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4.2.6Electrons, Waves and Photons

Determining the Resistivity of a Metal — OCR A Level Physics A H556 Revision Notes & Topical Questions

5 min read 6 parts Lesson 25 of 62 Unit quiz

📚 OCR A Level Physics A H556 Hub / Topical Revision
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Part 1 of 6Measurements Needed

4.2.6 Determining the Resistivity of a Metal
Diameter
  • Use a micrometer screw gauge to measure the wire diameter at several places along its length and in different directions.
Cross-sectional area
  • Calculate the area with A = πd²/4 using the mean diameter in metres.
Length
  • Use a metre rule to fix the length of wire between two clips or contacts.
Resistance
  • Measure potential difference with a voltmeter across the wire and current with an ammeter in series, then use R = V/I.

Part 2 of 6Method

1
Stretch the wire straight along a metre rule and attach crocodile clips at a measured length.
2
Connect the wire in series with an ammeter and low voltage supply, with a voltmeter across the length being tested.
3
Switch on only while taking readings, so the current stays small and the wire does not heat up.
4
Record the voltage and current, then calculate R = V/I for that length.
5
Repeat for lengths from about 0.20 m to 1.00 m, and plot resistance against length.

Part 3 of 6Analysis

Analysis
Graph
  • Because R = (ρ/A) L, a graph of R against L is a straight line through the origin.
Gradient
  • The gradient of the line is equal to ρ/A.
Resistivity
  • Multiply the gradient by the cross-sectional area to find ρ.
Check
  • Compare the value with data tables to identify the metal.

Part 4 of 6Improving Accuracy

Heating effect
  • A large current warms the wire and raises its resistance, so use a small current and short switch-on times.
Diameter error
  • The area depends on the diameter squared, so a small error in diameter has a large effect and repeats are essential.
Contact resistance
  • Clips add resistance, which is reduced by using the gradient and not a single value.
Zero error
  • Check the micrometer zero before measuring so that diameter readings are corrected.

Part 5 of 6Worked Example

Question

  • A graph of resistance against length for a constantan wire gives a gradient of 7.9 Ω/m.
  • The wire diameter is 0.28 mm.
  • Calculate the resistivity.

  1. Area A = π d² / 4 = π × (0.28 × 10⁻³)² / 4 = 6.16 × 10⁻⁸ m².
  2. Gradient = ρ/A, so ρ = gradient × A.
  3. ρ = 7.9 × 6.16 × 10⁻⁸ = 4.9 × 10⁻⁷ Ω m.

Answer The resistivity is 4.9 × 10⁻⁷ Ω m.

Part 6 of 6Exam Checklist & Tips

4.2.6 – Key Points for the Exam

  • Micrometer screw gauge An instrument used to measure small lengths such as wire diameter, to 0.01 mm.
  • Gradient The slope of the resistance against length graph, equal to ρ/A.
  • Resistivity A property of the material, equal to the gradient multiplied by area.
  • Heating effect The rise in temperature of a wire when current passes through it.
  • Zero error A fixed offset in an instrument reading when it should read zero.

Common Mistakes

  • Using a large current that heats the wire and changes its resistance.
  • Forgetting to square the diameter when finding the area.
  • Saying the gradient is ρ; it is ρ divided by the area.
  • Measuring the diameter only once, instead of at several places.

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