AQA AS Level Physics Paper 2, June 2024: Question 28
1 mark · Medium difficulty · Multiple Choice
Calculate the electrical resistance of an aluminium wire given its length, volume, and resistivity.
Practise this questionQuestion
Question text
28 An aluminium wire has a length of 12 cm and a volume of 3.7 × 10−4 m3. The resistivity of
aluminium is 2.7 × 10−8 Ω m.
What is the resistance of the wire?
[1 mark]
A 1.1 × 10−6 Ω
B 8.8 × 10−6 Ω
C 1.1 × 10−2 Ω
D 8.8 × 10−2 Ω
Mark scheme
Show the mark scheme
28 A 1.1 × 10−6 Ω
How to answer it
Calculating Resistance from Volume, Length, and Resistivity
What this question tests
This question assesses your ability to combine the definition of electrical resistivity ( R = ρL / A ) with geometric properties. Specifically, it tests whether you can use the volume of a wire ( V = A × L ) to eliminate the cross-sectional area ( A ) when it is not directly provided in the question stem, alongside strict unit conversion discipline.
Solution & Breakdown
✅ Correct Answer
A ( 1.1 × 10⁻⁶ Ω )
💡 Key Knowledge
- Resistivity equation: R = ρL / A
- Cylinder volume equation: V = A × L , which rearranges to give cross-sectional area A = V / L .
- Substituting area into the resistivity equation gives the powerful derived formula: R = ρL² / V .
🧠 Exam Technique
In multiple-choice calculations, avoid finding intermediate values (like calculating A first and writing it down). Substitute algebraic expressions ( A = V / L ) directly into your equation to minimize rounding errors and save valuable time.
❌ Common Errors
- Unit Neglect: Forgetting to convert length from centimeters ( cm ) to meters ( m ), leading to a factor of 10⁻² (or squared 10⁻⁴ ) error.
- Inverting Volume: Accidentally multiplying by volume instead of dividing by it because of confused transposition of A = V / L .
📐 Step-by-Step Calculation
- List known variables:
Length ( L ) = 12 cm = 0.12 m
Volume ( V ) = 3.7 × 10⁻⁴ m³
Resistivity ( ρ ) = 2.7 × 10⁻⁸ Ω m - Substitute into the combined formula ( R = ρL² / V ):
R = (2.7 × 10⁻⁸ × 0.12²) / (3.7 × 10⁻⁴) - Evaluate the numerator:
0.12² = 0.0144 m²
2.7 × 10⁻⁸ × 0.0144 = 3.888 × 10⁻¹⁰ - Divide by volume and find final answer:
R = (3.888 × 10⁻¹⁰) / (3.7 × 10⁻⁴) = 1.05 × 10⁻⁶ Ω (rounds to 1.1 × 10⁻⁶ Ω )
Topics
Physics · 3.5 Electricity
Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.