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Is MIT Prof. Lewin wrong about Kirchhoff's law?

  1. Dec 4, 2010 #1
    So I just watched Walter Lewin's lecture titled "complete breakdown of intuition". If you google it you can find it on youtube.

    He claims that measuring across one resistor of a two resistor network gives a different voltage than measuring across the other resistor, if you are inducing current in the circuit from EMF. In his circuit diagram, the voltage probes are on the same nodes. I think you have to watch the video for a better explanation, but my question is:

    Is he just not accounting for inductance in his experiment? He claims other professors don't believe him, and neither do I. I wish I could see his experimental setup, as his argument seemed really flawed to me. What do you guys think?

    I personally would like to see voltage measurements between his two voltage probes, which I think would show Kirchhoff's Voltage Law still applies.
  2. jcsd
  3. Dec 4, 2010 #2
    Voltage drop across the wire!!! You don't think of the wire is a short circuit, it is a one turn loop, it is a one turn inductor. This is like a transformer, the secondary winding is not just a wire, the turns make up an inductor, magnetic field through the coil produce voltage. It is no longer a wire that have 0 volt across it. In real world, you have to define where is point D and point A along the wire that connect the two resistor. If you argue that the resistor is connect directly to each other, then the resistor body has to form a loop in order to let the magnetic field past through the middle. there is no way out of this. To give the real picture of the circuit, you have to add two inductors between the two resistors then you see the whole picture.

    Good luck to measure in real world. The resistor is part of the loop and voltage drop not only consist of ohmic drop due to 1mA, but the induced voltage when the resistor body become part of the one turn loop. I don't think the Kirchhoff don't work, the professor is wrong about the model, he just assume the wire is 0 ohm and is only a point. This is common of for people in acadamic to think a return path or current path is ideal!!! In real world, these paths usually are the trouble makers!!!
    Last edited: Dec 4, 2010
  4. Dec 4, 2010 #3


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    Most of what he says is correct. You cannot define voltage at a point in a circuit if the integral of E around a closed circuit is non-zero. Id est, you have non-conservative field. You can still define voltage drop across the resistor, however.

    He is making a mistake with voltmeters, though. The voltmeter reading will depend on where the needles are attached, and the reasoning for that is pretty well covered by yungman.
  5. Dec 4, 2010 #4
    His argument is not flawed and his experiment and description of it are correct. This topic has come up a couple of times before, so you can do a search and dig up more information.

    The only issue I see is one of semantics. The good Professor clearly defines what he means by Kirchoff's Law, and specifically he defines it as the statement that the integral of the electric field around a closed path is equal to zero. If you accept this definition, then that's the end of the story - he is 100 % correct. However, there are at least two competing definitions of Kirchoff's Law in text books. Many books define Kirchoff's Voltage law as the statement that the sum of voltage drops around a loop is equal to the sum of EMFs around a loop. If you use this definition, you can let it conform to Faraday's law, and all is well.

    Personally, I hate arguing about semantics, so I won't detract from the thread with any claims that one definition is better than another. The last time we talked about this, I decided to go to the library and do a survey of books, both old and new, I was surprised to see that these competing definitions exist in physics and electrical engineering books throughout the 20'th century.

    Personally, as an electrical engineer, I prefer to carry around a version of KVL that is consistent with Faraday's Law. False laws don't really help me very much - not in theoretical work, nor in practical endeavors. They do make for very provocative and exciting lectures though. :smile:
  6. Dec 4, 2010 #5


    Staff: Mentor

    IMO Prof. Lewin is setting up a strawman argument here for pedagogical purposes. stevenb is correct to note that Prof. Lewin clearly defines what he means by KVL and then proceeds to show how his definition of KVL is incorrect by explaining some important physics. However, his assertion that KVL is wrong is a strawman argument because his definition of KVL is not the definition in general use; at least it is not the definition used by any of the three relevant textbooks (1 physics book, 2 circuits books) on my shelf.
  7. Dec 4, 2010 #6
    Prof. Lewin is right. KVL is a conditional law based on conditions that no time changing mag fields are present. It holds when this condition is met. KVL is not a universal law. When a mag field changes w/ time, the sum of voltages around a loop is non-zero.

    So 2 elements in parallel are not at the same voltage. The voltage from a to b depends upon the path taken. Dr. Lewin does a good job explaining this. I had to work with these principles for years when I was in magnetic component development. When designing inductors, transformers, rf chokes, motor drives, regenerative braking, etc., I became accustomed to knowing that KVL only holds when no time changing mag fields are present. It became second nature.

    Those whose experience w/ electronics does not include magnetics will at first struggle with Dr. Lewin's teachings. It seems counter-intuituve at first glance. But Maxwell & others have verified their claims & over a century of scientific testing/observation have afformed the same.

    Dr. Lewin is on solid ground, for sure.

    Last edited: Dec 4, 2010
  8. Dec 4, 2010 #7
    I don't see how can the professor be right, he just draw the schematic wrong. If you put two inductors between the two resistors, Kirchhoff holds, no if and buts about it. That is the reason when an academia talked about a real life circuit, I get very skeptical. I am stunned he actually talk as if this is an ingenious thing!!! It only take me but 3 minutes to see his problem in the eye of a practical engineer, how to set up the experiment in his case, to realize he is missing the moon.

