Define the resistivity of a material.

The resistivity of a material is the product of the resistance of a uniform sample and its cross-sectional area, divided by its length, ρ = RA/l, so it is numerically the resistance of a sample of unit length and unit cross-sectional area at a stated temperature.

How does the resistance of a wire depend on its cross-sectional area, at constant length and temperature?

The resistance is inversely proportional to the cross-sectional area, so doubling the area halves the resistance.

By what factor does the resistance of a wire change if its diameter is doubled while its length stays the same?

The resistance falls to one quarter, because the cross-sectional area is proportional to the square of the diameter and the resistance is inversely proportional to the area.

CCEA A-Level Physics 1210

Physical Quantities, Scalars and Vectors

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Resistance and Resistivity

Resistivity and the equation R = ρl/A

3 things to know
Unit AS 1

Overview

Recall questions on the definition of resistivity and the equation with every symbol, the unit and how it follows, the dependence on length and on cross-sectional area, the effect of doubling the diameter, worked calculations on copper and nichrome wires, and why a wire stretched to twice its length quadruples its resistance.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

State the equation relating resistance to resistivity and define every symbol with its unit.

Key term

State the SI unit of resistivity and show how it follows from the defining equation.

Key term

How does the resistance of a wire depend on its length, at constant cross-sectional area and temperature?

Questions from this subtopic

Each one with the model answer underneath.

1
Define the resistivity of a material.
Model answer
The resistivity of a material is the product of the resistance of a uniform sample and its cross-sectional area, divided by its length, ρ = RA/l, so it is numerically the resistance of a sample of unit length and unit cross-sectional area at a stated temperature.
2
State the equation relating resistance to resistivity and define every symbol with its unit.
Model answer
The equation is R = ρl/A, where R is the resistance in ohms, ρ the resistivity in ohm metres, l the length of the sample in metres and A its cross-sectional area in square metres.
3
State the SI unit of resistivity and show how it follows from the defining equation.
Model answer
Resistivity is measured in ohm metres, because ρ = RA/l has units of Ω × m² ÷ m, which is Ω m.
4
How does the resistance of a wire depend on its length, at constant cross-sectional area and temperature?
Model answer
The resistance is directly proportional to the length, so doubling the length of the wire doubles its resistance.
5
How does the resistance of a wire depend on its cross-sectional area, at constant length and temperature?
Model answer
The resistance is inversely proportional to the cross-sectional area, so doubling the area halves the resistance.
6
By what factor does the resistance of a wire change if its diameter is doubled while its length stays the same?
Model answer
The resistance falls to one quarter, because the cross-sectional area is proportional to the square of the diameter and the resistance is inversely proportional to the area.

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