Talk:Kirchhoff's circuit laws

This article needs some work
The vector calculus expressions are necessary, but a simpler, more practical explanation of the laws should also be included.

Also the copyright notices on the images are distracting and unnecessary in my opinion. — Preceding unsigned comment added by Rogerbrent (talk • contribs) 18:37, 30 March 2006 (UTC)

KCL derivation
User:Constant314 - Regarding my edits for the KCL derivation being reverted since it "proves the obvious", I do not think the proof is obvious. I would agree that it is obvious that conservation of charge and KCL are equivalent. However, this is not what the derivation shows. The derivation shows that if the time varying electric fields between the outside of each component are insignificant, then KCL holds. This is similar to the derivation that currently exists for KVL. If you think the derivation is too much detail (it is in an expandable box for that reason) or needs a citation (most derivations that I could find go from conservation of charge), or is not appropriate because most sources derive it via conservation of charge, then that is understandable. However, I think this derivation is much more useful to help understand when KCL holds and when it doesn't than starting from conservation of charge, which is practically a synonym for it (you might as well say, "Assume KCL, therefore KCL"). Thanks. Hddharvey (talk) 04:32, 18 September 2021 (UTC)
 * Long proofs are often inappropriate for an encyclopaedia article. In an article about a mathematical proof then it is expected, but here it serves only to drive away the vast majority of potential readers.  Kirchhoff's laws were never derived mathematically.  They were entirely experimental laws.  Imo, it is enough to simply state that they can be formally derived from Maxwell's equations and state the limitations.  Readers likely to be interested in the details of the proof are more than likely already able to work it out for themselves and those not interested are likely to go away and find a more readable website.  Also, per MOS:PRECOLLAPSE, Auto-collapsed (pre-collapsed) elements should not be used to hide content in the article's main body for accessibility reasons. Also WP:DONTHIDE. SpinningSpark 11:28, 18 September 2021 (UTC)
 * I agree with this approach. Kirchoff's laws predate Maxwell's work and do not depend on it. The summary of the relationship with Maxwell's laws in the lead is useful but more would be excessive here. We should say (as we do) that KCL is equivalent to conservation of charge and should add that KVL follows from conservation of charge and conservation of energy, but that's enough. Jonathan A Jones (talk) 12:58, 18 September 2021 (UTC)
 * I tend to think of KCL and KVL prescriptive rules for drawing a useful schematic rather than a theoretical result. By useful, I mean that the schematic can be solved and that the solutions are useful approximations of reality.  Real physical nodes have self-capacitance and coupling capacitance to other nodes.  Real physical nodes can violate KCL but a schematic mathematical node cannot.  You fix the situation by adding explicit capacitors to account for self-capacitance and coupling capacitance.  Likewise, a real physical loop in the presence of a changing magnetic field can violate KVL.  You fix it by adding an explicit voltage source or mutual inductance.  We should probably remove the “proof” of KVL.Constant314 (talk) 16:23, 18 September 2021 (UTC)
 * If your (User:Spinningspark) position is that in general derivations such as this shouldn't be present and readers should refer to citations instead, then OK (although it's a pattern I'd noticed in a few other pages for STEM topics, which is why I originally added the KVL one a few years ago). I personally always liked these sorts of pre-collapsed derivations when I saw them in other pages, but that is my opinion. The boxes that I've used appear to be uncollapsed by default on mobile or web browsers with JavaScript disabled, which means accessibility issues do not seem to be a problem but is understandably an issue for longer or more convoluted derivations.
 * User:Jonathan A Jones - Could you explain in what sense does KVL follow from conservation of charge and energy?
 * Hddharvey (talk) 23:50, 19 September 2021 (UTC)
 * Actually, that puzzles me, too. Constant314 (talk) 00:19, 20 September 2021 (UTC)
 * Maybe the derivation would be ok as a standalone article (I think enough sources cover this to make that a viable article). Readers going to a page like that will know what they are getting into.  On the accessibility issue, the practice of collapsing segments predates Wikipedia becoming concerned about accessibility, so there's a lot of it pre-existing in the encyclopaedia, but it is now considered deprecated.  It's not just the mobile view that's an issue, I believe it does something horrible to screenreaders as well.  Accessibility has rapidly evolved from "please consider" the issue if you can, to a set of hard rules.  Best not to use it from now on. SpinningSpark 12:07, 20 September 2021 (UTC)


