Worked example: comparing resistance of two different cylinders

Resistivity & Superconductivity — AQA A-Level Physics

Worked Example

A copper cylinder has length 8 mm and diameter 5 mm (ρ = 1.7 × 10⁻⁸ Ω m). An aluminium cylinder has length 16 mm and diameter 10 mm (ρ = 2.6 × 10⁻⁸ Ω m). Which is the better conductor?

Show Solution

Use $R = \rho L/A$ for each cylinder.

Copper

A = π(5 × 10⁻³/2)² = 2.0 × 10⁻⁵ m². R = (1.7 × 10⁻⁸ × 8 × 10⁻³) / 2.0 × 10⁻⁵ = 6.8 × 10⁻⁶ Ω.

Aluminium

A = π(10 × 10⁻³/2)² = 7.9 × 10⁻⁵ m². R = (2.6 × 10⁻⁸ × 16 × 10⁻³) / 7.9 × 10⁻⁵ = 5.3 × 10⁻⁶ Ω.

The aluminium cylinder has lower 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 difference 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). despite higher 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)., because it is wider (larger A).

The aluminium cylinder is the better conductor for this geometry.

Answer

The aluminium cylinder (R = 5.3 × 10⁻⁶ Ω) has lower resistance than the copper cylinder (R = 6.8 × 10⁻⁶ Ω).

Examiner Tips and Tricks

Lower resistivityA material property that quantifies how strongly it resists current. Measured in ohm-metres (Ω m). does not automatically mean lower resistanceThe opposition to current flow. The ratio of potential difference to current. Measured in ohms (Ω)..
Resistance depends on the combination of ρ, L, and A.
The question is testing whether you can apply R = ρL/A, not whether you know which material is 'better'.