5.2c Resistivity

THE IB SAYS

Essential idea: One of the earliest uses for electricity was to produce light and heat. This technology continues to have a major impact on the lives of people around the world.

Understandings: Resistivity

Applications and skills: Solving problems involving pd, current, charge, power, resistance and resistivity; Experimentally investigating factors that affect resistance

Data booklet equations: ρ=RA/L

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Resistivity

The resistance of an object or component was defined in the previous page. However, the actual value of that resistance depends on the object's dimensions (particularly length and cross-sectional area) and what it is made from. This was partially explained using the lattice model of conduction and drift speed, but it more general terms we can summarise the electrically resistant properties of particular materials by the concept of resistivity.

If the resistance (R) of an object is directly proportional to the length (L) and inversely proportional to the cross-sectional area (A) of an object, then the resistivity (ρ) is the constant of proportionality. Hence the equation: ρ=RA/L. The resistivity of a material (the units are Ωm) is equal to the resistance of a 1 m length of the material with a cross-sectional area of 1 m².

Temperature dependence of resistivity

The resistivity of a material depends on it's temperature. For most substances, including metals, the resistivity will increase with temperature.

For semiconductors however, the increased resistance due to thermal motion of the lattice ions is more than offset by the increased availability of electrons for conduction - thus decreasing the resistivity.

The equations for this relationship are not part of the core IB Physics subject guide, but the topic is common in investigations.

Resources from textbooks

Oxford Physics: pages 202 - 203

Hamper HL (2014): pages 220 - 221

Relevant questions from Dot Point Physics (5 Electric currents)

pages 236 - 239