 * It's an interesting idea. Is there much precedent for having "Derivation of X" articles? The derivations wouldn't be that long (as you can see from the page history), although it would give some room to do a little bit more. If the derivations aren't too long, another option is just having a section at the very end of the current article. That avoids the use of the expandable box while not getting in the way of the main article (as an aside, I don't know how sophisticated screen readers are these days, can they read Wikipedia equations at all? - are you really gaining anything). Although based on what you've all said before it sounds like you don't want such derivations in the article. Hddharvey (talk) 12:53, 20 September 2021 (UTC)
 * What we have now might be short, but there must be some history behind this and there must be sources for it. Since we know Kirchhoff didn't get there through Maxwell's equations, somebody else must have done it first at a later date.  As for comparable examples, there doesn't seem to be any shortage of them; Proof of Fermat's Last Theorem for specific exponents, Derivation of the Routh array, Derivation of the conjugate gradient method, Derivation of the Schwarzschild solution, Derivation of the Navier–Stokes equations to name just a few. SpinningSpark 14:05, 20 September 2021 (UTC)
 * That's beyond the scope of what I'm interested in doing on Wikipedia at the moment. Hddharvey (talk) 02:27, 21 September 2021 (UTC)
 * I just provided a derivation and discussion of the Kirchhoff Current Law. I do not know how to put it into Wikipedia format and would like help doing that.
 * The motivation for this work is that Kirchhoff's law is routinely applied to conditions that are not slow. But the discussion and derivation in Wikipedia and textbooks is for slow systems only. That should be dealt with.
 * It can ONLY be dealt with by using the Maxwell equations, because the essential issue is the displacement current that appears only in the Maxwell equations. Beisenbe (talk) 15:01, 2 March 2024 (UTC)

Image of KVL is incomplete
To completely specify a current, we must define its reference direction (arrow) and its value or symbol in the circuit diagram. Then, we can apply KCL. This was correctly done in the image of the section "Kirchhoff's current law", which has the caption "The current entering any junction is equal to the current leaving that junction. $$i_2 + i_3 = i_1 + i_4$$".

To completely specify a voltage, we must define its reference polarity (+ and - symbols) and its value or symbol in the circuit diagram. Then, we can apply KVL. However, in the image of the section "Kirchhoff's voltage law", which has the caption "The sum of all the voltages around a loop is equal to zero. $$v_1 + v_2 + v_3 + v_4 = 0$$", the reference polarities for the voltages weren't specified in the circuit diagram. So such definition of voltages is incomplete. Therefore, the equation $$v_1 + v_2 + v_3 + v_4 = 0$$ doesn't make sense until we define the reference polarities for the voltages in such image. Please do so, or use another image. It seems was the user who created the image, so I'd like to ask you to please add the "+" and "-" symbols for each voltage (except for the voltage which is obvious). — Preceding unsigned comment added by Alej27 (talk • contribs) 15:47, 10 January 2022 (UTC)


 * Those polarities are defined by the currents in each branch. Take a resistor: if you assume that a current is flowing from its terminal A to its terminal B, then terminal A is (must be!) at a higher potential (~voltage) than terminal B. The +/– symbols can be added, but don't need to: if you're traversing a branch of the loop in the direction of the current you take one sign for the voltages, and the other if you're traversing a branch going against the (assumed direction of the) current in the branch. Ponor (talk) 03:57, 11 January 2022 (UTC)


