing is ElectroBoom since he is after the "apparent voltage" on the two points but is doing so in a way that cause the probes to significantly affect the reading. He should likely have used the setup suggested by this post: https://www.eevblog.com/forum/chat/does-kirchhoffs-law-hold-disagreeing-with-a-master/msg1972940/#msg1972940 .This would cause the inductive coupling coefficient to the probe wires to become negligibly low, giving the voltage that he is after and so solving the bad probing error. Solving the same circuit setup using Maxwells equations would return a similar result, except that the two values it gives for each path would be nearly identical (Keep in mind we are solving for voltage across the voltmeter terminals, not the voltage inside the ferrite shield).


So who is wrong about what?
ElectroBoom is wrong about using a oscilloscope to measure voltage as formally defined in literature. He needed to use that elusive voltmeter that drags an electron around and measures the mechanical work taken to do so, it would have given him the result Dr. Lewin predicted. But he is using Kirchhoffs law correctly by using it for circuit analysis and not to describe electric fields. He is also using it correctly to determine the voltage across the oscilloscope terminals by correctly interpreting the "apparent voltage" result of the abstracted circuit analysis math.

Dr. Lewin is wrong about using Kirchoffs law for describing what happens to electric fields. Kirchhoffs laws actually describe the behavior of ideal electrical circuits (That are merely an simplified but accurate abstraction of what happens in real circuits with actual fields and electrons). If you look up KVL on wikipedia it explicitly calls them in the title "Kirchhoffs's cirucit laws" ( https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws ). He is however correct in using Faradays law to determine the voltage as per formal definition on the two points, but he never includes the oscilloscope and its connections into his calculation and does not explain why the voltage seen on the terminals of the oscilloscope is equal to the voltage at the two nodes of interest.

Its all a case of comparing apples to oranges. They are simply not the same thing even if they seam to fit in the same basket. Part of it is because Kirchhoffs circuit laws predate Maxwells equations and its likely that his laws ware used to describe the physics until Maxwell came around with his more elegant and physically accurate way simply because that's the best theory they had at the time. This is just how science works.
« Last Edit: November 21, 2018, 07:31:53 pm by Berni »
 

Offline In Vacuo Veritas

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #194 on: November 21, 2018, 07:37:31 pm »
Seems to me it's simple to resolve, put the meter HALFWAY and see what you read...
 

Offline firewalker

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #195 on: November 21, 2018, 08:12:12 pm »
He still doesn;t undestand the mistake he is making.
Become a realist, stay a dreamer.

 

Online GeorgeOfTheJungle

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #196 on: November 21, 2018, 08:48:20 pm »
Seems to me it's simple to resolve, put the meter HALFWAY and see what you read...

When you do that, what are you supposed to read? Because there's two different resistors in parallel that are in series too, with the same current going through both... I*R1? -I*R2?
« Last Edit: November 21, 2018, 08:50:11 pm by GeorgeOfTheJungle »
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Online ogden

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #197 on: November 21, 2018, 09:33:01 pm »
Seems to me it's simple to resolve, put the meter HALFWAY and see what you read...

When you do that, what are you supposed to read? Because there's two different resistors in parallel that are in series too, with the same current going through both... I*R1? -I*R2?

If two meters that are part of super experiment circuit shows 0.1V and 0.9V accordingly, then such "halfway" meter shall read 0.4V. It is discussed/explained in this thread many times by the way
 

Offline EEVblog

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #198 on: November 21, 2018, 10:56:22 pm »
KVL is not a special case of Faradays law even if it looks similar. Instead it is a tool used in analysis of abstracted schematic circuits. If you are to unravel all of these mathematical circuit modeling tools far enough you would eventually get to Maxwells equations, but its not as simple as sticking an extra voltage into KVL, you would end up with multiple pages of math before you get there. Our circuit schematics are the equivalent of "spherical cows in vacuum" in physics, its an abstraction that optimizes and simplifies the math for quick and easy computation. In physics the well known F=m*a equation(Often called Newtons 2nd law) is also wrong in certain cases (Rockets and mass–energy equivalence) and we still use it with its limitations in mind rather than saying its for the birds.

It's kinda similar with that "current flowing through a capacitor" video. Electrons don't actually flow through the capacitor, but that interpretation along with AC impedance is the practical and easiest way to design and analyse circuits and that's why it's used and is a perfectly valid way of thinking. Ironically, it's Maxwell's displacement current theory that helps validate the concept here. So the deeper into the theory you go, the more it backs up the "incorrect" current flow viewpoint.

Quote
So is it bad probing? I think we need a definition of what that is first. Its hard to find a formal definition of it but lets say we use something like this:
Quote
Bad probing is the result of performing a measurement of a desired quantity in such a way that the resulting measured value differs from the actual value of the quantity by more than than our defined error margin allows for.
So by this definition Dr. Lewin is not doing bad probing since he is indeed measuring the voltage he is after within tolerances required by the particular demonstration.

I'd call it "deceptive" probing  ;D
 

Offline rfeecs

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Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #199 on: November 21, 2018, 11:21:34 pm »
It's kinda similar with that "current flowing through a capacitor" video. Electrons don't actually flow through the capacitor, but that interpretation along with AC impedance is the practical and easiest way to design and analyse circuits and that's why it's used and is a perfectly valid way of thinking. Ironically, it's Maxwell's displacement current theory that helps validate the concept here. So the deeper into the theory you go, the more it backs up the "incorrect" current flow viewpoint.

Yes, not only is KVL for the birds, but KCL is too!

Here's a rough derivation of Kirchoff's laws from Maxwell's equations:  KVL from Faraday's law, KCL from Ampere's law:
https://bit.ly/2Fy2svN

Quote
Let’s look at when are Kirchoff’s Laws would be violated.  Notice that both laws assume the
time rate of change of something is approximately 0.  This means they are true in the ‘static’
or ‘low frequency’ limit.  The circuits that you will deal with in this course work under this
limit.  However, it’s interesting to note that KCL is violated inside the capacitor because
charge can build up on the capacitor plates, so if part of your closed surface passes between
the plates the net charge changes significantly with time.  However if you consider the
capacitor as a whole ‘lumped element’ and include both plates inside the closed surface, the
charges on opposite plates cancel out and KCL will still work.
  Similarly, KVL is violated
inside the inductor
because a significant magnetic flux passes through the coil, so if your
closed path runs along the coil’s wiring a voltage drop occurs even across the perfect metal
wire.  However if you consider the inductor as a whole ‘lumped element’ and recognize its
total voltage as the induced electromotive force due to Lenz’s Law, KVL will still work.
 
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