Resistivity

Current Electricity — AQA A-Level Physics

Key Definition

Resistivity — A property of a material. The resistance of a 1 m length with a cross-sectional area of 1 m². Units: Ω m.

$$\rho = \frac{RA}{L}$$

Where:
- $ρ$ = resistivity (Ω m)
- $R$ = resistance (Ω)
- $A$ = cross-sectional area (m²)
- $L$ = length (m)

ResistivityA material property that quantifies how strongly it resists currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A).. Measured in ohm-metres (Ω m). (ρ) depends on the material, not the shape or size of the sample.
ResistanceThe opposition to currentThe rate of flow of chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C).. Measured in amperes (A). flow. The ratio of potential differenceThe energyThe capacity to do work. Measured in joules (J). transferred per unit chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). between two points. Measured in volts (V). to currentThe rate of flow of charge. Measured in amperes (A).. Measured in ohms (Ω). depends on length (L), cross-sectional area (A), and the material.
Doubling the length doubles the resistanceThe opposition to current flow. The ratio of potential differenceThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). to current. Measured in ohms (Ω)..
Doubling the cross-sectional area halves the resistanceThe opposition to current flow. The ratio of potential differenceThe energyThe capacity to do work. Measured in joules (J). transferred per unit charge between two points. Measured in volts (V). to current. Measured in ohms (Ω)..
ResistivityA material property that quantifies how strongly it resists current. Measured in ohm-metres (Ω m). can change with temperature and light intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared..

Examiner Tips and Tricks

The unit of resistivityA material property that quantifies how strongly it resists current. Measured in ohm-metres (Ω m). is Ω m, NOT Ω m⁻¹.
Derive it: $\rho = RA/L gives \Omega \times m^{2} / m = \Omega m$.

Required Practical: Measuring Resistivity of a Wire

Measure the diameter of the wire using a micrometerA precision measuring instrument used to measure small distances or thicknesses, typically to the nearest 0.01 mm. at three or more points.
Calculate the mean diameter, then the cross-sectional area: $A = \pi d^{2}/4$.
Clip the wire to a ruler at a known length using crocodile clips.
Connect to a circuit with an ammeterAn instrument that measures current. Connected in series with the component. Has very low resistance so it doesn't affect the circuit. (series) and voltmeterAn instrument that measures potential difference. Connected in parallel across the component. Has very high resistance. (parallel).
Measure V and I for different lengths (e.g. 0.1 m to 1.0 m).
Plot R (y-axis) against L (x-axis). $Gradient = \rho/A$.
Calculate $\rho = gradient \times A$.

Circuit diagram for resistivity experiment: power supply, ammeter in series, voltmeter in parallel across wire, crocodile clips on ruler.

Common Mistake MEDIUM

Forgetting to convert diameter from mm to m before calculating area. 0.22 mm = 0.22 × 10⁻³ m.

Common Mistake MEDIUM

Not taking multiple diameter readings along the wire. The micrometer should be used at at least three points to check uniformity.