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Author Topic: Kirchhoff is for the birds...  (Read 27233 times)
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[youtube]http://www.youtube.com/watch?v=EwIk2gew-R8[/youtube]

[youtube]http://www.youtube.com/watch?v=gJSEgANEkOo[/youtube]


When dealing with B fields, your position of measurement matters.



Just noticed, you guys are on top of this:
http://www.overunityresearch.com/index.php?topic=739.0
   

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I am rebooting this topic.
There is a larger one as listed by Matt,but that has changed course in the later posts.

As this topic has come up again in another thread,i will restart this one,so as to not over run the other thread with this topic.

This thread is about the following-->

https://www.youtube.com/watch?v=eqjl-qRy71w

https://www.youtube.com/watch?v=LzT_YZ0xCFY&t=934s

And ElectroBOOMs reply

https://www.youtube.com/watch?v=0TTEFF0D8SA

The circuit is below,although i have change the circuit i am using for testing,as will be seen in the next post i make that contains the video.

Brad
« Last Edit: 2019-06-22, 16:59:37 by TinMan »


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And here is the video of my test setup,and the results obtained from those tests.

https://www.youtube.com/watch?v=ldjIkYqV9xo


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I made a comment on one of Lewins video's just yesterday,and he replied today-oddly enough.

His reply
Quote: You should first learn some very basic 1st year college Physics. *I demonstrated at the end of my lecture #16 of my E&M course at MIT that two identical voltmeters attached to the same 2 points in a circuit can show very different values. The reason is that in the case of an induced EMF (Faraday's Law) potentials are no longer determined and thus potential differences depend on the path. This is first year college Physics.* The same physics applies to the secondary windings of transformers as the EMF in the closed loop of secondary windings is induced (Faraday's Law). https://www.youtube.com/watch?v=b7i2uMx7gHo&list=PLyQSN7X0ro22zanLsOcvkaSY-IZqheFYM5&index=8 My demo was suggested by Romer in 1982. I first did it in 1984 in my MIT course (8.02) and I have done it every time that I lectured 8.02. *Electroboom insulted me* *by mentioning in one of his videos that: "The entire reason Dr. Lewin was reading two different voltages was due to bad probing".* It would have been fine if this comment had been made by someone who has little background in Physics. But it's quite worrisome if it is made by someone who has a masters degree in EE. This demo has now become a classic; it's done all over the world at many colleges and universities. In addition, Kirchhoff's loop rule (KVL) is older than Faraday's Law. My translation of the *original work by Kirchhoff from 1845 which was after the publication of Faraday's Law* "(...) it becomes easy to find the requirement, which [voltage] you must fulfill, so that the electrical condition on the [metal] disk can be a stationary one. When we look at a closed loop in [the disk], inside of which no electricity is being fed into [the disk], then the sum of all amounts of electricity in this loop must be 0." The original text can be found at google books in the following link, book pages 497-514: https://books.google.de/books?id=Ig8t8yIz20UC. *Clearly Kirchhoff was fully aware of the prerequisite for his "loop rule", i.e. that d_phi(t)/dt must be equal to zero! If d_phi(t)/dt is not zero, then Faraday's Law has to be used.* *Faraday's Law always holds regardless of the value of dphi(t)/dt that's why it is one of Maxwell's eqs and Kirchhoff's Loop Rule (KVL) is not.*

So it seems Lewin is still insistent that he is correct,and kirchhoff's law dose not apply to this circuit.


Brad


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In the below video,i decided to try something a little different,where i use LEDs to prove a voltage difference across each resistor.

Once again,we find the total sum of voltages in the loop do not =0

https://www.youtube.com/watch?v=Lm0gGQQtcws

Kirchhoff's Loop Rule Formula
In any "loop" of a closed circuit, there can be any number of circuit elements, such as batteries and resistors. The sum of the voltage differences across all of these circuit elements must be zero. This is known as Kirchhoff's Loop Rule. Voltage differences are measured in Volts (V). When the current I in the loop is given in Amperes (A) and resistance of circuit elements is given in Ohms (Ω), the voltage difference across a resistor can be found using the formula V=IR .



