Chapter 8 - Batteries, Kirchhoff's Rules, and Complex Circuits

Abstract

The concept of an electric circuit did not exist when electrostatic was the only type of electromotive force (emf). This chapter reviews the properties of the battery as a combination of individual voltaic cells. Most circuits cannot be analyzed solely in terms of series and parallel resistors with a battery here or there. To deal with bridge circuits, or systems with multiple arms containing sources of chemical emf, or systems with both resistors and capacitors, one must use the Kirchhoff's rules, first stated around 1850. This systematic approach to circuits uses solely the macroscopic properties of circuits: resistances, capacitances, and emfs (both electrostatic and non-electrostatic). Kirchhoff's rules are a set of two rules that describe any sort of circuit with connecting wires of zero resistance, resistors R, capacitors C, and non-electrostatic sources of emf ɛ. However, before they can be applied to any circuit, the currents and voltages for that circuit must be defined precisely. Instead of perfectly straight wires, real circuits have sloppily placed wires that run over and under one another. It can be a difficult task to disentangle and trace their connections. But these connections are precisely what are needed to apply Kirchhoff's rules.