   # Resistivity

There are three factors that affect the resistance of a specimen of material:
(a) the temperature
(b) the dimensions of the specimen - the smaller the cross sectional area and the longer the specimen the larger the resistance
(c) the material from which the specimen is made

The property of the material that affects its resistance is called the resistivity of the material and is given the symbol r.

Resistivity is defined as follows:

The resistivity of a material is defined as the resistance between two opposite faces of a 1 m3 specimen of the material.

The units for resistivity are Wm.

Resistivity is related to resistance of a specimen of length L and cross sectional area A by the formula:

Resistivity (r) = RA/L

The following table gives the resistivities of a number of common materials.

 Material Resistivity (Wm) Material Resistivity (Wm) Copper 1.69x10-8 Non-metals 104 Nichrome 130x10-8 Insulators 1013 - 1016 Aluminium 3.21x10-8 Germanium 0.65 Eureka 49x10-8 Silicon 2.3x10-5 Lead 20.8x10-8 Carbon 33-185x10-6 Manganin 44x10-8 Silver 1.6x10-8

The resistivities of solutions cannot be quoted generally because they depend on the concentrations and are therefore variable quantities. However, as an example, the resistivity of pure water is about 2.5x105 Wm and that of a saturated solution of sodium chloride about 0.04 Wm at 20oC.

The reciprocal of resistivity is known as the conductivity of the material (s)

Conductivity (s) = 1/r = L/RA (units siemens per metre (Sm-1)

Example problems
(use the data in the above table)

1. Calculate the resistance of a 1.5 m long piece of eureka wire of diameter 0.5 mm
Resistance = resistivity x length/area = 49x10-8x1.5/1.96x10-7 = 3.7 W

2. A piece of wire needed for a heater is to be made of manganin. It is to have a cross sectional area of 1.5x10-7 m2 and a resistance of 5 W. How long must it be?
Length = Resistance x area/resistivity = 5x1.5x10-7/44x10-8 = 1.7 m