Brad
« Last Edit: 2019-06-22, 16:38:53 by TinMan »


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One of Lewins later video's about Kirchhoff's loop rule .

https://www.youtube.com/watch?v=wz_GqO-Urk4


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Well, I think it is also the solution for Tariel Kapanadze device. The current in single loop can be different in various parts of circuit  IF there is a transformer which speed up electrons in coil by the use of polarized RADIO wave aka Tesla longitudinal wave aka radiant energy. The schematic I saw recently which may leaked from some source close to Kapanadze (or may not - I don't know) seem to confirm what I thought long time ago.
Would be interesting to know whatis Dr Lewin opinion on such hypothesis
   
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Brad

By not using a solenoid to drive both chunks of wire you have deviated from the original circuit whereby both connecting wires are induced.

If you redraw your circuit such that the bottom loop is the secondary of the toroid transformer, then the 82 mV is the correct reading across that chunk of wire, as it threads the toroid.

However, by also threading the ground lead through the toroid, you have effectively nulled out the useful 82 mV for the measurement  so surely you measured zero mV.

The top loop is just a wire connecting the two resistors, there is no induction in it as it does not actually thread the toroid. It is"downstream" of the resistors.

Then the correctly measured 82mV equates to 74.5 uA in the loop. (82mV/1100 ohms=74.5uA)

Using the current then we can find the voltage on each resistor

For the 1k ohm we have 74.5 uA X 1000 ohms = 74.5 mV

For the 100 ohms we have 74.5 uA X 100 ohms = 7.45 mV

Adding those to values we arrive back at the 82 mV

Surely you see that if you removed the resistors and only left the bottom wire loop, you have a transformer with a single turn secondary of 82mV, so that reading is correct for that chunk of wire that threads the toroid and takes part in the induction, whereas the top wire does not.

Your idea to use the toroid does have merit in reducing measurement artifacts but it must be applied to both chunks of wire to simulate a solenoid induction method in that each chunk of connecting wire will act as the secondary of a transformer. You can do this by also looping the top wire through the toroid with the correct phasing or using an additional identically driven toroid on the top wire.

In this last case you would put the toroid primaries in series and then wind up with 41mV measured on each secondary chunk of wire, which if properly phased will add to give you 82mV of drive.

Hope this helps

edit: corrected mA to uA per Gyula who noticed the error
« Last Edit: 2019-06-23, 02:06:07 by ion »


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Brad

By not using a solenoid to drive both chunks of wire you have deviated from the original circuit whereby both connecting wires are induced.

If you redraw your circuit such that the bottom loop is the secondary of the toroid transformer, then the 82 mV is the correct reading across that chunk of wire, as it threads the toroid.

However, by also threading the ground lead through the toroid, you have effectively nulled out the useful 82 mV for the measurement  so surely you measured zero mV.

The top loop is just a wire connecting the two resistors, there is no induction in it as it does not actually thread the toroid. It is"downstream" of the resistors.

Then the correctly measured 82mV equates to 74.5 mA in the loop. (82mV/1100 ohms=74.5mA)

Using the current then we can find the voltage on each resistor

For the 1k ohm we have 74.5 mA X 1000 ohms = 74.5 mV

For the 100 ohms we have 74.5 mA X 100 ohms = 7.45 mV

Adding those to values we arrive back at the 82 mV

Surely you see that if you removed the resistors and only left the bottom wire loop, you have a transformer with a single turn secondary of 82mV, so that reading is correct for that chunk of wire that threads the toroid and takes part in the induction, whereas the top wire does not.

Your idea to use the toroid does have merit in reducing measurement artifacts but it must be applied to both chunks of wire to simulate a solenoid induction method in that each chunk of connecting wire will act as the secondary of a transformer. You can do this by also looping the top wire through the toroid with the correct phasing or using an additional identically driven toroid on the top wire.

In this last case you would put the toroid primaries in series and then wind up with 41mV measured on each secondary chunk of wire, which if properly phased will add to give you 82mV of drive.

Hope this helps


I would agree. ;)  It is not the same where only one resistor connection is the source to the circuit.

Reminds me of when TK was working on the Rose Ainsley circuit where it was suggested that using 2 leds in parallel but opposite polarity in line with the circuit loop to see which way current was flowing more. But Tk inserted a 1:1 transformer primary with one led across that and the other led across the secondary.  To me, that is not the same as 2 leds alone.

