Does Kirchhoff's Law Hold?

Is it about Mehdi and/or Mabilde against Prof. Lewin and/or Robert H. Romer or is it about Gustav Robert Kirchhoff against Michael Faraday and/or James Clerk Maxwell ?

1845 Gustav Robert Kirchhoff - still being a student at this time - wrote an article in a scientific physics journal “Annals of Physics”

https://gallica.bnf.fr/ark:/12148/bpt6k151490/f509.itemAbout electric current passing through a plane, in particular through a circular one; from the student Kirchhoff.

And at

https://gallica.bnf.fr/ark:/12148/bpt6k151490/f525.item last 3 paragraphs at this page you find his two rules.

As well as next page

https://gallica.bnf.fr/ark:/12148/bpt6k151490/f526.item first paragraph.

Rule 2) being, what everybody calls the KVL today.

As it is in German, a very good translation you find in ‘Elementary Treatise on Electricity’ from James Clerk Maxwell (Oxford 1881) - page 127.

https://archive.org/details/elementarytreati00maxwrich/page/126…Kirchhoff has stated the conditions of a linear system in the following manner, in which the consideration of the potential is avoided.

(1) (Condition of ‘continuity.’) At any point of the system the sum of all the current which flow towards that point is zero.

(2) In any complete circuit formed by the conductors the sum of electromotive forces taken round the circuit is equal to the sum of products of the currents in each conductor multiplied by the resistance of that conductor….

Kirchhoff did not say

Σ V

_{k} = 0

But he basically said, the sum of voltage drops (he expressed as product of resistance and current) equals to the sum of EMFs.

He did not say if emf needs to be based on:

• electrochemical effects (galvanic cells)

• electromagnetic induction (motional emf or transformer emf)

• solar cell or photodiode

• fuel cell based

• Peltier effect

• Seebeck effect

• Hall effect

• or thermopiles responding on radioactive radiation, laser radiation or pressure

Hence, applying Kirchhoff’s second rule would lead to:

I * R

_{1} + I * R

_{2} = Σ EMFs

1 mA * 100 Ω + 1 mA * 900 Ω = Σ EMFs

1 V = Σ EMFs

and not to ‚1V = 0‘

Although the Σ EMFs within a mesh can be as well zero, in case the mash contains no emf, only power consuming elements. But then the sum of voltage drops is zero as well.

How, to know if you measure an emf or a voltage drop? Somehow funny some people argue, ‘you cannot measure an emf’! Partly true, as you measure a small current and conclude to a voltage drop (via a known high resistor) - hence you measure a voltage drop on your internal resistor. But, still you can measure the voltage (even of an emf)! You can measure the voltage of your car battery, the voltage of a transformer, a generator, a solar cell…

To be sure if acertain element is an emf or a voltage drop you need only to watch the current flow direction. For emf current flow is from minus to plus!

Although, Kirchhoff is not wrong and thus his rule holds, he won’t tell us where the emf is hidden exactly !

And he won't help you too much with induction in you probe wires.

Now we need to consult Mr. Faraday.