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Resistivity (Cambridge (CIE) AS Physics)

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Katie M

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Katie M

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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 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

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

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 space equals fraction numerator rho L over denominator A end fraction

  • 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

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

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

 Silicon

2.3 x 103

Insulators

 Glass

1012

 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 space equals space fraction numerator rho L over denominator A end fraction

Step 2: Determine the resistance of the copper cylinder

A space equals space pi space r squared space equals space pi space stretchy left parenthesis d over 2 stretchy right parenthesis squared equals pi space stretchy left parenthesis fraction numerator 5 space cross times space 10 to the power of negative 3 end exponent over denominator 2 end fraction stretchy right parenthesis squared equals space 2.0 space cross times space 10 to the power of negative 5 end exponent space straight m squared

R space equals space fraction numerator open parentheses 1.7 space cross times 10 to the power of negative 8 space end exponent close parentheses space open parentheses 8 cross times 10 to the power of negative 3 end exponent close parentheses over denominator 2.0 cross times 10 to the power of negative 5 space end exponent end fraction equals 6.8 cross times 10 to the power of negative 6 end exponent space straight capital omega

Step 3: Determine the resistance of the aluminium cylinder

A space equals space pi space r squared space equals space pi stretchy left parenthesis d over 2 stretchy right parenthesis squared equals pi space stretchy left parenthesis fraction numerator 10 cross times 10 to the power of negative 3 end exponent over denominator 2 end fraction stretchy right parenthesis squared equals 7.9 cross times 10 to the power of negative 5 end exponent space straight m squared

R space equals fraction numerator 2.6 cross times 10 to the power of negative 8 end exponent space cross times space 16 cross times 10 to the power of negative 3 end exponent over denominator 7.9 cross times 10 to the power of negative 5 end exponent end fraction equals 5.3 cross times 10 to the power of negative 6 end exponent space straight capital omega

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 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 increases by a factor of four, causing the resistance to drop by a quarter.

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    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.