Like why have the transformer at all? If one led across the primary is biased alone, then why couldnt the other led also just be in parallel with the other but opposite polarity? ;)

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Then the correctly measured 82mV equates to 74.5 mA in the loop. (82mV/1100 ohms=74.5mA)

...

Dear Ion,

Please check : 82 mV / 1100 Ohm = 74.5 uA  (the mA is surely a typo).

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Dear Ion,

Please check : 82 mV / 1100 Ohm = 74.5 uA  (the mA is surely a typo).

Gyula0
Surely for some people the danger of being old and doing quick math in your head, the error applies to the other current transforms also.

But is the concept I am implying correct, can you comment on that?

Thanks


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 author=ion link=topic=2369.msg75449#msg75449 date=1561227390]
Brad


Quote
If you redraw your circuit such that the bottom loop is the secondary of the toroid transformer, then the 82 mV is the correct reading across that chunk of wire, as it threads the toroid.

I would disagree with that ION (but i could be wrong here),and here is why.
As the current flowing through the loop is the same at every point,then the bottom circuit link having the same resistance value as the top circuit link must also have the same voltage value across it !ohms law!.

Quote
By not using a solenoid to drive both chunks of wire you have deviated from the original circuit whereby both connecting wires are induced.

Both connecting wires are induced by the electric field of the toroid transformer.
The induction is not limited to the small portion of wire threaded through the toroids center.

Quote
The top loop is just a wire connecting the two resistors, there is no induction in it as it does not actually thread the toroid. It is"downstream" of the resistors.

As above.
Tests i have carried out before show that the secondary loop can be induced at any point throughout the loop,and is not limited to the small portion threading the toroid.

Quote
Then the correctly measured 82mV equates to 74.5 mA in the loop. (82mV/1100 ohms=74.5mA)

Using the current then we can find the voltage on each resistor

For the 1k ohm we have 74.5 mA X 1000 ohms = 74.5 mV

For the 100 ohms we have 74.5 mA X 100 ohms = 7.45 mV

Adding those to values we arrive back at the 82 mV

I know it is only a typo,but it is uA not mA
The 82mV is the maximum voltage obtainable from the single loop with the turn ratio and frequency used regardless of the total resistance value.

Quote
Surely you see that if you removed the resistors and only left the bottom wire loop, you have a transformer with a single turn secondary of 82mV, so that reading is correct for that chunk of wire that threads the toroid and takes part in the induction, whereas the top wire does not.

 Ohms law states that if the current flowing through the loop is the same at all points of the loop(which it is),then the voltage across any two resistances with the same value within that loop must have the same voltage across them. As the bottom loop has the same resistance value as the top loop,and has the same value of current running through it,then the voltage across that bottom loop must be the same as the voltage across the top loop.

As stated above,the secondary loop is induced by the electric field,and not the magnetic field. The magnetic field is confined to the core,while the electric field is not. All parts of the loop are induced by the electric field,and induction is not limited to just the small portion of the loop that threads the toroid.

By placing the scope across the bottom loop,where it is around the outside of the toroid,you now have created a second circuit-which is the scope it self,where the resistance value of that circuit is now the impedance value of the scope.

As i said,i could be wrong here,but there is a quick test i can do to see if i am correct,which i will do shortly.


Brad


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Quote
I would disagree with that ION (but i could be wrong here),and here is why.
As the current flowing through the loop is the same at every point,then the bottom circuit link having the same resistance value as the top circuit link must also have the same voltage value across it !ohms law!.

Note that the bottom wire is an active voltage source as it is the single turn secondary of your toroid. This voltage feeds two resistors and a piece of wire which is also a resistor although very low in value, so we can expect it will have close to zero volts across it. It is a load, not a voltage source.

Quote
Both connecting wires are induced by the electric field of the toroid transformer.
The induction is not limited to the small portion of wire threaded through the toroids center.
.

I would disagree here.

Quote
As above.
Tests i have carried out before show that the secondary loop can be induced at any point throughout the loop,and is not limited to the small portion threading the toroid.

But you measure zero volts on the top wire, thus it is not induced the same as the bottom wire when measured normally (as you would normally measure the secondary of a transformer) You assume the 82mV is an error that you must correct by nulling it with the ground lead of the scope passing through the core. I say 82mV  is the correct voltage and the nulling trick is not needed and confuses the issue.

Quote
I know it is only a typo,but it is uA not mA
The 82mV is the maximum voltage obtainable from the single loop with the turn ratio and frequency used regardless of the total resistance value.

