AQA AS Level Physics Paper 2, June 2023: Question 19

1 mark · Medium difficulty · Multiple Choice

Calculate the resistance of wire Y given the length, cross-sectional area, and resistance of wire X made of the same metal.

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Question

Multiple choice question 19 with a table giving the length and cross-sectional area of two wires X and Y. Wire X has a length of 47 cm and cross-sectional area 0.10 mm squared, with a resistance of 6.0 ohms. Wire Y has a length of 23 cm and cross-sectional area 0.40 mm squared. Four options A through D are provided: A 0.12 ohms, B 0.73 ohms, C 1.2 ohms, D 3.1 ohms.
Question text

19 The table shows the lengths and cross-sectional areas of two wires X and Y of the same

metal.

Wire Length / cm Cross-sectional area / mm2

X 47 0.10

Y 23 0.40

The resistance of X is 6.0 Ω.

The temperature of Y is the same as the temperature of X.

What is the resistance of Y?

[1 mark]

A 0.12 Ω

B 0.73 Ω

C 1.2 Ω

D 3.1 Ω

Mark scheme

Show the mark scheme Mark scheme indicating the correct answer is B, corresponding to 0.73 ohms.

19 B 0.73 Ω

How to answer it

Comparing Resistance of Two Wires

AQA AS Level Physics • Electricity • 1 Mark Multiple Choice

What this question tests

This question assesses your ability to apply the resistivity equation R = rho * L / A to proportional scaling problems without needing to calculate the absolute value of resistivity ( rho ). It tests unit awareness (converting lengths and areas consistently) and proportional reasoning.

Question 19: Resistance of Wire Y

✅ Correct Answer

B (0.73 Omega)

Awarded for selecting option B based on correct proportional scaling of length and cross-sectional area.

💡 Key Knowledge

  • Resistance is directly proportional to length ( R is proportional to L ).
  • Resistance is inversely proportional to cross-sectional area ( R is proportional to 1 / A ).
  • Since both wires are made of the same metal at the same temperature, resistivity ( rho ) is constant and cancels out in ratios.

🧠 Exam Technique

Instead of calculating rho for wire X and substituting it back, set up a ratio equation: R_Y = R_X * (L_Y / L_X) * (A_X / A_Y) . This saves time and minimizes rounding errors during multiple-choice questions.

❌ Common Errors

  • Unit conversion traps: Forgetting to convert units, though because length and area ratios are dimensionless, consistent units ( cm to cm and mm² to mm² ) cancel out safely. However, mixing units (e.g., cm and m ) will ruin the ratio.
  • Inverting factors: Accidentally multiplying by area instead of dividing, or inverting the length ratio.

📐 Step-by-Step Calculation

  1. Identify the formula: R = rho * L / A , therefore rho = (R * A) / L .
  2. Equate resistivities (since the metal is identical):
    (R_X * A_X) / L_X = (R_Y * A_Y) / L_Y
  3. Rearrange for R_Y:
    R_Y = R_X * (L_Y / L_X) * (A_X / A_Y)
  4. Substitute the values:
    R_Y = 6.0 * (23 / 47) * (0.10 / 0.40)
  5. Evaluate step-by-step:
    R_Y = 6.0 * 0.48936 * 0.25 = 0.734 Omega
  6. Match with options: Rounds to 0.73 Omega, which corresponds to option B.

Topics

Physics · 3.5 Electricity

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.