Resistivity (OCR A Level Physics)

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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

Electrons and resistance, downloadable AS & A Level Physics revision notes

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

Resistivity equation, downloadable AS & A Level Physics revision notes

 

  • The resistivity equation shows that:

    • The longer the wire, the greater its resistance

    • The thicker the wire, the smaller its resistance

Factors affecting resistance, downloadable AS & A Level Physics revision notes

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

Resistivity of some materials at room temperature

Table of resistivity of materials at room temperature, downloadable AS & A Level Physics revision notes
  • 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.

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:

Worked example - resistivity (2), downloadable AS & A Level Physics revision notes

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 by 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

Resistance & Temperature in a Metal, downloadable AS & A Level Physics revision notes

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 ∝ (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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Ashika

Author: Ashika

Expertise: Physics Project Lead

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.