 * Three things. 1) The branch current isn't even labeled in the figure, nor the direction in which the loop was traveled (recall we can apply KVL without assuming a direction for the current), so there's no way to infer the voltage polarities of the three resistors (sure, we may say the current travels clockwise due to the source, but if I want I can define the positive reference direction for the current to be counterclockwise, and now all the voltage polarities of the resistors in the figure are wrong). 2) If we follow what you say, then the image caption is wrong, the equation should be $$v_4 = v_1 + v_2 + v_3$$ or $$v_1 + v_2 + v_3 - v_4 = 0$$ or $$-v_1 - v_2 - v_3 + v_4 = 0$$, not $$v_1 + v_2 + v_3 + v_4 = 0$$, because the voltages across the resistors are potential drops while the voltage across the source is a potential rise. 3) We shouldn't mix up KVL with Ohm's law; I mean, I understand what you say, but that's true because of Ohm's law, and I believe this article shouldn't bring Ohm's law to the discussion; I can define the polarity for two resistors to be opposite and still get a correct equation from KVL. Thanks for your reply anyway. Let's see what the others think. :) Alej27 (talk) 09:33, 12 January 2022 (UTC)


 * I agree that the figure could be improved. Perhaps  can comment.  Anyway, the rule is that as you go around the loop (typically clockwise, but it doesn't matter), you always assign polarities the same way.  That is, is you assign + to the first node of the first element that you encounter, then you assign + to the first node of every element as you encounter it. Constant<b style="color: #1100cc;">314</b> (talk) 07:06, 11 January 2022 (UTC)


 * That's common in mesh analysis, though it's not a necessary rule. We can arbitrarily choose the reference polarities for the voltages of the three resistors, then apply KVL (and later on Ohm's law) and still get a correct result. Because of this, I think we should specify the reference polarity for the three voltages in the figure, and perhaps clarity in the article that they can be arbitrarily chosen. Of course, as you know, once we've arbitrarily chosen the voltage polarities, if we want to apply Ohm's law for a given resistor, the current direction for that resistor is such that the passive sign convention is satisfied in that resistor, so the current direction is not arbitrary if we already chose the voltage polarity; however I believe that should be discussed in the article on Ohm's law, not assumed here. Alej27 (talk) 09:33, 12 January 2022 (UTC)
 * KVL says that the sum of the voltage drops around a loop adds to zero. For that to work, you must assign the voltage drops as I have outlined.  That does not preclude you from assigning other voltages inside the device.  In the example, if you went around the loop clockwise, then you would assign the + sign for $$v_4$$ at the bottom of the symbol.  If the symbol was a 10 volt source, then $$v_4 = -10$$.  That is how it must work.  If you want to assign arbitrary polarities, then it is a bookkeeping problem.  For example, using primes to indicate arbitrarily assigned polarities, you could have $$v_4^' = -v_4 = 10$$. Constant<b style="color: #1100cc;">314</b> (talk) 17:03, 12 January 2022 (UTC)

Which statement describes cybersecurity?
Which statement describes cybersecurity? 2401:4900:3133:3E98:0:57:4BCC:BD01 (talk) 14:36, 23 September 2022 (UTC)
 * You are thinking of Kerckhoffs's principle which is completely unrelated. Jonathan A Jones (talk) 16:06, 23 September 2022 (UTC)

Current law needs a sensible derivation
It is outrageous to have a law used as widely as Kirchhoff's current law presented without a derivation that applies to its actual usage. The derivation needs to apply to the modern usage of the law, which is to circuits that are NOT slow. Indeed, computer circuits operating on time scales of nanoseconds or faster are designed successfully with the circuit. Furthermore, the statement about constant charge is ridiculous: " If the net charge in a region is constant, the current law will hold on the boundaries of the region. This means that the current law relies on the fact that the net charge in the wires and components is constant." Kirchhoff's current law is used widely, indeed nearly universally to derive properties of circuits on time scales of nanoseconds. Charge is NOT constant in such systems.

In fact, Kirchhoff's current law can be derived in three ways

1) as an approximation for slow systems and long times. This approximation is seriously incorrect for modern applications that are nothing like slow.

