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
- Measure the diameter d of the wire at three positions using the micrometer; calculate mean cross-sectional area $A = \pi(d/2)^2$.
- 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.
- Set L, record voltmeter reading V and ammeter reading I; calculate $R = V/I$.
- Vary L from ~0.10 m to ~1.0 m in steps; record R for each L.
- 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.
Q14 marks
A nichrome wire of diameter 0.45 mm has a resistance of 8.0 $\Omega$ per metre. Calculate the resistivity of nichrome.
Q23 marks
Explain why the student keeps the current through the wire as low as possible during this experiment.
Q32 marks
Suggest how the accuracy of the cross-sectional area measurement could be improved.