Resistivity

All materials have some resistance to the flow of charge
As free electrons move through a metal wire, they collide with the vibrating ions
As a result of the collisions, the electrons transfer some of their kinetic energy to the metal ions in the wire
The faster the ions vibrate, the greater the temperature of the wire
In this way, resistance causes heating of the wire

Free electrons and resistivity

Free electrons collide with metal ions in the wire, which resists their flow

Resistance depends on:
- the length of the wire
- the cross-sectional area through which the current is passing
- the resistivity of the material

$R = \frac{ρ L}{A}$

Where:
- R = resistance (Ω)
- ρ = resistivity (Ω m)
- L = length (m)
- A = cross-sectional area (m²)

The resistivity equation shows that:
- the longer the wire, the greater its resistance
- the thicker the wire, the smaller its resistance

Wire properties and resistance

The length and width of the wire affect its resistance

Resistivity is a property of a material
- It describes the extent to which a material opposes the flow of electric current through it
- It is dependent on temperature only

Resistivity is measured in Ω m

Resistivity of materials at room temperature table

	Material	Resistivity ρ/Ωm
Metals	Copper	1.7 x 10^-8
	Gold	2.4 x 10^-8
	Aluminium	2.6 x 10^-8
Semiconductors	Germanium	0.6
Semiconductors	Silicon	2.3 x 10³
Insulators	Glass	10¹²
Insulators	Sulfur	10¹⁵

The higher the resistivity of a material, the greater its resistance
- For example, copper has a relatively low resistivity at room temperature, making it the ideal material for use in electrical wires, as current flows through it very easily

Insulators have such a high resistivity that virtually no current will flow through them

Worked example

Two electrically-conducting cylinders made from copper and aluminium respectively.

Their dimensions are shown below.

WE - resistivity question image, downloadable AS & A Level Physics revision notes

Copper resistivity = 1.7 × 10^-8 Ω m

Aluminium resistivity = 2.6 × 10^-8 Ω m

Which cylinder is the better conductor?

Answer:

Step 1: State the resistivity equation:

$R = \frac{ρ L}{A}$

Step 2: Determine the resistance of the copper cylinder

$A = π r^{2} = π {(\frac{d}{2})}^{2} = π {(\frac{5 \times 10^{- 3}}{2})}^{2} = 2.0 \times 10^{- 5} m^{2}$

$R = \frac{(1.7 \times 10^{- 8}) (8 \times 10^{- 3})}{2.0 \times 10^{- 5}} = 6.8 \times 10^{- 6} Ω$

Step 3: Determine the resistance of the aluminium cylinder

$A = π r^{2} = π {(\frac{d}{2})}^{2} = π {(\frac{10 \times 10^{- 3}}{2})}^{2} = 7.9 \times 10^{- 5} m^{2}$

$R = \frac{2.6 \times 10^{- 8} \times 16 \times 10^{- 3}}{7.9 \times 10^{- 5}} = 5.3 \times 10^{- 6} Ω$

Step 4: State which is the better conductor

The better conductor will have lower resistance
The resistance of the aluminium cylinder is less than the copper cylinder
Therefore, the aluminium cylinder is the better conductor

Examiner Tip

You won’t need to memorise the value of the resistivity of any material, these will be given in the exam question.

Remember if the cross-sectional area is a circle e.g. in a wire, it is proportional to the diameter squared. This means if the diameter doubles, the area increases by a factor of four, causing the resistance to drop by a quarter.

Resistivity (CIE AS Physics)

Revision Note

Resistivity

Free electrons and resistivity

Wire properties and resistance

Resistivity of materials at room temperature table

Worked example

Examiner Tip

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Author: Katie M