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)