    I am not argue about the non conservative field that is path dependent, that is all beside the point and he was correct. This has nothing to do with it. He was just wrong and he did not have the “common sense” to even see it. AND he was plain wrong to say Kirchhoff is wrong when he did not see that the wire is an inductor. If he want to teach engineering EM, he really need to get a job for a few years to get some common sense.

    FYI, if he set up the field into the loop so he actually get 1mA through the loop, the loop voltage is not 1V, he did not take into consideration of the voltage drop across the inductance of the wire loop. The loop voltage is more, at least 0.8V more in order to get 0.1V across the 100 ohm and 0.9V across the 900 ohm.

    I my 27 years as a senior EE and manager of electrical engineering, I had seen people from ivy league college that can’t make the transition from books and theories to real world and part of it was because they think too highly of themselves to see that they were wrong and drowned in their little theory. This is partly because the professor that taught them were like this one.
    Last edited: Dec 4, 2010
  9. Dec 4, 2010 #8


    Staff: Mentor

    You are partly correct. KVL is indeed an approximation to Maxwell's equations based on the assumptions of circuit theory which are, as follows:
    1) the circuit is small relative to the wavelengths involved (lumped-parameter system)
    2) no net charge on any component at any time
    3) no magnetic coupling between components

    You can have changing magnetic fields within a component (e.g. in an inductor) as long as there is no magnetic coupling between components.
  10. Dec 4, 2010 #9
    Here is a handout where Walter Lewin explicitly describes how most physics books apply KVL wrong in the case of inductors.
    Last edited: Dec 4, 2010
  11. Dec 4, 2010 #10
    Last edited: Dec 4, 2010
  12. Dec 4, 2010 #11


    Staff: Mentor

    The usual KVL is fine in the circuit he draws in that handout. The third assumption is not violated in that case since the magnetic field is confined to the inductor and does not couple to the rest of the circuit. But I do very much like his treatment of induced currents and fields in non-uniform loops.

    Of course, his strawman version of KVL is wrong, but that is the point of a strawman.
  13. Dec 4, 2010 #12
    I am partly correct?!?!?! So I must also be partly wrong? Just where am I wrong?

    Re 1), that is the criteria for neglecting t-line behavior, treating wires as mere conductors. I don't think that is relevant here.

    Re 2), no net charge?! Capacitors have a net charge yet KVL still may or may not hold, depending on presence of time varying fields. Net charge is irrelevant.

    Re 3), net coupling between components is mutual inductance. A lumped parameter mutual inductance may be included in the circuit model to account for it. That does not change whether or not the E field is conservative or non-conservative.

    Please elaborate where I'm wrong. The 3 issues you raised do not determine whether KVL holds or not. What matters is whether the E field is conservative or not. This is established law.

    Dr. Lewin is dead on, spot on, dead right, right there, etc. Not one statement he made can be knocked down. I'm a little surprised that something so basic can be controversial. The non-conservative nature of E fields involving induction is not open to debate. The law is established.

  14. Dec 4, 2010 #13
    I read about two and half pages and my mind started to wander away. I have no problem understanding about his presentation about the basic varying magnetic field causing varying electric field. Those are all correct. BUT that is so not the point!!! The point is he need to include the rest of the circuit voltage like the [itex] L \frac{d I}{d t}[/itex]. Seems like people put all the emphasis on the basic theory and nobody talk about the practical aspect. AND this was my experience of how engineers got into hopeless trouble making their simple circuit work.

    It is so funny at the end of the paper, he try to tell people at the last part that the voltmeter read incorrectly because the loop formed by the probe lead form a loop and pickup the induced emf!!! The kind of arrogance he has to think people miss this kind of basic things and other people making mistake. If I were to do this experiment, I would use a coax to point solder across the resister with no loop and connect to the voltmeter to make sure no loop to pickup the magnetic field. This is such basic precausion!!!! In my experience, if you don’t get a measurement you want to see, 50% of the time is the error of your setup. The % go higher as frequency goes up or the current goes up because the “parasitic” effect become more prominent.

    You know, the academia create the term “parasitic” element to cover what they left out on their model….Like what he draw on the blackboard. The whole thing is not even hard to understand if he would have just presented in the correct way.

    Sorry that I am so critical about the academia, this is compounded from the past experience and looking at those academia trying to fix the economy of this country and is going nowhere. Academia need to get a real job before they talk so loud and the sad part is people listen to them because of their titles……..PHD!!!!

    Last edited: Dec 4, 2010
  15. Dec 4, 2010 #14
    @DaleSpam: I'm interested in the other version of KVL. Is it "sum of voltage drop = sum of emf"? Anyway, how do we define the term "voltage" in the case of varying magnetic field?

    The above criterion of the lumped circuit discipline holds. Capacitor and inductor are simply modeled in a clever way to fit in the restriction.

    The 3rd restriction that DaleSpam wrote, I think, is not the direct result of the physics behind the lumped circuit discipline. It is only correct after all the components are modeled. The best, and also worst, thing is, accepting KVL (the two versions as far as I have known) does give correct applicable results and does not show the real nature of the physics.

