AQA AS Level Physics Paper 2, June 2024: Question 9

1 mark · Medium difficulty · Multiple Choice

Calculate the resistance R of an LDR in a potential divider circuit given two sets of voltmeter readings and a fixed battery emf.

Practise this question

Question

A circuit diagram showing a 12 V battery connected in series with a fixed resistor and a light-dependent resistor (LDR). A voltmeter V is connected in parallel across the fixed resistor. Below the diagram are multiple-choice options A (48 ohms), B (96 ohms), C (120 ohms), and D (160 ohms).
Question text

09 A circuit contains a battery with an emf of 12 V and negligible internal resistance.

At a certain light intensity, the LDR has a resistance of 480 Ω and the voltmeter reading

is 2.0 V.

At a different light intensity, the resistance of the LDR is R and the voltmeter reading is

now 8.0 V.

What is R?

[1 mark]

A 48 Ω

B 96 Ω

C 120 Ω

D 160 Ω

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer for question 09 is option A, which corresponds to 48 ohms.

09 A 48 Ω

How to answer it

Potential Divider and LDR Circuit Analysis

What this question tests

This question assesses your understanding of potential divider circuits, how resistance changes in a Light Dependent Resistor (LDR) affect potential differences, and how to apply the potential divider equation or ratio methods to find unknown component resistances.

Question 09

Exam Breakdown & Step-by-Step Solution

✅ Correct Answer

The correct option is A (48 Ω).

Awarded 1 mark for selecting option A.

💡 Key Knowledge

  • In a series circuit acting as a potential divider, the total supply emf is shared between components in direct proportion to their resistance: V₁ / V₂ = R₁ / R₂ .
  • The fixed resistor's resistance ( R_fixed ) remains constant throughout both states.
  • As light intensity changes, only the LDR resistance changes.

🧠 Exam Technique

For multiple-choice ratio questions, always start by identifying which values stay constant (the fixed resistor) and find that value first before moving on to the changed scenario.

❌ Common Errors

  • Assuming the fixed resistor changes value along with the LDR.
  • Forgetting to subtract the voltmeter reading from the total supply voltage ( 12 V ) to find the potential difference across the LDR.

📐 Step-by-Step Calculation

  1. Find the fixed resistor value using initial conditions:
    Supply emf = 12 V . When the voltmeter reads 2.0 V across the fixed resistor, the voltage across the LDR is 12 V - 2.0 V = 10.0 V .
  2. Apply the potential divider ratio:
    Using V_fixed / V_LDR = R_fixed / R_LDR :
    2.0 / 10.0 = R_fixed / 480
    R_fixed = 480 × (2.0 / 10.0) = 96 Ω .
  3. Calculate the new LDR resistance ( R ) for the second condition:
    New voltmeter reading = 8.0 V (across the fixed resistor).
    New voltage across the LDR = 12 V - 8.0 V = 4.0 V .
  4. Set up the ratio for the second state:
    V_fixed / V_LDR = R_fixed / R
    8.0 / 4.0 = 96 / R
    2 = 96 / R
    R = 96 / 2 = 48 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.