Wait, What? A wire can appear to have a different resistivity simply because you let it get warm.

Resistivity is meant to describe a material property under stated conditions. But a classroom experiment does not measure resistivity directly. It measures voltage, current, wire length and diameter, then infers resistivity through a model. If temperature drifts, contacts add resistance, or diameter is measured badly, the final number can change even though the material itself has not.

This practical is therefore not just “measure resistance of a wire.” It is a lesson in how a material property is extracted from several imperfect measurements while controlling the physical conditions that property depends on.

The model behind the experiment

For a uniform conductor under suitable conditions:

R = ρL/A

where R is resistance, ρ is resistivity, L is conductor length and A is cross-sectional area.

For a round wire:

A = πd²/4

so diameter enters the calculation squared. That immediately tells you something important: a small percentage error in diameter can produce a much larger percentage error in area.

Why the experiment usually starts with R against L

If material, diameter and temperature are held constant, R should increase approximately linearly with L. Plotting resistance against length gives a stronger test than calculating ρ from one single reading.

From:

R = (ρ/A)L

the gradient of an R-versus-L graph is ρ/A. Therefore:

ρ = gradient × A

The Institute of Physics uses this structure explicitly in its resistivity teaching sequence and emphasises both wire dimensions and experimental error. See IOPSpark Episode 112: Resistivity.

Measuring resistance: current and voltage are not independent of the wire

Resistance is commonly found using:

R = V/I

An ammeter is placed in series; a voltmeter is placed across the chosen wire section. But the current itself can heat the wire. In metals, rising temperature generally increases resistance. If current differs between trials, or the wire gets progressively hotter, the comparison no longer isolates length cleanly.

IOPSpark specifically warns that overly large currents can warm the wire and affect the result. See the IOPSpark resistance-of-wires investigation.

Heating: the experiment can change its own independent variable structure

Suppose you increase wire length and keep the same supply setting. Longer wire may have higher resistance, so current may change. That alters electrical power dissipation. Temperature then changes by a different amount. Now length is not the only thing changing in practice.

To reduce this problem, use small currents, take readings promptly, switch off between measurements where appropriate, and allow cooling. Temperature does not have to be measured in every school version, but it should be recognised as a controlled condition.

Wire length: where exactly does the measured section begin and end?

If crocodile clips contact the wire at 20 cm and 70 cm marks, the effective measured length is about 50 cm—but only if contact positions are well defined. Broad or inconsistent clip positions introduce uncertainty in L.

Taping the wire along a metre rule and using clearly positioned contacts improves repeatability. The measurement should refer to the actual conducting section between voltage measurement points, not simply the visible piece of wire on the bench.

Diameter: one reading is not enough

Use a micrometer screw gauge where appropriate. Measure diameter at several positions along the wire and, if the wire may not be perfectly circular, in more than one orientation. Then calculate a representative mean.

Why? Real wire may vary slightly in thickness, and one local defect can distort a single reading. Because area depends on d², diameter deserves high-quality measurement.

Quantitative window: why diameter uncertainty matters so much

Suppose d = 0.50 mm. Then:

A = π(0.50 × 10⁻³)² / 4 ≈ 1.96 × 10⁻⁷ m²

If diameter is actually 0.52 mm, area becomes about 2.12 × 10⁻⁷ m²—roughly 8% larger from only a 4% diameter change.

This is why students should never say “diameter is just one small measurement.” In the model, it is mathematically amplified.

Contact resistance: the wire is not the only resistor in the circuit

Clips, leads and junctions have resistance. If your measured wire segment has relatively high resistance, contact contributions may be small. If you measure a short, thick, low-resistance wire, contact resistance can become a large fraction of the total.

A non-zero intercept on an R-versus-L graph can sometimes indicate fixed resistance contributions from contacts or leads, though interpretation should be cautious because other systematic effects can also shift the graph.

A graph is a model test, not just a way to get a gradient

If R is proportional to L, points should lie approximately on a straight line. Curvature can indicate heating, non-uniform diameter or changing contact conditions. Large scatter can indicate unstable connections or noisy measurements.

Do not force a straight line merely because the equation says it should be straight. The graph is where theory meets the actual apparatus.

Observation versus inference

Observation: “At 0.80 m, V = 1.20 V and I = 0.30 A.”

Transformation: “R = 4.0 Ω.”

Inference: “The wire’s resistance increased with length.”

Further inference: “The material’s resistivity is approximately constant over the tested conditions.”

That last claim is stronger and depends on diameter and temperature really being controlled.

Failure modes that cap marks and understanding

• Large current: wire heats and R changes during the experiment.
• One diameter reading: local thickness variation can bias A.
• Wrong unit conversion: mm must be converted to m before SI resistivity calculation.
• Loose clips: contact resistance changes unpredictably.
• Too-short lengths: wire resistance becomes comparable to contact/lead resistance.
• Using diameter instead of area in R = ρL/A: gives a dimensionally and physically wrong result.

Unfamiliar transfer: conducting paper instead of wire

Suppose the conductor is a rectangular strip of conducting paper. The same logic applies: resistance depends on path length and cross-sectional geometry. But “cross-sectional area” now depends on width and thickness, and contact shape may matter more.

The formula has not changed; the practical meaning of its variables has.

Secondary → JC → deeper Physics

Secondary: investigate how wire resistance changes with length, use ammeters and voltmeters correctly, control material and thickness, and recognise heating.

JC: determine resistivity using gradients, propagate diameter uncertainty into area, analyse intercepts, control temperature and evaluate contact effects.

Deeper Physics: precision resistivity measurement uses four-terminal Kelvin methods, temperature control, calibrated geometry and material-specific transport models.

Checkpoint 1: the curved graph

A student obtains an R-versus-L graph that bends upward at the longest lengths. During those measurements the wire feels noticeably warm.

What is a plausible explanation, and what should be changed?

Checkpoint 2: diameter disagreement

Micrometer readings are 0.48, 0.51, 0.49, 0.61 and 0.50 mm. Should the student simply average all five?

Answer key and WHY reasoning

Checkpoint 1: heating may be increasing the metal’s resistance, especially at later or higher-power measurements. Reduce current, shorten measurement time, switch off between readings and allow cooling so temperature stays more nearly constant.

Checkpoint 2: investigate the 0.61 mm reading before averaging. It may represent a true thicker region, a burr, crossed micrometer position or reading error. Repeat nearby measurements. An outlying result should be examined, not deleted automatically and not accepted blindly.

How to study resistivity practicals

Build your revision around the model R = ρL/A. For each symbol, write: how it is measured, which apparatus is used, the dominant uncertainty, and what would make the variable drift during the experiment.

Then practise predicting errors. If d is overestimated, A is overestimated and calculated ρ is overestimated for a given gradient. If wire heating raises R, gradient may become too large and ρ may also be overestimated. This equation-mechanism linkage is the standard to aim for.

Evidence boundaries

Your result estimates resistivity for the tested wire under the experimental temperature, geometry and contact conditions. Resistivity changes with temperature and can depend on composition, defects and microstructure. A single school measurement should not be presented as an exact universal constant.

Authoritative next steps

• Institute of Physics: Resistivity
• Institute of Physics: Investigating the resistance of wires
• Institute of Physics: Ohm’s law and resistance practicals
• SEAB A-Level syllabus directory

Teaching Guide

For teachers and parents: require students to explain why diameter measurement deserves disproportionate attention, and let them compare one-point calculation with a graph-gradient method. Ask them to diagnose a deliberately warmed wire. Practical understanding improves when the student sees resistivity as an inferred material property rather than a number produced by a formula.