3.5.1.3
Resistivity is a material property, not a component property
Resistivity & Superconductivity — AQA A-Level Physics
Key Definition
Resistivity — A property of a material that quantifies how strongly it opposes current. It is the resistance of a specimen 1 m long with a cross-sectional area of 1 m². Symbol: ρ. Unit: Ω m.
$$\rho = \frac{RA}{L}$$
- Where:
- $ρ$ = resistivity (Ω m)
- $R$ = resistance (Ω)
- $A$ = cross-sectional area (m²)
- $L$ = length (m)
- 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 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 ohms (Ω). depends on shape (length, area) and material. ResistivityA material property that quantifies how strongly it resists currentThe rate of flow of charge. Measured in amperes (A).. Measured in ohm-metres (Ω m). depends on the material alone.
- Two copper wires of different thickness have different resistances but the same resistivityA material property that quantifies how strongly it resists current. Measured in ohm-metres (Ω m)..
- Rearranging: $R = \rho L / A. Use this$ form in calculations.
- Doubling the length doubles the resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω). (R is proportional to L).
- Doubling the cross-sectional area halves the resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω). (R is inversely proportional to A).
- Doubling the diameter quadruples the area ($A = \pi d^{2}/4)$, so resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω). drops to one quarter.
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 from ρ = RA/L: Ω × m² ÷ $m = \Omega m$.
- This is a common 1-mark question.
Common Mistake
MEDIUM
Students often: Forgetting to convert diameter from mm to m before calculating area.
Instead: A wire of diameter 0.22 mm: d = 0.22 × 10⁻³ m, then A = π(0.22 × 10⁻³)² / 4.
Instead: A wire of diameter 0.22 mm: d = 0.22 × 10⁻³ m, then A = π(0.22 × 10⁻³)² / 4.