Chapter 17. Electrical Properties

Electrical Conduction
Ohm’s Law
When an electric potential V is applied across a material, a current of magnitude I flows. In most metals, at low values of V, the current is proportional to V, according to Ohm's law:
I = V/R
where R is the electrical resistance. R depends on the intrinsic resistivity r of the material and on the geometry (length l and area A through which the current passes).
R = rl/A

Electrical Conductivity
The electrical conductivity is the inverse of the resistivity: s = 1/r.
The electric field in the material is E=V/l, Ohm's law can then be expressed in terms of the current density j = I/A as:
j = s E
The conductivity is one of the properties of materials that varies most widely, from 107 (W-m) typical of metals to 10-20 (W-m) for good electrical insulators. Semiconductors have conductivities in the range 10-6 to 104 (W-m).

Electronic and Ionic Conduction
In metals, the current is carried by electrons, and hence the name electronic conduction. In ionic crystals, the charge carriers are ions, thus the name ionic conduction