AQA AS Level Physics Paper 2, June 2023: Question 21

1 mark · Medium difficulty · Multiple Choice

Determine the order of three networks of resistors (X, Y, and Z) from largest total resistance to smallest total resistance.

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Question

Multiple choice question showing three resistor networks labelled X, Y, and Z. Network X has two parallel resistors of resistance R in series with a resistor of resistance 2R. Network Y has a parallel combination of two resistors in series (each of resistance R) and a single resistor of resistance 2R. Network Z has three parallel resistors: two of resistance R and one of resistance 2R. Four options A, B, C, D give different orderings of the networks from largest to smallest total resistance.
Question text

21 X, Y and Z are three networks of resistors.

Which gives the networks in order of largest total resistance to smallest total resistance?

[1 mark]

A X, Y, Z

B Y, X, Z

C Z, X, Y

D Z, Y, X

Mark scheme

Show the mark scheme Mark scheme table indicating the correct answer is A, corresponding to the order X, Y, Z.

21 A X, Y, Z

How to answer it

Comparing Total Resistance in Resistor Networks

What this question tests

This question assesses your ability to combine resistors in series and parallel configurations, calculate (or logically deduce) equivalent resistance, and order values from largest to smallest. It tests fundamental circuit rules under AS Level Physics DC circuits.

Question Part: Multiple Choice (Networks X, Y, Z)

Determining Total Resistance Order

✅ Correct Answer

A (X, Y, Z)

Mark awarded: 1 / 1 for selecting option A.

💡 Key Knowledge

  • Series resistors: Add directly: R_total = R₁ + R₂ . Adding resistors increases total resistance.
  • Parallel resistors: Total resistance decreases. Two equal resistors in parallel of value R give a combined resistance of 0.5R .

🧠 Exam Technique

You don't always need exact numerical values to the final decimal place. Quick analytical estimation or proportional reasoning saves time in multiple-choice questions.

❌ Common Errors

Confusing parallel and series formulas, or failing to add the series component correctly onto the parallel branch combination in network X.

📐 Step-by-Step Calculation & Breakdown

  1. Network X: Two resistors of resistance R are in parallel, combined with a series resistor 2R .
    Parallel part: R × R / (R + R) = 0.5R .
    Total resistance: 0.5R + 2R = 2.5R .
  2. Network Y: A parallel branch containing R + R = 2R in series, wired in parallel with 2R .
    Parallel branches are both equal to 2R .
    Total resistance: 2R / 2 = R .
  3. Network Z: Three branches in parallel: two of resistance R and one of 2R .
    Using 1/R_total = 1/R + 1/R + 1/(2R) = 2/R + 1/(2R) = 5/(2R).
    Total resistance: 2R / 5 = 0.4R .
  4. Comparison: Network X ( 2.5R ) > Network Y ( R ) > Network Z ( 0.4R ). Therefore, the descending order is X, Y, Z.

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.