(Co)homology theory and electrical circuit

Solution 1:

John Baez in "Circuit Theory" states: "In 1923, Hermann Weyl published a paper in Spanish which described electrical circuits in terms of the homology and cohomology of graphs (W). In this approach, Kirchhoff’s voltage and current laws simply say that voltage is a 1-coboundary and current is a 1-cocycle. Furthermore, the electrical resistances labelling edges of the graphs put an inner product on the space of 1-chains, allowing us to identify them with 1-cochains. Ohm’s law then says that voltage may then be identified with the current." http://ncatlab.org/johnbaez/show/Circuit+theory+I

The Weyl paper is H. Weyl, Repartición de corriente en una red conductora, Rev. Mat. Hisp. Amer. 5 (1923), 153-164. http://math.ucr.edu/home/baez/weyl1923.pdf

Solution 2:

An additional reference is "Graphs and Networks. The Picard-Lefschetz Theory and Feynman Integrals" by Lefschetz . Chapter electrical circuit