Core practical 7: measuring resistivity

Method

• Measure the wire's diameter with a micrometer at several points and orientations; find the mean and A = πd²/4.
• Tape the wire along a metre rule. Connect one end in a circuit with an ammeter, and use a flying lead (crocodile clip) to make contact at different lengths l.
• Connect a voltmeter across the length l. For each length, record V and I and calculate R = V / I (or use an ohmmeter).
• Use at least six lengths.

Analysis

R = ρl / A, so a graph of R (y-axis) against l (x-axis) is a straight line with gradient ρ / A. Therefore ρ = gradient x A. Contact resistance at the clips adds a constant to every reading: it shifts the line up (an intercept) but does not change the gradient.

Good practice

• Keep the current small, and switch off between readings, so the wire does not heat up (resistance rises with temperature).
• Measure the diameter carefully: it is squared, so its percentage uncertainty is doubled in A.
• Use a long wire to make R large enough to measure precisely.

Worked example

A graph of R against l has gradient 2.6 Ω/m. The wire's diameter is 0.30 mm. Find ρ.

1. A = π(0.15 x 10^-3)² = 7.07 x 10^-8 m²
2. ρ = gradient x A = 2.6 x 7.07 x 10^-8

Answer: ρ = 1.8 x 10^-7 Ω m

Check yourself

1. The gradient of a graph of R against l is 8.0 Ω/m, and the wire's cross-sectional area is 1.5 x 10^-7 m². Find ρ, in units of 10^-6 Ω m.
   Show answer

   1.2 x 10^-6 Ω m. ρ = gradient x A = 8.0 x 1.5 x 10^-7 = 1.2 x 10^-6 Ω m.

2. A constantan wire (ρ = 4.9 x 10^-7 Ω m) is 0.80 m long with a diameter of 0.40 mm. Find its resistance in Ω, to 3 s.f.
   Show answer

   3.12 Ω. A = π(0.20 x 10^-3)² = 1.26 x 10^-7 m²; R = 4.9 x 10^-7 x 0.80 / 1.26 x 10^-7 = 3.12 Ω.

3. What length of nichrome wire (ρ = 1.1 x 10^-6 Ω m, A = 2.0 x 10^-7 m²) has a resistance of 11 Ω? Answer in m.
   Show answer

   2 m. l = RA / ρ = 11 x 2.0 x 10^-7 / 1.1 x 10^-6 = 2.0 m.

4. Why is ρ found from the gradient of R against l rather than from a single reading?
   • The gradient is not affected by contact resistance and averages out random errors
   • A single reading cannot be calculated
   • The gradient gives the area directly
   • It makes the wire cooler
   Show answer

   The gradient is not affected by contact resistance and averages out random errors. Constant contact resistance only shifts the line up; the gradient uses all the data.

5. Why should the current be kept small?
   • To protect the voltmeter
   • To make the wire longer
   • To stop the wire heating up and changing its resistance
   • To reduce the resistivity
   Show answer

   To stop the wire heating up and changing its resistance. A temperature rise increases the resistance of a metal.

6. A wire is replaced by one of the same material and length but half the diameter. What happens to its resistance?
   • It becomes 4 times as large
   • It doubles
   • It halves
   • It stays the same
   Show answer

   It becomes 4 times as large. Halving d makes A a quarter, and R = ρl / A, so R is 4 times larger.

7. What is the unit of resistivity?
   • Ω/m
   • Ω m²
   • Ω m
   • Ω
   Show answer

   Ω m. ρ = RA / l has units Ω x m² / m = Ω m.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)
• Cognito: Edexcel International A level Physics specification and core practicals

Last updated 7 November 2026. Spotted a mistake? Tell us.