A2 Daily A Level Physics question

2026-05-12 OCR A Practical skills (M1): Required practicals & data handling; uncertainty propagation (no calculus) OCR Physics A Module 1.3: Processing, analysing and evaluating data (uncertainties; percentage vs absolute; combining uncertainties for products and powers) OCR Physics A Module 1.1: Practical skills assessed in the written examination (planning measurements; identifying dominant sources of uncertainty) PAG (Electrical measurements): Determination of resistivity of a metal wire

In a lab to determine the resistivity of a metal wire, a student measures: length L = 1.000 m with a metre rule (±1 mm), resistance R from a V–I graph (current kept low; about 3% uncertainty in the slope), and diameter d with a micrometer (±0.01 mm on a wire of about 0.50 mm, giving about 2% for d). They can make one change to most reduce the percentage uncertainty in the final resistivity. Which option should they choose, and why?

A Replace the metre rule (±1 mm) with one of ±0.5 mm; keep everything else the same.
B Take four times as many independent diameter readings at different positions/orientations and average them, roughly halving the percentage uncertainty in d. (correct)
C Extend the V–I range and take many more points so the percentage uncertainty in R is reduced from about 3% to about 1.5%.
D Double the measured length to 2.000 m using the same ruler, leaving the V–I and diameter measurements unchanged.

Answer

The correct answer is B.

Correct: B — Take four times as many independent diameter readings at different positions/orientations and average them, roughly halving the percentage uncertainty in d. The resistivity depends on the square of the diameter, so the percentage contribution from d is doubled; cutting %d in half therefore reduces the overall percentage uncertainty by about twice as much as halving %R, and far more than any change to L. A Reducing the length uncertainty from ~0.1% to ~0.05% changes a term that is already negligible compared with those from R and d, so the overall effect is minimal. B Halving the percentage uncertainty in d cuts its doubled contribution most, giving the largest reduction in the final percentage uncertainty. C Halving the percentage uncertainty in R helps, but its contribution is not multiplied; this reduction is smaller than halving %d, whose effect is doubled. D Doubling L only halves an already tiny percentage uncertainty in length and does not affect the dominant contributions from R and d.

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