Electric Power Principles, 2nd Edition

5Electrical and Magnetic Circuits

Magnetic circuits offer, as do electric circuits, a way of simplifying the analysis of magnetic field systems, which often can be represented as having a collection of discrete elements. In electric circuits the elements are sources, resistors, and so forth, which are represented as having discrete currents and voltages. These elements are connected together with wires and their behavior is described by network constraints (Kirchhoff's voltage and current laws, KVL and KCL) and by constitutive relationships such as Ohm's law. In magnetic circuits the lumped parameters are called reluctances (the inverse of reluctance is called permeance). The analog to a wire is referred to as a high permeance magnetic circuit element. Of course high permeability is the analog of high conductivity.

By organizing magnetic field systems into lumped parameter elements and using network constraints and constitutive relationships we can simplify the analysis of such systems.

5.1 Electric Circuits

Start with two conservation laws: conservation of charge and Faraday's law. From these one can, with appropriate simplifying assumptions, derive the two fundamental circuit constraints embodied in Kirchhoff's laws.

5.1.1 Kirchhoff's Current Law

Conservation of charge can be written in integral form as

(5.1)

This simply states that the sum of current out of some volume ...