Determining the resistivity of a wire

Practical method

Aim

Determine the resistivity of a metal wire from the gradient of a graph of resistance against length.

Variables

Independent variable: length of wire L
Dependent variable: resistance R
Control variables: the same wire (material and diameter); temperature: small current, switch off between readings.

Apparatus

• Constantan wire taped to a metre rule
• Crocodile clip (flying lead)
• Ammeter and voltmeter (or ohmmeter)
• Low-voltage supply and switch
• Micrometer

Method

1. Measure the wire's diameter with a micrometer at several points and orientations; calculate A = \(\dfrac{\pi d^{2}}{4}\).
2. Connect the wire in series with an ammeter and supply, with a voltmeter across the length between the fixed end and the flying lead.
3. For lengths from 0.20 m to 1.00 m, record V and I with a small current, switching off between readings; R = \(\dfrac{V}{I}\).
4. Plot R against L: a straight line with gradient \(\dfrac{\rho }{A}\).
5. Resistivity ρ = gradient × A.

Sample results

Constantan wire, d = 0.32 mm, so A = 8.04 × 10⁻⁸ m².

Analysis

R is proportional to L with gradient 6.09 Ω m⁻¹. ρ = 6.09 × 8.04 × 10⁻⁸ = 4.9 × 10⁻⁷ Ω m, the accepted value for constantan.

Uncertainty

The diameter (0.32 ± 0.01 mm, 3%) doubles to 6% in A and dominates. Contact resistance at the clip adds a constant offset, which affects the intercept but not the gradient.

Errors and improvements

Risk assessment

Common mistakes

• Using the radius as the diameter in A.
• Calculating ρ from one reading instead of the gradient.
• Using a large current so the wire heats.

Worked analysis

Gradient = 6.09 Ω m⁻¹; A = π(0.16 × 10⁻³)² = 8.04 × 10⁻⁸ m². ρ = 6.09 × 8.04 × 10⁻⁸ = 4.90 × 10⁻⁷ Ω m.

Common misconception

Resistivity is a property of the material; resistance also depends on the wire's length and area.