Talk:Reciprocity theorem

Leading link

I have reverted this edit because an editor has created an article at reciprocity theorem. The leading link of a dab page should refer to the article of that name, if it ezxists (and at the very least it needs to be on the dab page somewhere). Whether or not the editor should have created an article at that title is a different question, but not an issue for here at the dab page. All I have done here is rescue the dab page from a botched article creation which overwrote it. Spinning Spark 01:27, 6 June 2011 (UTC)[reply]

Three problems:

First, the editor should have created a page like Reciprocity theorem (electrical networks) or something like that, rather than making it "the" reciprocity theorem page, since there was no argument that this meaning is the most central one. Reciprocity theorem should be a disambiguation page (or redirect to one).
Second, Reciprocity (electromagnetism) already exists, and gives the application of electromagnetic reciprocity to electrical networks (as well as to more general cases). Because of that, I have removed the extremely incomplete stub at Reciprocity theorem and changed it back to a disambig redirect. There is no need to link to a page which no longer exists.
Third, even if a Reciprocity theorem (electrical networks) page is created, that should be listed as only one of the possible meanings on the disambig page, with the others being additional meanings, not as the first or most important meaning (without evidence that this is widely accepted as the case).

— Steven G. Johnson (talk) 01:52, 6 June 2011 (UTC)[reply]

No real argument with removing the new article, it was very bad - I was just trying to be kind to a newbie by cleaning it up rather than revert out of hand. I do, however, support the creation of such an article; to all electrical engineers what the editor was talking about is indeed their understanding of reciprocity theorem. Although reciprocity (electromagnetism) does give a one sentence nod to this, it is buried in mathematics that is likely to be beyond the capability of the average reader. I have had it on my to do list for some time to create an article in terms of electric networks understandable by the average engineer which is another reason why I did not remove this rather bad contribution straight away. As for whether it is the main meaning, I am not attempting to defend that, my edits to the dab page were entirely based on what actually existed, not what should exist. It would be easy to demonstrate, I think, that the simple circuit theorem is the main meaning to electrical engineers, but what the main meaning is in a wider context is pretty hard to judge, I would not know where to begin. Spinning Spark 15:31, 6 June 2011 (UTC)[reply]

Reciprocity (electromagnetism) has a whole section on the electrical-network case, not just one sentence. But I agree that a good sub-article focused on the simplified circuit case, just giving the result without proof (referring to the main article for most of the proof, technical conditions, and generalized cases), perhaps garnished with one or two simple circuit examples, would be appropriate.

(Actually, there is an elementary proof in the case of electrical networks described by simple linear lumped elements with complex impedances, for sources at a given frequency. If A is the incidence matrix of the directed graph of the network, v is the vector of voltages at each node, and j is the vector of currents injected at each node, then it is a simple matter to show that Kirchhoff's laws reduce to A^TDAv=j, where D is a diagonal matrix of admittances across each edge [1]. Reciprocity in this case is essentially just the observation that A^TDA is a symmetric matrix. However, things become much more complicated if you want to include e.g. antennas.) — Steven G. Johnson (talk) 16:50, 6 June 2011 (UTC)[reply]