A LevelPhysicsAQARevision NotesElectricityResistance & ResistivityResistivity

Resistivity (AQA A Level Physics): Revision Note

Exam code: 7408

Written by: Katie M

Reviewed by: Tim

Updated on 25 September 2026

Guided study available on this topic

Understand this topic with deeper explanations and understanding checks.

Resistivity

All materials have some resistance to the flow of charge
As free electrons move through a metal wire, they collide with ions which get in their way
As a result, they transfer some, or all, of their kinetic energy on collision, which causes electrical heating

Free electrons moving through a metal wire and colliding with fixed positive ions. — **Free electrons collide with ions which resist their flow**

Since current is the flow of charge, the ions resisting their flow causes resistance
Resistance depends on the length of the wire, the cross-sectional area through which the current is passing and 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

A wire of resistance R and length L doubles in length to 2L and says “Doubling the length of a wire will double the resistance”. A wire of resistance 2R and cross-sectional area A doubles in cross-sectional area 2A and says “Doubling the cross-sectional area of a wire will half the resistance”. — **The length and width of the wire affect its resistance**

Resistivity is a property that describes the extent to which a material opposes the flow of electric current through it
It is a property of the material, and is dependent on temperature
Resistivity is measured in Ω m
The following table gives the resistivity of some materials at room temperature

	Material	Resistivity $ρ$ / Ω m
Metals	Copper	$1.7 \times 10^{- 8}$
	Gold	$2.4 \times 10^{- 8}$
	Aluminium	$2.6 \times 10^{- 8}$
Semiconductors	Germanium	$0.6$
Semiconductors	Silicon	$2.3 \times 10^{3}$
Insulators	Glass	$10^{12}$
Insulators	Sulfur	$10^{15}$

The higher the resistivity of a material, the higher its resistance
- This is why copper, with its relatively low resistivity at room temperature, is used for electrical wires — 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.

Copper (Cu) cylinder has 5 mm diameter and is 8 mm long. Aluminium (Al) cylinder has 10 mm diameter and is 16 mm long.

Copper resistivity = 1.7 × 10^-8 Ω m

Aluminium resistivity = 2.6 × 10^-8 Ω m

Which cylinder is the better conductor?

[3]

Answer:

Step 1: Calculate the resistance of the copper cylinder

The cross-sectional area of a cylinder is a circle

$A = π \times {(\frac{d}{2})}^{2} = π \times {(\frac{5 \times 10^{- 3}}{2})}^{2} = 1.96 \times 10^{- 5} m^{2}$

$R = \frac{ρ L}{A} = \frac{(1.7 \times 10^{- 8}) \times (8 \times 10^{- 3})}{1.96 \times 10^{- 5}} = 6.93 \times 10^{- 6} Ω$ [1 mark]

Step 2: Calculate the resistance of the aluminium cylinder

$A = π \times {(\frac{d}{2})}^{2} = π \times {(\frac{10 \times 10^{- 3}}{2})}^{2} = 7.85 \times 10^{- 5} m^{2}$

$R = \frac{ρ L}{A} = \frac{(2.6 \times 10^{- 8}) \times (16 \times 10^{- 3})}{7.85 \times 10^{- 5}} = 5.30 \times 10^{- 6} Ω$ [1 mark]

Step 3: Conclusion

The resistance of the aluminium cylinder is less than the resistance of the copper cylinder
Therefore, the aluminium cylinder is the better conductor [1 mark]

Examiner Tips and Tricks

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 quadruples causing the resistance to drop by a quarter.

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