    @yungman: Maybe you can give us some qualitative analysis on the point that inductance of the wire should be taken into account and that retains the validity of KVL? The experiment seems to be so unbelievable, and so is your statement, to me (though it's true that the wire might be significant when it comes down to 100 micro-meter-long transistors).
    Last edited: Dec 4, 2010
  16. Dec 4, 2010 #15


    Staff: Mentor

    Where you said that "KVL only holds when no time changing mag fields are present". In an inductor there is a time changing magnetic field, but KVL does just fine with inductors.

    A capacitor does not have a net charge.
  17. Dec 4, 2010 #16
    Basically, yes. You have to take the 'old' definition of EMF though.

    It is also what K wrote in the original German. SteveB dug this out for another website once before.

    This has also been noted here in previous threads, as has the originating video.


  18. Dec 4, 2010 #17
    You can look up, there are data about inductance of a straight wire and it is not high, but if you look at the professor's example, the create the voltage in the one turn loop, you need high [itex] \frac{di}{dt} [/itex] and opening the switch will do that.

    There is formula of rise time to the frequency translation of something like the period is 3 times the rise time. With sub nano second rise time, even 1/4" wire become significant. If you are familiar with the Smith Chart, you'll see the line go through transistion between short circuit and open circuit and inductance. I did a lot of design on fast rise time pulsing circuit and RF design, we use grounded line as short as 3/8" to create an open circuit ( quarter wave Tx line ). It is the frequency component that is important.

    Your statement about 100 micro meter long transistors has NO bearing on the length of the wire. Depend on how the wire is, it vary a little, but basically it is a H/m spec on the wire. It might sound low, but under high [itex] \frac{di}{dt} [/itex], it does become significant. If you use the scope to moniton the switch when it open, the voltage rise time is in sub nano second range ( limited by speed of the scope ). That kind of speed will induce significan voltage in even a very short length. If you use a slow varying field, you won't see that.

    If you still don't believe, I see sub nano second rise time on a mechanical switch open and close!!! In his paper he open the switch and the current go immediately from 1mA to 0 in sub nano seconds, no if and but about it. You see arc when you open switch on circuit with inductor in series because it can generate very high voltage and it actually ionize the air around the contact and arc.
    Last edited: Dec 4, 2010
  19. Dec 4, 2010 #18
    I meant time varying fields present in the circuit loop. Time varying fields on the interior of the inductor is modeled by circuit theory, w/o the need to consider fields. The Lewin paper explicitly stated the field inside the circuit loop, not that on the interior of an inductor. Did you read the paper by Dr. Lewin?

    As far as a cap having " no net charge", this is very semantical. "Charge" as used by the science community implies "differential". An "uncharged cap" has lots of charge, but zero difference. A "charged cap" has the same total absolute charge but is displaced forming a differential. If you define "net charge" as total charge on both plates, then of course there is no "net charge" in either case, energized or not.

    Whan I say "charge" in ref to a cap, I infer the differential quantity, not the absolute total which you define as "net charge".

    Dr. Lewin is correct on all counts. He simply illustrated how non-conservative fields differ from conservative. You're trying to look for reasons to poke holes in his case by bringing in arbitrary arguments based on your own semantics. In the final analysis Dr. Lewin states the following.

    1) With conservative E fields, KVL holds, & the potential from a to b is independent of the path.

    2) With non-conservative E fields, KVL does not hold, & the potential from a to b is dependent on the path.

    Introducing hyperbole does not alter this basic tenet. Is there any issue with the above 2 statements?

  20. Dec 5, 2010 #19
    @Studiot: I guess the 'old' definition of emf has something to do with the supply - things that propel electricity? So on the other side of the equation, what is the voltage drop of, say, a power supply V?

    @yungman: I think when it comes down to nano seconds, Kirchhoff's laws don't even hold. The characteristic length = speed of light x time = around 10cm, significant enough for the set-up in Prof. Lewin's experiment (he has quite a big coil obviously!). And yes, during the time after he switched on the coil and the current goes up *instantaneously* to 1mA, wires are no longer "nothing". However, during this period, no conclusion can be drawn.

    But the point is that, after this period, when dB/dt decreases, the period is about mili-seconds. The current also decreases from 1mA to zero during this period, so di/dt is no longer that large. The graph of V1 and V2 during this period can be seen, and they are not the same.

    And one more point: Though personally I also want to see with my own eyes the set-up of the experiment, I think even if no conclusion can be drawn from this experiment, what Prof. Lewin said is based on the fundamental - Faraday's law or Maxwell-Faraday equation. He is NOT making a new theory. The subtlety is that, accepting KVL (provided that the characteristic length >> dimensions of the circuit) does give out correct final results, though KVL is not true in this case.

    @cabraham: The term "potential" should be redefined in your #2 statement. IMHO, strictly speaking, this term should NOT (and does NOT, as mathematics says) exist for non-conservative field. Prof. Lewin tried to avoid the term in his papers.
    Last edited: Dec 5, 2010
  21. Dec 5, 2010 #20
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