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# Module 1.4

# Resistivity

- After studying this section, you should be able to:
- • Describe the property of resistivity.
- • Carry out calculations involving resistivity.
- • Use appropriate electrical units (Ωm) to describe the resistivity of common conductor & insulator materials

## How Materials Affect Resistance

Provided that the dimensions (length and cross sectional area) of any conductor do not change, its resistance will remain the same. If two conductors of exactly the same dimensions have a different resistance, they must be made of different materials.

One way to describe a material (any material) is by its RESISTIVITY. This is the amount of resistance present in a piece of the material OF STANDARD DIMENSIONS. Every material can be defined in this way. The resistivity of a material is defined as the resistance of a piece of material having a length of one metre and a cross sectional area of one square metre (i.e. a cube of material one metre square). The resistivity of the material being the resistance across opposite faces of this standard cube.

Resistivity is given the symbol **ρ.** This is not a letter p but a lower case Greek letter r (called rho) and is measured in a unit called the OHM METER, written Ω•m
. (Note: this is not the same as ohms/metre or ohms per metre)

So the resistance of any conductor can be found by relating the three factors;

**Length: = L Cross Sectional Area: = A Resistivity: = ρ**

The following formula can be used to find the resistance of any conductor, providing that its dimensions and its resistivity are known.

Remember that, as conductors are usually circular in section, the cross sectional area may need to be found using the basic formula for the area of a circle. i.e. A = π r^{2} or A = π(d/2)^{2} where r and d are the given radius and given diameter, respectively, and π = 3.142.

### Important.

When using this (or any) formula you must convert any sub-unit (mm, cm etc.) into its STANDARD SI UNIT e.g Metres (m). Otherwise your result may be out by a factor of 100 or 1000 or more.

Resistivity problems can be tricky to work out since you have to remember several things at once, using the cross sectional area formula AND the resistivity formula together, converting to standard SI units, and using resistivity constants. Maybe you could use a little practice? Try a short Resistivity Quiz and if you need a little help with the maths, download our "Maths Tips" booklet to get you started.

### Approximate Resistivity of some common materials. (in Ωm)

### CONDUCTORS

- Aluminium 2.7 x 10
^{-8} - Copper 1.72 x 10
^{-8} - Iron 10.5 x 10
^{-8} - Mercury 96 x 10
^{-8} - Nichrome 1.1 x10
^{-6}

### INSULATORS

- P.V.C. 5.4 x 10
^{15} - Glass 1.0 x 10
^{14} - Mica 9.0 x 10
^{13} - Teflon 1.0 x 10
^{24} - Hard Rubber 10 x 10
^{12}

It can be seen from the above list that the resistivity of insulators is much higher than that of conductors.

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