AQA AS Level Physics Paper 2, June 2024: Question 18

1 mark · Medium difficulty · Multiple Choice

Determine the ratio of the power dissipated in resistor RX to the power dissipated in resistor RY for a circuit containing a battery and three identical resistors.

Practise this question

Question

Multiple choice question 18 shows a circuit diagram with a battery connected in series with a resistor RX, which is then in series with a parallel combination of two identical resistors RY and RZ. Below the diagram, four options A (0.25), B (0.5), C (2), and D (4) are listed to find the ratio of the power in RX to the power in RY.
Question text

18 A circuit contains a battery and three identical resistors RX, RY and RZ.

power in RX

What is ?

power in RY

[1 mark]

A 0.25

B 0.5

C 2

D 4

Mark scheme

Show the mark scheme The mark scheme table shows question number 18 with the correct answer D.

18 D 4

How to answer it

Power Ratios in Series-Parallel Resistor Circuits

What this question tests

This question assesses your understanding of current distribution in parallel branches, power equations in electrical circuits (specifically using P = I²R and P = V²/R ), and how to manipulate ratios for identical components.

Question 18 [1 Mark]

Comprehensive Solution & Examiner Breakdown

✅ Correct Answer

D (4)

Mark Awarded: 1/1 for selecting option D.

💡 Key Knowledge

  • Resistors R_Y and R_Z are connected in parallel, sharing the total current from the circuit equally because they are identical ( R_Y = R_Z = R ).
  • Resistor R_X is in series with this parallel combination, meaning it carries the total current ( I_total ) of the circuit.
  • Power formula linked to current: P = I²R .

🧠 Exam Technique

When dealing with ratios of identical components, assign algebraic variables (let resistance = R and total current = I ) rather than picking arbitrary numbers. This prevents arithmetic slips under timed conditions.

❌ Common Errors

Students often incorrectly assume all resistors carry the same current, leading to a ratio of 1. Another common trap is mixing up parallel current splitting, resulting in a ratio of 2 or 0.5.

📐 Step-by-Step Calculation

  1. Identify current through R_X: Resistor R_X is in the main branch, so the current flowing through it is I_total .
  2. Identify current through R_Y: Since R_Y and R_Z are identical and in parallel, the total current I_total splits equally between them. Therefore, current through R_Y is I_total / 2 .
  3. Set up the power equation for R_X: P_X = (I_total)² × R
  4. Set up the power equation for R_Y: P_Y = (I_total / 2)² × R = (1/4) (I_total)² × R
  5. Calculate the ratio P_X / P_Y :
    P_X / P_Y = ((I_total)² × R) / ((1/4) (I_total)² × R) = 1 / (1/4) = 4

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.