2) as an approximation, by supplementing the original circuit with stray capacitances. The values of the stray capacitances are chosen empirically to fit with measurements from real circuits. The relation of Kirchhoff's law and the Maxwell equations is not discussed in approach and the fact that real circuits always show transients is glossed over.

This is the approach taken without ceremony by practicing engineers and it works remarkably well for circuits. This approach does not work in three dimensional systems without an obvious circuit representation like the cells and organelles of biological systems (which by the way have important electrical properties). It also has difficulties for circuits of complex geometry, as abound in computer chips, where there may be more than one scheme for supplementation.

3) by using the definition of total or true current that Maxwell used. This definition includes a time derivative term that is called displacement current. This approach works in circuits and three dimensional systems. It can be derived by mathematics, following Maxwell's approach, without approximation. It does not correspond, however, to the usual approach of engineers because time dependence is always present in this approach, as in the real world, whereas time dependence is not always present in the classical derivations and persentations of Kirchhoff's current law. Thus, this approach of Maxwell himself has not been used in the modern literature for the most part (except by Landauer). Beisenbe (talk) 15:36, 18 February 2024 (UTC)


 * @Beisenbe I don't profess to understand this topic at all, but could I invite you to add links to published sources which can be used to support the content you wish to see, and maybe even to provide the best form of words that would fill the gaps you have identified to make it more of an encyclopaedic article? Thanks, Nick Moyes (talk) 01:02, 19 February 2024 (UTC)
 * This article on Kirchhoff’s laws is an introduction to the topic. It matches the introduction typically found in textbooks for high school students of physics and college students of electrical engineering. The article does not yet claim to be a comprehensive presentation of Kirchhoff’s circuit laws at the advanced level advocated by Beisenbe. This is not surprising - the reliable published sources cited in the article do not cover the topic at the depth advocated by Beisenbe. For example, Beisenbe advocates that Wikipedia’s presentation of Kirchhoff’s laws should mesh with Maxwell’s laws; but reliable published sources introduce Kirchhoff’s circuit laws without requiring the reader to be familiar with Maxwell’s laws. In any course in physics or electrical engineering, Kirchhoff’s circuit laws are more fundamental than Maxwell’s laws.
 * Beisenbe is resorting to sensationalism to present their ideas - for example “It is outrageous...” and “Charge is NOT constant ...” Our experience tells us that Users who are able to substantially build Wikipedia content are usually positive and constructive from their first appearance; Users who are motivated by a desire to criticise the encyclopaedia and promote their own expertise usually don’t stay for long. It appears that Beisenbe wishes to display their expertise and tell us what we should be doing to build the content of the article, but I don’t sense that they are about to roll up their sleeves and start on the hard work required to build content. <i style="color: green;">Dolphin</i> ( t ) 09:16, 19 February 2024 (UTC)
 * You will need a reliable source (WP:RS) that has words that say, in effect, "the following is a derivation of KCL from Maxwell's equations." <b style="color: #4400bb;">Constant314</b> (talk) 12:42, 19 February 2024 (UTC)

Kirchhoff Current Law needs a derivation relevant to modern, high speed applications
February 29, 2024

Concerning treatment of Kirchhoff’s Current Law

Dear Editors,

There is a serious problem with the Wikipedia Article on Kirchhoff’s Current Law (viewed February 29, 2024) that directly affects readers interested in modern circuits.

The law is not derived in a way that can be applied to modern circuits. The law is presented as an approximation for slow systems, but modern circuits are not slow.

Here is the formal argument

The current in the discussion of Kirchhoff’s law is the flux of charges with mass.

Kirchhoff’s law then says that charges do not accumulate.

However, the Maxwell Ampere law of electrodynamics says otherwise.

Take the divergence of both sides of the Maxwell Ampere Law, remember that the divergence of curl is zero (as long as the operators are defined), and see that the divergence of conduction current is NOT zero Thus, the Maxwell Ampere Law says conduction current DOES accumulate. Kirchhoff’s Current Law says conduction current does NOT accumulate. Experiments (e.g., with any circuit of 1 megohm resistors) show transients of the order of 0.1 to 1 microseconds. These transients settle down but on a time scale very much slower than those of modern circuits. Engineers deal with these contradictions by changing the circuit they are analyzing. They add supplemental elements to the circuit [1-3] creating a new supplemented circuit. They place parasitic (stray) capacitances in parallel with circuit elements. This is the approach in modern design texts [3-10].

