A resistivity measurement with an uneven wire

10 marks · A-level · original practice case

Write your working and explanations below or on paper. Your responses stay in this page; PhysicsHelp does not submit or save them. Copy anything you want to keep before closing it. Check calculations separately from method marks. Use unrounded working between parts.

The situation

A wire of length 1.00 m has resistance 2.20 Ω. A micrometer reads to 0.01 mm. Measurements at different positions are listed below; they are simulated. Use the mean diameter and a circular cross-section. The spread may include real non-uniformity as well as measurement variation.

Diameter at four positions
Position	d / mm
1	0.34
2	0.35
3	0.36
4	0.35

Part (a)

Calculate the mean diameter. [2 marks]

Give the numerical answer to 2 significant figures.

Final value / mm

Working

Part (b)

Calculate the resistivity using the mean diameter. [3 marks]

Give the numerical answer to 2 significant figures.

Final value / Ω m

Working

Part (c)

Explain the effect of an uncorrected positive micrometer zero error on this result. [2 marks]

Your explanation

Part (d)

Evaluate treating half the diameter range as the entire measurement uncertainty. [3 marks]

Your explanation

Marking rubric and worked answers

Indicative practice marks. Method marks assess valid working; accuracy marks require the associated valid method. Independent points stand on their own. Tick only points supported by your response. Do not award the same explanation twice. These ticks record your judgement, not an examiner’s result.

Part (a) marking points

Final answer: 0.35 mm. Numerical checks assess the final value only; they do not check working or the number of digits typed.

Sum the four diameters and divide by four. (1 method mark)
Obtain 0.35 mm. (1 accuracy mark)

No earlier numerical result is required. Award method credit for valid working and accuracy credit for the stated answer. Accept a defensible equivalent method; wrong physics cannot earn dependent accuracy credit.

Common errors: This is the sum; divide by the number of readings.

Part (b) marking points

Final answer: 2.1 × 10^-7 Ω m. Numerical checks assess the final value only; they do not check working or the number of digits typed.

Convert diameter to metres and use A = π(d/2)². (1 method mark)
Use ρ = RA/L. (1 method mark)
Obtain 2.1 × 10^-7 Ω m. (1 accuracy mark)

Use the mean diameter from part (a), convert mm to m, and calculate ρ = Rπd²/(4L). Allow arithmetic follow-through; treating diameter as radius is a new error.

Common errors: This uses diameter as radius, making area four times too large.

Part (c) marking points

Diameter is overestimated. (1 independent mark)
Cross-sectional area, and therefore RA/L, is overestimated. (1 independent mark)

Award each distinct physical point once. Equivalent scientifically correct wording is creditable; a contradictory statement cannot earn the same point.

Part (d) marking points

Half-range here is 0.01 mm and reflects spread across the selected measurements. (1 independent mark)
It does not establish or remove a shared zero/calibration error. (1 independent mark)
Actual diameter variation makes the uniform-cylinder area model an additional limitation. (1 independent mark)

Award each distinct physical point once. Equivalent scientifically correct wording is creditable; a contradictory statement cannot earn the same point.

Acceptable alternatives: Resolution must also be considered; four positions may miss variations elsewhere. These may replace a corresponding limitation point, not earn extra marks.

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Related skills

Scope and reference sources

AQA practical/mathematical skills with selected 3.4/3.5; OCR A Modules 1/2 and selected 3/4. These are shared original exercises; wording, indicative marks and difficulty have not been endorsed by either board.

AQA specification · OCR A specification

Case reference: wire-diameter · version 1.1.0 · seed 0. Choose another case