ABSTRACT
This chapter aims to develop the application of the axioms presented to the analysis of circuits. Circuit analysis, like Euclidean geometry, can be treated as a mathematical system; that is, the entire theory can be constructed upon a foundation consisting of a few fundamental concepts and several axioms relating these concepts. Nodal analysis of electric circuits, although using all several of the fundamental axioms presented in the introduction, concentrates upon Kirchhoff’s current law explicitly. If the circuit under consideration contains op amps, one can first replace each op amp by a voltage-controlled voltage source, using the procedure, and then allow the voltage gain to go to infinity. Circuits exist, however, in which one or more mesh currents are impossible to measure. The superposition theorem shows how to solve for a variable in a circuit that has many independent sources, by solving simpler circuits, each excited by only one source.