We agree here.

 
Quote
Ohms law states that if the current flowing through the loop is the same at all points of the loop(which it is),then the voltage across any two resistances with the same value within that loop must have the same voltage across them. As the bottom loop has the same resistance value as the top loop,and has the same value of current running through it,then the voltage across that bottom loop must be the same as the voltage across the top loop.

True if all resistances are passive, but you have one as an active voltage source so it is not a passive loop.

Quote
As stated above, the secondary loop is induced by the electric field, and not the magnetic field. The magnetic field is confined to the core,while the electric field is not. All parts of the loop are induced by the electric field,and induction is not limited to just the small portion of the loop that threads the toroid.

I believe this is true for solenoid induction, not so for a toroid singly threaded.

Quote
By placing the scope across the bottom loop, where it is around the outside of the toroid, you now have created a second circuit-which is the scope it self, where the resistance value of that circuit is now the impedance value of the scope.

Then I must ask how you would normally use your scope to measure the secondary of a transformer? Do you always try to null the voltage to zero?

Quote
As i said, i could be wrong here,but there is a quick test i can do to see if i am correct,which i will do shortly.
Brad


We shall see. I maintain that with the toroid feeding the loop, you have a simple transformer secondary feeding three resistors, 1000, 100 and one is a fraction of an ohm (the connecting wire). Trying  not to confuse the issue, as this is not the same circuit as solenoid induction, whereby the upper wire would have induction thus becoming an active voltage source like the bottom wire.

All for now, good luck with further test and discussion,  I may not be back as I entered the Lewin fray reluctantly.

Regards


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All for now, good luck with further test and discussion,  I may not be back as I entered the Lewin fray reluctantly.

Regards

I would encourage you to stay,as if i am incorrect,i would like you to correct me.
If i am correct,then would this not also help you further your understandings?,even though it is more likely that i am wrong.

Below is your picture i have added a question to.
That question is-->if there is 87mV across R2,then what would be the voltage across R1 ?
Dose not ohms law state that it should be 870mV,as the current flowing through the loop must be the same at all points of that loop?.


Brad


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With 87 mV across the 100 ohm R2, the loop current must be  0.87mA

Thus the voltage across 1000 ohm R1 must be 870mV (naturally as it is  10X higher in resistance it will have 10X higher voltage)

The total applied voltage must be 957mV (not 82mV as shown on my drawing)

This 957mV being the sum of 87mV plus 870mV (this is the new transformer output)

Hope I haven't created another slipped decimal.

Regards


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It's not as complicated as it may seem...
I beat this topic to death years ago, and I think proved beyond a doubt that KVL holds in all cases.

ElectroBOOM is absolutely correct, and Lewin is simply being short-sighted and stubborn.

ElectroBOOM went to great lengths to explain things, but another easier way in my opinion is to simply remove the measurement probes from the experiment. How do we do this? Easy, just bring your probe leads down from a hook situated above the ring so that the leads are placed across the resistors and wire segments perpendicular to the plane the ring is situated. I would suggest at least 1m above the apparatus.

This effectively removes the probes and leads from the experiment apparatus and will allow you to not only measure the actual voltage across the 2 resistors, but across the 2 wire segments as well. If one does this and then adds all 4 voltages (going the same direction) in the loop, the result will be close to zero.


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I beat this topic to death years ago, and I think proved beyond a doubt that KVL holds in all cases.

ElectroBOOM is absolutely correct, and Lewin is simply being short-sighted and stubborn.

ElectroBOOM went to great lengths to explain things, but another easier way in my opinion is to simply remove the measurement probes from the experiment. How do we do this? Easy, just bring your probe leads down from a vertical hook so that the leads are placed across the resistors and wire segments perpendicular to the plane the ring is situated.

This effectively removes the probes and leads form the measurement and will allow you to not only measure the actual voltage across the 2 resistors, but across the 2 wire segments as well. If one does this and then adds all 4 voltages (going the same direction) in the loop, the result will be close to zero.

That's why I reluctantly got into the fray as this has all been worked out by Poynt years ago.

I only jumped in when Brad added a new twist by using a toroid to inject the current into the loop and this is not the same as Lewins solenoid induction method that affects all wires in the loop.

