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
