AQA AS Level Physics Paper 2, November 2021: Question 33

1 mark · Medium difficulty · Multiple Choice

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

Practise this question

Question

A multiple-choice question showing a table of percentage uncertainties for potential difference (0.3%), current (5.0%), diameter (4.0%), and length (0.2%). Below the table, four options A (1.6%), B (9.5%), C (13.5%), and D (21.5%) are listed alongside empty check boxes.
Question text

33 Measurements are taken to determine the resistivity of a uniform metal wire.

The table shows the quantities measured and their percentage uncertainties.

Quantity Percentage uncertainty

potential difference across wire 0.3%

current in wire 5.0%

diameter of wire 4.0%

length of wire 0.2%

What is the percentage uncertainty in the calculated value for the resistivity of the metal of

the wire?

[1 mark]

A 1.6%

B 9.5%

C 13.5%

D 21.5%

Mark scheme

Show the mark scheme The mark scheme table indicating that question 33 corresponds to correct answer C with a value of 13.5%.

33 C 13.5%

How to answer it

Question 33: Percentage Uncertainty in Resistivity

What this question tests

This question assesses your ability to combine percentage uncertainties when quantities are multiplied or divided in a physics formula, with a specific focus on handling powers (squared terms) for circular cross-sectional areas.

Question Part (3.3)

Determining Uncertainty in Resistivity

✅ Correct Answer

C (13.5%)

💡 Key Knowledge

  • The formula for resistivity is ρ = (R × A) / L .
  • Since resistance R = V / I , substituting gives ρ = (V × π × d²) / (4 × I × L) .
  • Rule for uncertainties: When quantities are multiplied or divided, you add their percentage uncertainties.
  • Rule for powers: If a quantity is raised to a power n (like d² ), you must multiply its percentage uncertainty by n (i.e., 2 × % uncertainty of d ).

📐 Step-by-Step Calculation

  1. Identify formula components and their given percentage uncertainties:
    • Potential difference ( V ) = 0.3%
    • Current ( I ) = 5.0%
    • Diameter ( d ) = 4.0%
    • Length ( L ) = 0.2%
  2. Account for the squared term in area ( A = πd²/4 ):
    Uncertainty contribution from diameter = 2 × 4.0% = 8.0% . Note that constants like π and 4 contribute zero uncertainty.
  3. Add all percentage uncertainties together:
    % uncertainty in ρ = %V + %I + (2 × %d) + %L
    % uncertainty in ρ = 0.3% + 5.0% + 8.0% + 0.2% = 13.5%

❌ Common Errors & Examiner Pitfalls

  • Forgetting to multiply the diameter uncertainty by 2: Students who forget this often calculate 0.3 + 5.0 + 4.0 + 0.2 = 9.5% , which incorrectly leads to distractor B.
  • Radius vs. Diameter confusion: Some students try to convert diameter to radius and get confused with the factor of 2. Always remember: percentage uncertainty in radius equals percentage uncertainty in diameter ( %uncertainty of r = %uncertainty of d ), but because A = πr² , you still multiply that uncertainty by 2 either way!
Examiner note: This is a classic 1-mark multiple-choice question designed to quickly check if candidates remember to scale up the uncertainty of squared terms. Top-level candidates spot the d² dependency instantly and write down the addition in seconds.

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, November 2021. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.