Talk:Tellegen's theorem

Conservation of energy?

So the branch currents times the branch potential differences sum to zero; isn't that just conservation of energy? Or is it the point that Kirchoff's laws imply conservation of energy? Or am I being dense? --catslash (talk) 11:41, 20 April 2010 (UTC)

In fact, the relation is more general than energy conservation because it holds for any voltages and any currents compatible with Kirchhoff's laws (so possibly the voltages apply to a different 'state' than the currents). I like to present Tellegen's theorem in terms of a Helmholtz decomposition of functions on the graph. The branch voltages are in the image of d, V=dφ, and the branch currents are in the kernel of the transposed of d, δI = 0. If φ are the node potentials and d is the transposed of the matrix A in the article (which is also the boundary operator, ∂, of the graph as a cell complex) you see the relation between algebraic topology, the theory of functions on the graph and Helmholtz/Tellegen's theorem. I am being a bit short here, but I guess you see what I mean. Bas Michielsen (talk) 13:04, 21 April 2010 (UTC)

Thanks, it's clearer to me now; the proof does not assume any relationship between the currents and voltages. --catslash (talk) 09:19, 22 April 2010 (UTC)

Is the proof right?

I am not following the proof given in the article. How can this be correct,

$\sum _{k=1}^{b}W_{k}F_{k}=\mathbf {W^{T}} \mathbf {F}$

the RHS is a matrix, but the LHS is a scalar. Does the "apples and oranges" rule not apply here? SpinningSpark 09:32, 30 May 2010 (UTC)

Ok, got it, but it could be made clearer. SpinningSpark 11:59, 30 May 2010 (UTC)

Why does "Reciprocity" redirect here?

I don't see reciprocity discussed, or even mentioned, on this page. 16:14, 11 April 2011 (UTC) — Preceding unsigned comment added by Selinger (talk • contribs)

It is because Tellegen's theorem can be used to prove the reciprocity theorem. In fact, as far as students are concerned, it is the only thing Tellegen's theorem is used for. You won't find that anywhere on Wikipedia though: at least, not yet - feel like writing an article? SpinningSpark 20:29, 11 April 2011 (UTC)

You are making a rather bold statement here! Tellegen's theorem applies to functions on a graph and reciprocity theorems (what is "the" reciprocity theorem) one might find in network/circuit theory apply to multi-port models of physical systems. So what do you mean actually? Bas Michielsen (talk) 15:48, 17 June 2014 (UTC)

I mean the moving an emf from one mesh to another thingy when the current in the other mesh is the same in both cases, as described in Farago, or more formally here. I meant EE students of course; philosophy students can probably do something completely different with it and art students can use it to make papier-mâché. SpinningSpark 17:39, 17 June 2014 (UTC)

OK, thanks for the references which illustrate what you were saying. I'll think about a python script making papier-mâché from a theorem found on wikipedia. Bas Michielsen (talk) 07:59, 18 June 2014 (UTC)

$n_{f}$ and b

Shouldn't $n_{f}$ read b in the definitions section? In the first section the number of branches reads b. — Preceding unsigned comment added by 185.44.54.65 (talk) 11:58, 29 November 2022 (UTC)

The variable name ought to be consistent throughout the article. The choice of name is more-or-less arbitrary, but $b$ seems a little clearer, being more distinct from $n_{t}$ than is $n_{f}$ (and perhaps $n_{t}$ could be plain $n$). Since nobody else has expresses a preference, I shall change all the $n_{f}$ to $b$. catslash (talk) 23:57, 4 December 2022 (UTC)

Done - also some attempt to improve consistency of terminology (network/graph, flow/current). catslash (talk) 01:08, 5 December 2022 (UTC)

Thanks for doing that. I would have commented but I was afraid I had missed something fundamental and they really were different parameters. SpinningSpark 13:57, 5 December 2022 (UTC)