Required Practicals / AQA / Practical 5
5 AS 3.5.1.3

Determination of resistivity

Determine the resistivity of a metal wire using measurements of resistance at different lengths.

Apparatus

  • Length of resistance wire (e.g. nichrome or constantan, ~1 m)
  • Micrometer screw gauge
  • Ammeter and voltmeter
  • Low-voltage DC power supply (2-6 V)
  • Crocodile clips and connecting leads, metre rule

Safety

  • Keep current low to avoid heating the wire, as resistivity of metals increases with temperature.
  • Check all connections are secure before switching on the power supply.

Method

  1. Measure the diameter d of the wire at three positions using the micrometer; calculate mean cross-sectional area $A = \pi(d/2)^2$.
  2. Connect the circuit: power supply and ammeter in series with the wire; voltmeter connected directly across a measured length L of wire via crocodile clips.
  3. Set L, record voltmeter reading V and ammeter reading I; calculate $R = V/I$.
  4. Vary L from ~0.10 m to ~1.0 m in steps; record R for each L.
  5. Plot R against L: straight line through origin. Calculate resistivity $\rho = \text{gradient} \times A$.

Key Variables

Independent Wire length L
Dependent Resistance R
Controlled Cross-sectional area A (same wire throughout); Temperature (keep current low)

Analysis and Results

  • $R = \rho L/A$, so gradient of R vs L graph $= \rho/A$, giving $\rho = \text{gradient} \times A$.
  • The graph should pass through the origin; a non-zero intercept indicates contact resistance at the crocodile clips.
  • Calculate the uncertainty in rho from the uncertainties in the gradient and in A.

Common Errors

  • Not zeroing the micrometer before use, or measuring diameter at only one position.
  • Including contact resistance at the clips in the measurement (use clips as close as possible, or use a Kelvin four-terminal connection).
  • Heating the wire with excessive current, which increases resistivity and gives a non-linear graph.
  • Measuring the length of the whole wire rather than only the length between the clips.

Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.

Q1 4 marks

A nichrome wire of diameter 0.45 mm has a resistance of 8.0 $\Omega$ per metre. Calculate the resistivity of nichrome.

Q2 3 marks

Explain why the student keeps the current through the wire as low as possible during this experiment.

Q3 2 marks

Suggest how the accuracy of the cross-sectional area measurement could be improved.