ASPhysicsOCRRevision Notes4. Electrons, Waves & PhotonsResistance & ResistivityResistivity

Resistivity (OCR AS Physics): Revision Note

Exam code: H156

Written by: Ashika

Reviewed by: Caroline Carroll

Updated on 8 October 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 flowing through a metal from the negative to the positive end, colliding with the vibrating metal ions in their path.

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

Wires of different dimensions. Doubling the length of a wire from L to 2L doubles its resistance from R to 2R; doubling the cross-sectional area from A to 2A halves the resistance from 2R to R.

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	$10^{15}$

For wires of the same length and cross-sectional area, the higher the resistivity of the material, the higher the 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.

Two cylinders: a copper (Cu) cylinder of diameter 5 mm and length 8 mm, and an aluminium (Al) cylinder of diameter 10 mm and length 16 mm.

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: Calculate the resistance of the copper cylinder

The cross-sectional area of a cylinder is a circle

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

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

Step 2: Calculate the resistance of the aluminium cylinder

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

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

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

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 (× 4) causing the resistance to drop to a quarter.

Variation of the Resistivity of Metals and Semiconductors

The resistivity of a material depends on its temperature
- How it varies depends on whether the material is a metal or a semiconductor

Metals

All solids are made up of vibrating atoms
As the temperature rises, the ions vibrate with a greater frequency and amplitude
Electric current is the flow of free electrons in a material
- The electrons collide with the vibrating atoms which impede their flow, hence the current decreases

Metal atoms and free electrons at 20 °C and at 70 °C. At the higher temperature the atoms vibrate more, so the free electrons collide with them more and it is harder for the electrons to flow (the resistance increases).

Metal atoms and free electrons at low and high temperatures

So, if the current decreases, then the resistance will increase (from V = IR)
- Therefore, its resistivity will increase since ρ ∝ R (if the area A and length L is constant)
For a metallic conductor which obeys Ohm's law:
- An increase in temperature causes an increase in resistance and resistivity
- A decrease in temperature causes a decrease in resistance and resistivity

Semiconductors

The resistivity of semiconductors behaves in the opposite way to metals
The number density of charge carriers (such as electrons) increases with increasing temperature
Therefore, for a semiconductor:
- An increase in temperature causes a decrease in resistance and resistivity
- A decrease in temperature causes an increase in resistance and resistivity
One example of this is a thermistor
- This is often used in temperature sensing circuits such as thermometers and thermostats
This is only for semiconductors with a negative temperature coefficient (NTC)

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