Resistivity vs Temperature: Four-Wire Lab Skills for H2 Physics

TL;DR
Build a four-wire (Kelvin) measurement rig with a constant-current source, thermocouple probe, and Logger Pro or Google Sheets to capture resistance as a function of temperature.
Linearise the data to extract temperature coefficients for copper, nichrome, and graphite, then discuss systematic errors like self-heating and thermal gradients.
The experiment deepens Paper 4 understanding of resistive materials and gives you a real dataset for planning-style questions on resistivity control.

Why This Lab Merits a Slot in Your Practical Calendar

• It extends the familiar internal-resistance experiment into material science, matching examiner emphasis on real-world instrumentation.
• Students practise proper four-wire techniques that appear in university physics and engineering labs — a valuable talking point for UCAS and admissions essays.
• The investigation integrates thermal physics, circuits, and error analysis, reinforcing multiple chapters of the 9478 syllabus at once.

Apparatus and Instrumentation

Data Collection Strategy

1. Calibrate sensors. Perform an ice–water bath test for the thermocouple and zero the digital voltmeter using its relative function.
2. Mount the sample. Suspend the wire/rod in the water bath with only the sensing region submerged to avoid short circuits.
3. Apply constant current. Start with 0.20 A to limit Joule heating; note the current uncertainty from the supply display.
4. Heat in stages. Increase bath temperature in 5 °C increments, waiting for thermal equilibrium (temperature change <0.2 °C over 30 s) before logging.
5. Record voltage drop. Use the sense leads to capture the true potential difference; convert to resistance via R = V/I and then resistivity using \rho = RA/L.
6. Plot R vs T. Fit a straight line R = R_0[1 + \alpha (T - T_0)] and extract the temperature coefficient \alpha.

Error Budget and Discussion Prompts

• Thermal gradients: Discuss how incomplete thermal equilibrium leads to underestimates of \alpha; suggest stirring or insulating sleeves.
• Self-heating: Estimate the power dissipated and show how lowering current or using pulsed measurements mitigates the effect.
• Contact resistance: Demonstrate the dramatic error introduced if you revert to a two-wire connection — a perfect comparison graph for your write-up.
• Thermocouple accuracy: Include the ±0.1 °C specification in uncertainty propagation, showing its contribution to \alpha.

Extensions for High-Ability Students

• Repeat the experiment with carbon or manganin, contrasting near-zero or negative temperature coefficients.
• Export data to Python and perform linear regression with uncertainty weighting to mirror university lab expectations.
• Compare experimental \alpha with datasheet values and generate a short briefing for Eclat’s electronics enrichment class.
• Link to Internal Resistance of Batteries so students see how the Kelvin technique supports both experiments.

References

• Texas Instruments, Accurate low-resistance measurements using the 4-wire method (Application Report SBOA323)
• Keysight Technologies, Basics of four-wire resistance measurements
• Encyclopædia Britannica, Resistivity