This fix-up works remarkably well [10-13], for reasons derived in [14] but the fix-up is not complete, and in that sense, is not correct. The values of the capacitances are unspecified and the large numbers of capacitors needed in modern high speed circuits is problematic, and probably unable to deal with all the time dependence that occurs in real circuits.

Maxwell resolved this paradox by defining a true current that includes a time derivative terms, as does the right hand side of the Maxwell Ampere Law, as discussed at length [14].

Maxwell said (in slight paraphrase) that analysis must include a time derivative term. The logical implication is that analysis without the time derivative term is incorrect. Kirchhoff’s law is thus incorrect in his view.

Whatever one’s view of Maxwell’s comments, the argument in this note is based only on mathematics.

My Request:

Please correct the Wikipedia entry on the Kirchhoff current law so

a)      It includes a derivation of Kirchhoff’s law that is useful on the time scale of modern applications.

b)      The current law is not in conflict with the Maxwell Ampere Law

c)      The derivation and discussion does not confuse students who observe transients in circuits made of only resistors, when Kirchhoff’s law says there should be none.

Reference should be made to the literature with [15] and [16] and moving to the more complete review [14]. My knowledge of that literature is foreshortened by human prejudice and further references should be provided.

Ever yours,

Bob Eisenberg

References

1.           Horowitz, P. and W. Hill, The Art of Electronics. Third Edition ed. 2015: Cambridge University Press. 1224.

2.           Scherz, P. and S. Monk, Practical electronics for inventors. 2006: McGraw-Hill, Inc. 1056.

3.           Sedra, A.S., et al., Microelectronic Circuits. 2020: Oxford University Press, Incorporated.

4.           Ayers, J.E., Digital Integrated Circuits: Analysis and Design, Second Edition. 2018: CRC Press.

5.           Dobkin, B. and J. Williams, Analog circuit design volume 2: immersion in the black art of analog design. Vol. 2. 2012: Newnes.

6.           Gielen, G. and W.M. Sansen, Symbolic analysis for automated design of analog integrated circuits. Vol. 137. 2012: Springer Science & Business Media.

7.           Gray, P.R., et al., Analysis and Design of Analog Integrated Circuits. 2009: Wiley.

8.           Lienig, J. and J. Scheible, Fundamentals of layout design for electronic circuits. 2020: Springer Nature.

9.           Muller, R.S., M. Chan, and T.I. Kamins, Device Electronics For Integrated Circuits, 3rd Ed. 2003: Wiley India Pvt. Limited.

10.        Okoshi, T., Planar circuits for microwaves and lightwaves. Vol. 18. 2012: Springer Science & Business Media.

11.        Schwierz, F. and J.J. Liou, Modern microwave transistors: theory, design, and performance. 2003: Wiley-Interscience.

12.        Fukunaga, K. and S. Kurahashi. Dielectric properties of printed circuit board insulations at microwaves and millimetre waves. in ''Electromagnetics in Advanced Applications, 2007. ICEAA 2007. International Conference on''. 2007. IEEE.

13.        Mei, K.K. From Kirchoff to Lorentz modifying-circuit theory for microwave and mm-wave structures. in ''Infrared and Millimeter Waves, 2000. Conference Digest. 2000 25th International Conference on''. 2000. IEEE.

14.        Eisenberg, R.S., Maxwell’s True Current. Computation, 2024. 12(2): p. 22.

15.        Eisenberg, B., et al., What Current Flows Through a Resistor? arXiv preprint arXiv:1805.04814, 2018.

16.        Eisenberg, R.S., Kirchhoff's Law can be Exact. arXiv preprint available at https://arxiv.org/abs/1905.13574, 2019. Beisenbe (talk) 14:54, 2 March 2024 (UTC)