AQA AS Level Physics Paper 2, June 2025: Question 27

1 mark · Medium difficulty · Multiple Choice

Calculate the percentage uncertainty in the determined resistivity of a metal wire given the percentage uncertainties in current, diameter, length, and potential difference.

Practise this question

Question

Question 27 asks for the percentage uncertainty in the calculated resistivity of a wire from a given set of measurements. A table lists four measurements and their percentage uncertainties: current in wire (0.1%), diameter of wire (3.0%), length of wire (0.5%), and potential difference across wire (0.2%). Four multiple-choice options are provided: A 3.8%, B 6.8%, C 9.8%, and D 10.3%.

Mark scheme

Show the mark scheme Mark scheme for question 27 shows the correct answer is B (6.8%) under assessment objective AO2.

How to answer it

Combining Percentage Uncertainties in Resistivity

📌 What this question tests

This question assesses practical and mathematical skills in combining uncertainties. Specifically, you must link the resistivity formula to circuit quantities (voltage, current, length, and diameter) and apply the rules of combining percentage uncertainties when quantities are multiplied, divided, or raised to a power.

Question 27 [1 Mark]

Percentage Uncertainty in Calculated Resistivity

Multiple Choice (AO2)

✅ Correct Answer

Option B: 6.8%

Mark Scheme Breakdown:
• B (6.8%) = 1 mark [AO2]

💡 Key Knowledge

  • Resistivity formula: ρ = RA / L
  • Ohm's Law substitution: R = V / I
  • Cross-sectional area of a wire: A = πd² / 4
  • Combined equation: ρ = (V × πd²) / (4 × I × L)
  • Rules of Uncertainty:
    • When quantities multiply or divide: add percentage uncertainties.
    • When a quantity is raised to a power n : multiply its percentage uncertainty by n .

📐 Step-by-Step Calculation

  1. Express resistivity in terms of measured variables:
    ρ = (V × πd²) / (4 × I × L)
    Constants like π and 4 carry zero uncertainty.
  2. Write the total percentage uncertainty formula:
    % uncertainty in ρ = (% in V) + 2 × (% in d) + (% in I) + (% in L)
    Notice the factor of 2 in front of the diameter uncertainty because d is squared!
  3. Substitute the given values:
    • • % uncertainty in V = 0.2%
    • • % uncertainty in d = 3.0% → 2 × 3.0% = 6.0%
    • • % uncertainty in I = 0.1%
    • • % uncertainty in L = 0.5%
  4. Sum the components:
    Total % = 0.2% + 6.0% + 0.1% + 0.5% = 6.8%

🧠 Exam Technique

  • Always write the full formula first: Students who try to combine uncertainties without writing out ρ in terms of fundamental measurements frequently miss power terms like d² .
  • Ignore pure numbers: Numbers like π or 4 have no experimental uncertainty—never add anything for them.
  • Quick mental check: The diameter has by far the largest uncertainty (3.0%), so doubling it gives 6.0%. The final answer must be slightly above 6.0%, which immediately narrows your choices down to B (6.8%)!

❌ Common Errors & Distractor Traps

  • Choosing A (3.8%): Simply adding all values directly without doubling the diameter uncertainty ( 0.1 + 3.0 + 0.5 + 0.2 = 3.8% ). This is the most common trap!
  • Choosing C (9.8%): Incorrectly multiplying diameter uncertainty by 3 ( 3 × 3.0% = 9.0% ), confusing cross-sectional area with volume.
  • Choosing D (10.3%): Squaring the percentage uncertainty itself instead of multiplying it by 2 ( 3.0² = 9.0% ; then 0.1 + 9.0 + 0.5 + 0.2 = 9.8% , plus misreading/extra addition error). Remember: %Δ(xⁿ) = n × (%Δx) , NOT (%Δx)ⁿ .

Topics

Physics · Practical skills · Required Practicals · 3.1 Measurements and their errors · 3.5 Electricity · Uncertainty and evaluation · AS practicals (1–6)

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.