Linear electrical circuits

To finish this first part devoted to lumped models we deal with general linear electrical circuits, the RLC circuit studied in previous chapter being a particular case. We model the circuit as a directed graph where the edges are the electrical elements, namely, resistors, inductors, capacitors, magnetically coupled sub-circuits, and generators. Firstly, we write the equations for the charge conservation at the nodes and then the constitutive equation for each element. The unknowns are the electric potential at the nodes and the current intensities along the edges. This chapter intends to be a general simple introduction the subject. A more complete and deeper approach can be found, for instance in the references [ 1, 30]. Moreover, a brief summary of graph theory is given in Appendix A.