I was trying to show that Brad's circuit is a simple transformer circuit, but as I have now exceeded my mental capacity, I will exit left.

Good to see you here Darren.

Regards


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It's not as complicated as it may seem...
Hey Ernie, if we never push the envelope, then... :)

Keep pushing my friend.


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Note that the bottom wire is an active voltage source as it is the single turn secondary of your toroid. This voltage feeds two resistors and a piece of wire which is also a resistor although very low in value, so we can expect it will have close to zero volts across it. It is a load, not a voltage source.
.

I would disagree here.

But you measure zero volts on the top wire, thus it is not induced the same as the bottom wire when measured normally (as you would normally measure the secondary of a transformer) You assume the 82mV is an error that you must correct by nulling it with the ground lead of the scope passing through the core. I say 82mV  is the correct voltage and the nulling trick is not needed and confuses the issue.

We agree here.

 
True if all resistances are passive, but you have one as an active voltage source so it is not a passive loop.

I believe this is true for solenoid induction, not so for a toroid singly threaded.

Then I must ask how you would normally use your scope to measure the secondary of a transformer? Do you always try to null the voltage to zero?
Brad


We shall see. I maintain that with the toroid feeding the loop, you have a simple transformer secondary feeding three resistors, 1000, 100 and one is a fraction of an ohm (the connecting wire). Trying  not to confuse the issue, as this is not the same circuit as solenoid induction, whereby the upper wire would have induction thus becoming an active voltage source like the bottom wire.

All for now, good luck with further test and discussion,  I may not be back as I entered the Lewin fray reluctantly.

Regards

Here is the first video in relation to the above.

https://www.youtube.com/watch?v=HKoC3yOEtkw

The next one is uploading now.
I have also added a diagram showing the electric field around a toroid transformer.
As you can see,the whole loop of my secondary would be within that electric field,thus allowing induction via that field to take place anywhere around that loop,and not confined to the portion of the loop that is through the center hole of the toroid.

Brad


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I beat this topic to death years ago, and I think proved beyond a doubt that KVL holds in all cases.

ElectroBOOM is absolutely correct, and Lewin is simply being short-sighted and stubborn.

ElectroBOOM went to great lengths to explain things, but another easier way in my opinion is to simply remove the measurement probes from the experiment. How do we do this? Easy, just bring your probe leads down from a hook situated above the ring so that the leads are placed across the resistors and wire segments perpendicular to the plane the ring is situated. I would suggest at least 1m above the apparatus.

This effectively removes the probes and leads from the experiment apparatus and will allow you to not only measure the actual voltage across the 2 resistors, but across the 2 wire segments as well. If one does this and then adds all 4 voltages (going the same direction) in the loop, the result will be close to zero.

As you know Poynt,i did all these tests along side you,and with your guidance,and we did end up with a sum of 0v.
But something was wrong there,and it would seem that we can place our measurement equipment in any position to gain the results we want to see.

In my test setup,i have removed the magnetic field problem,and now use only the electric field to induce the secondary loop. Now we can have our scope leads where ever we want,and there is no adverse effect due to the magnetic field.

I have already tried having the scope probes vertical as we did in the last test,and it makes no difference what so ever,as it shouldn't in this case.

The video's i am uploading show that my measurements are correct,and if you see a problem with them,then let me know.


Brad


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That's why I reluctantly got into the fray as this has all been worked out by Poynt years ago.

I only jumped in when Brad added a new twist by using a toroid to inject the current into the loop and this is not the same as Lewins solenoid induction method that affects all wires in the loop.


Regards

No it is not the same as Lewins tests.
My setup still induces a current through the closed loop,but eliminates the magnetic field problems associated with Lewins setup.

However,the results still show the same non 0 voltage around the loop.
Ohms law also states the voltages cannot sum to 0 in either case as we found when i did the tests with Poynt,so something is wrong here,and i want to find out what.

Looking at lewins circuit below,we can see that both the top link and bottom link will cancel each other out,and there sumed voltage will be 0.
This leaves the two different value resistors,and the voltage across them.
If the current through the circuit is the same at all points in time,then the voltage across each resistor cannot be the same value to cancel each other out,and result in 0 volts-->ohms law says no way.


Brad


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I beat this topic to death years ago, and I think proved beyond a doubt that KVL holds in all cases.

ElectroBOOM is absolutely correct, and Lewin is simply being short-sighted and stubborn.



