Resistivity of a wire

What you are trying to do

Determine the resistivity of the metal of a wire from its resistance, length and cross-sectional area.

Apparatus

• A metre of bare resistance wire (nichrome or constantan) taped along a metre rule
• Micrometer screw gauge for the diameter
• Low-voltage supply, ammeter and voltmeter (or a calibrated ohmmeter)
• Crocodile clip to make the moving contact

Variables

• Independent: the length of wire in the circuit
• Dependent: its resistance
• Control: the wire's diameter and temperature — same wire, low current, readings taken briefly

Method

1. Measure the diameter at several places along the wire and in two perpendicular directions at each place; take the mean, and check the micrometer's zero error first.

1. Clip onto the wire at a series of measured lengths, and record V and I (or R directly) at each. Keep the current small and switch off between readings so the wire does not warm up: resistivity rises with temperature.

Analysis

1. R = ρL/A, so a graph of R against L is a straight line through the origin with gradient ρ/A.
2. Compute the area from the mean diameter, A = πd²/4, then ρ = gradient × A.
3. A small intercept is contact resistance at the clip; the gradient shrugs it off, which is exactly why the graph beats a single reading.

A worked set of readings

Nichrome wire of mean diameter 0.36 mm (A = 1.02 × 10⁻⁷ m²):

The gradient of R against L is 10.8 Ω m⁻¹, so ρ = gradient × A = 10.8 × 1.02 × 10⁻⁷ = 1.10 × 10⁻⁶ Ω m, the right value for nichrome.

Where the uncertainty comes from

• Diameter: The dominant term: it is squared in the area, doubling its percentage uncertainty. Multiple readings in two directions catch an oval or tapering wire.
• Temperature: Current heats the wire and raises its resistance mid-experiment; low current, brief readings.
• Contact position: The crocodile clip has width; clip to the same edge each time and read the length at that edge.
• Meter resolution: At short lengths the resistance is small and the meter's last digit matters more; the graph weights the long-length readings naturally.

What earns the marks

Safety