Kirchhoff laws are incorrect: Dr Lewin´s experiment

THE EXPERIMENT AND CONCLUSIONS OF DR. LEWIN: MISTAKEN REASONINGS

Hello everyone, in this time we are going to talk about something different. This post is not only for educational purposes, it is for arguing. And the topic is about the Kirchhoff laws and Dr. Lewin´s experiment. Doctor Walter Lewin is a professor of Physics in the MIT (Massachusetts Institute of Technology). Recently he did a experiment which consisted in a pair of cables connected to form a ring, a solenoid which produces a time varying magnetic field and two voltimeters to measure the voltage between some strategic points as shown:

  

Figure 1: Circuit of the experiment. The direction of the currents are supposed. The inductances of the two cables are not represented in this image (see Figure 6)

Description of the experiment 

A solenoid is a coil with a specific number of turns N and it has an inductance L. The conductor carry the electric current generated by a source (Function generator, power supplies, etc). As 4rth Maxwell law says magnetic fields are produced by currents, and are proportional to the number of turns.

Figure 2: 4rth Maxwell Law (The integral in a closed loop is equal to the multiply of the number of turns and the enclosed current). 

As the current depends on the time the magnetic field generated also depends on it. This is a time varying magnetic field. Ignoring the magnetic flux leakage (produced by the dielectric material between the ring and the solenoid, which is air) the entire magnetic flux concatenates in the ring, inducing an ElectroMotive Force (or EMF). This is given by the Faraday-Henry´s law as shown:

Figure 3: The electromotive force is equal to the multiply of the number of turns and the derivative of the magnetic flux respect to time. 

The unit of the EMF is the volt (V). It is a common mistake confunding voltage and the EMF. As it was explained the electromotive force is generated by inductive elements, such as a coil, with an inductance L and a specific number of turns. The voltage can be generated with anything, it is only the potential energy given to the electrons for generating currents and power supplying. This is the reason why engineers like us usually describes the Faraday´s Law with voltage, and not with EMF. Nevertheless the correct term is electromotive force for induced voltage. 

The ring is the induced element. Also it is formed by the connection of two cables, each one with different resistance. A cable always has an inductive and a resistive effect. The inductive effect explains why an EMF is induced, so inductances L1 and L2 are considered, and EMF1 and EMF2 are induced. Also has a resistive effect, because all standard materials oppose to the electrons that are flowing through them. 

Then voltimeters V1 and V2 are used. Each one has a high internal resistance value R, which is the same in both devices. The real measurements of the experiment showed that EMF1 and EMF2 are not the same. So Dr. Walter Lewin concludes that this can not be possible considering Kirchhoff laws because 2nd Kirchoff law says that the sum of the voltages across the loop must be zero. EMF1+EMF2 is not zero, so here is the contradiction. Also Dr. Lewin says that it is not possible that two resistors in paralell have different voltage. 

Here are the mistaken reasonings

The main problem with Dr. Lewin´s conclusion is the interpretation of the circuit. Every circuit has active and passive components that need power to work. This power is given by a source and doesn´t matter if the voltage is induced. For example, the equivalent circuit of synchronous generators include a voltage source that represents the electromotive force induced in the stator. In this particular case the Kirchhoff laws are correct:

Figure 4: Equivalent circuit of the synchronous generator. The EMF induced in the stator is Ea. It is represented by an ideal voltage source. 

So in this case we need to consider the EMF generated (we are going to call it "V") in 2nd Kirchhoff law, so it is true that V-EMF1-EMF2=0. This Kirchhoff law is correct. I will put a video link at the end of the article about this topic. The youtuber "Electroboom" shows this facts perfectly with real experimental values. 

Dr. Lewin also says that Kirchhoff law only considers "voltage" and not EMF. The second law is based in the conservation of energy. As I said, voltage and EMF are potential energy given to the charges, the only difference is the origin of the energy. The first one is generated by a source like a battery and the second one with inductors. So 2nd Kirchoff law also considers the electromotive force. If this were not true, every circuit designed by electrical engineers would not work. 

The last thing we need to talk about is the configuration of the two resistors. As I demonstrated in my previous posts in Spanish, two resistors are in paralell when the voltages across them are the same. This is not the case. Two resistors are in series if the currents that flow through them are the same. This last statement is correct, as Dr. Lewin showed in the experiment results. If the two resistors are in series the voltages generated are not the same, because the resistance values are not equal. This is a voltage divider, and if we use Ohm´s law the potential difference of the resistor R1 is different from the potential difference of the resistor R2 as I show:

Figure 5: Demonstration of the different measures of the induced voltage.

So this is the equivalent circuit of the experiment: 

Figure 6: Equivalent circuit of the experiment. 

See that I summed the two inductances of the cables. This is explained in the next figure:

Figure 7: Demonstration of the previous statement. 

Now we are going to consider the effect of the voltimeters. The internal resistance of the two devices is bigger than any of the resistance values of the cables. So this means that the current drawning by the voltimeters has a too low value, so we can ignore this "leakage current" and consider a unique current flowing through the ring. This is proven in the following figure: 

Figure 8: Demonstration of the low current drawning.

FINAL CONCLUSION

The conclusion of all of these is that Kirchoff laws are correct in this particular experiment. The second law shows that the energy generated by the source (the solenoid in this case) is equal to the sum of the energy consumed by cable 1 and cable 2. As far as I know, Kirchhoff laws are correct in every circuit and work. Also are two of the most important statements in electricity and circuit analysis. 

Doctor Walter Lewin is an incredible physicist with amazing explanations of different experiments and other knowledge. But in this time I can´t be agree with him about this experiment. 

I hope you like this article. If you didn´t understand something please send me an email or leave a comment. Also if you think there is some mistakes about my conclusions we can discuss it. I am opened for learning more.

The links of the youtuber "Electroboom" talking about the issues: https://www.youtube.com/watch?v=0TTEFF0D8SA  ; and the other one: https://www.youtube.com/watch?v=Q9LuVBfwvzA