AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
RA Resistivity, ρ = L Description of the qualitative effect of temperature…
Full specification wording
Resistivity: RA Resistivity, ρ = L Description of the qualitative effect of temperature on the resistance of metal conductors and thermistors.
Resistivity is defined by ρ = RA/L, where R is resistance, A is cross-sectional area and L is length.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 1 of 6
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Resistivity is defined by ρ = RA/L, where R is resistance, A is cross-sectional area and L is length. Rearranged, R = ρL/A, so resistance rises with length and falls with area for a given material. The unit of resistivity is the ohm metre (Ω m). Temperature affects resistance differently in metals and thermistors. In a metal conductor, heating increases lattice ion vibration, so electrons collide more often and resistance rises; the change is roughly linear over a limited range. In a negative temperature coefficient thermistor, heating releases more charge carriers, so resistance falls steeply. A thermistor therefore acts as a temperature sensor in a potential divider.
What earns the marks
- States and rearranges ρ = RA/L, using consistent SI units of Ω m for resistivity, m² for area and m for length.
- Explains that increasing temperature in a metal increases lattice vibrations, increasing electron scattering and so increasing resistance.
- Explains that increasing temperature in an NTC thermistor increases the number of charge carriers, decreasing resistance.
- Describes a practical use of a thermistor, such as in a potential divider circuit for temperature sensing or control.
- Distinguishes between the small, roughly linear change in a metal and the large, non-linear change in a thermistor.
Common mistakes and how to put them right
Using the diameter instead of the radius when calculating cross-sectional area.
Put it right: Halve the diameter first, then use A = πr².
Mixing units, such as using mm² or cm in the resistivity equation.
Put it right: Convert all lengths to metres and areas to m² before substituting.
Claiming that heating always increases resistance.
Put it right: Specify that this applies to metal conductors, whereas an NTC thermistor shows a decrease.
Exam tips
- Write the rearranged equation before substituting values so the examiner can follow your method.
- When describing temperature effects, name the mechanism: lattice vibration and scattering for metals, charge carrier release for thermistors.
- Link thermistor behaviour to a circuit context, such as the output potential difference of a potential divider changing with temperature.
Try the lesson
The start of the Resistivity: RA Resistivity, ρ = L Description of the qualitative effect of temperature on the resistance of metal conductors and thermistors. lesson, made from checked teaching notes for this specification point.
Have a go first
Which equation relates the resistance R of a uniform wire to its resistivity ρ, length L and cross-sectional area A?
Listen
Resistivity is defined by ρ = RA/L, where R is resistance, A is cross-sectional area and L is length. Rearranged, R = ρL/A, so resistance rises with length and falls with area for a given material. The unit of resistivity is the ohm metre (Ω m). Temperature affects resistance differently in metals and thermistors. In a metal conductor, heating increases lattice ion vibration, so electrons collide more often and resistance rises; the change is roughly linear over a limited range. In a negative temperature coefficient thermistor, heating releases more charge carriers, so resistance falls steeply. A thermistor therefore acts as a temperature sensor in a potential divider. A strong answer earns marks for these points. States and rearranges ρ = RA/L, using consistent SI units of Ω m for resistivity, m² for area and m for length. Explains that increasing temperature in a metal increases lattice vibrations, increasing electron scattering and so increasing resistance. Explains that increasing temperature in an NTC thermistor increases the number of charge carriers, decreasing resistance. Describes a practical use of a thermistor, such as in a potential divider circuit for temperature sensing or control. A common slip: Using the diameter instead of the radius when calculating cross-sectional area. Instead, halve the diameter first, then use A = πr². Exam tip: Write the rearranged equation before substituting values so the examiner can follow your method.
See it
Key words
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Resistivity
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Temperature and resistance
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Charge carriers and scattering
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Sensor circuits
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See every definition
- Resistivity
- Defined by ρ = RA/L, where R is resistance, A is cross-sectional area and L is length, with unit the ohm metre (Ω m).
- Temperature and resistance
- In a metal conductor, heating increases lattice ion vibration, so electrons collide more often and resistance rises; in a negative temperature coefficient thermistor, heating releases more charge carriers, so resistance falls steeply.
- Charge carriers and scattering
- In a metal, increased lattice vibrations increase electron scattering; in an NTC thermistor, heating releases more charge carriers.
- Sensor circuits
- A thermistor acts as a temperature sensor in a potential divider.
Label the diagram
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