This chapter “applies” the theory of strategic action fields (SAFs) to present a schematic history of the electrical power industry as a sequence of SAF settlements, each with a reconfiguration of the constitutive rules of exchange that preserves the incumbent’s central position in the SAF: the Wisconsin settlement, the Hope settlement, the marginal cost price settlement, the wholesale markets settlement, and the Reforming the Energy Vision settlement.

In the previous two chapters we introduced electric charges and electric fields, using primarily the force between charged bodies as the starting point. Charges in motion, of course, constitute electrical currents, with which you have a working knowledge from your previous study in circuit analysis. In this chapter we will take a closer look at electrical currents. Specifically, we’ll introduce current density, which describes the spatial distribution of a current. Then the relation between the ideas of electrostatics discussed in Chapters 1 and 2 and the laws that govern simple electric circuits, such as Kirchhoff’s Current Law, Kirchhoff’s Voltage Law, and Ohm’s Law, will be discussed. You may have already recognized the connection between these circuits concepts and some of the ideas from electrostatics that we introduced earlier. The circuit laws are but special cases of the more general treatment that we will now discuss in detail.

Electrical conductivity and resistance obey Ohm’s law. Specific resistance may be measured in two- or four-electrode schemes. Mechanisms of electrical conductivity in rocks are ionic, electronic, anionic and protonic. Some mantle minerals, i.e. olivine, possess polaron conductivity. Conduction bands and density of states are considered for some minerals. Effective conductivity in heterogeneous rocks can be estimated from Wiener or Hashin–Shtrikman bounds, effective medium approximation (EMA) and resistor network models. The electrical conductivity of mineral aggregates can be effectively described by brick and percolation models. Diluted electrolytes and Kohlrausch’s law of independent movement of ions are considered in fluid-bearing rocks, whose electric conductivity obeys Archie’s law. Formation factor and cementation exponent are analyzed for sedimentary rocks. The relationship between rock conductivity and pore saturation is described by the Waxman–Smith model. Focus Box 8.1: Calculations of density of states (Fermi gas model). Focus Box 8.2: Reciprocal lattice and band gaps. Focus Box 8.3: Olivine structure.