Message received via email today from Walter.

Quote:  *By teaching students that KVL always works, makes many believe that the closed loop integral of E dot dL is always zero. Which is not true.* Even ElectroBOOM who has a masters in EE believed that, and he therefore concluded (he was not the only one) that two identical voltmeters attached to the same 2 points in a circuit MUST always show the same values. In other words he does not even know that in the case of an induced EMF potential differences are no longer determined. None of my thousands of MIT students who take my 8.02 would make this mistake which is a HUGE BLUNDER! They have seen my Lecture #16 and the great demo with the 2 voltmeters which I do at the end! I believe that I teach Faraday's Law in the way it should be taught. All my students know that KVL is part of Faraday's Law and they have no problems with the concept that potential differences in a circuit can be path dependent. *In conclusion I believe that teaching students that KVL always holds is not only wrong Physics but you set them up for making terrible mistakes/blunders as ElectroBOOM did.*


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I have been reading the other thread listed in Matts first post here--

https://www.overunityresearch.com/index.php?topic=739.25

It would seem to me that more attention should have been paid to what member Harvey had to say,but it also seems that !some! had no interest in what he had to say,and just dismissed him like he was nothing at all--very sad,as he seemed to be very switched on in the art of EE.


Brad


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Here is another video regarding the placement of the scope probe leads across the link that passes through the toroid.

As you will see,things do not add up,and having the scope hooked up around the toroid is a no go.

The video also eliminates the thought that the connecting link wire passing through the toroid is the only point of induction in the circuit.
Along with it,2 other videos i made regarding the same thing,only on a larger scale.

https://www.youtube.com/watch?v=UkUNZ5ik4go

https://www.youtube.com/watch?v=n84bPUWLLLY

https://www.youtube.com/watch?v=cqXC7Qjrh1Y



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I beat this topic to death years ago, and I think proved beyond a doubt that KVL holds in all cases.

ElectroBOOM is absolutely correct, and Lewin is simply being short-sighted and stubborn.

ElectroBOOM went to great lengths to explain things, but another easier way in my opinion is to simply remove the measurement probes from the experiment. How do we do this? Easy, just bring your probe leads down from a hook situated above the ring so that the leads are placed across the resistors and wire segments perpendicular to the plane the ring is situated. I would suggest at least 1m above the apparatus.

This effectively removes the probes and leads from the experiment apparatus and will allow you to not only measure the actual voltage across the 2 resistors, but across the 2 wire segments as well. If one does this and then adds all 4 voltages (going the same direction) in the loop, the result will be close to zero.

But mistakes still could have been made,and i think they were.

Walter Lewin has been at this sort of stuff for years on end,and he knows his stuff.
You also know your way around electronics,that is for sure.
But if the great Walter Lewin can make a mistake,is it no possible you could have as well?.

I would like to draw your attention to the following test i carried out.
 The circuit is hard to draw out,due to multiple loops going through a toroid,so i will explain it instead.

If it is true that all voltage sums around a loop equal 0,then the same should be true for multiple loops, as 1 x 0 or 10 x 0 =0

In the video,i took two identical lengths of wire of the same size.
I soldered the 100 ohm resistor to one end of one length of wire. I glued the resistor to the former,and then wound the wire around the former. This gave me 15 turns. I then soldered the 1K ohm resistor to the end of that wire. I then soldered the second length of wire to the other end of the 1K resistor,and wrapped the second length of wire around the former in the same direction as the first. This of course gave me another 15 turns,where i then soldered that end to the leftover end of the 100 ohm resistor.

Now we have a total of 30 turns going through the hole of the toroid,which means 15 turn on each side of each resistor.

As we have 2 lots of 15 turns,the voltages across each of those 15 turns will cancel each other out,and give us a value of 0v. This leaves only the two resistor voltages,which must also sum to 0v in order for Kirchhoff's loop rule to hold. A visual method was used instead of using the scope,in that an LED was placed across each resistor.
As you can clearly see in the video,1 LED lights brightly,and the other dose not.

Using your measurement method at each of the 4 measurement point's,we can clearly see that the sum voltage is not 0,and Kirchhoff's loop rule dose not apply.

https://www.youtube.com/watch?v=Lm0gGQQtcws


Brad


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Never let your schooling get in the way of your education.
   
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