AQA AS Level Physics Paper 2, June 2022: Question 31

1 mark · Medium difficulty · Multiple Choice

Calculate the terminal potential difference when a 12 ohm resistor is connected across a cell with an emf of 2.0 V and an internal resistance of 4.0 ohms.

Practise this question

Question

Multiple choice question numbered 31 asking to find the terminal pd when a 12 ohm resistor is connected across a cell of emf 2.0 V and internal resistance 4.0 ohms. Four options are given: A 0.50 V, B 0.75 V, C 1.30 V, and D 1.50 V, each with an associated selection box.
Question text

31 A 12 Ω resistor is connected across the terminals of a cell that has an emf of 2.0 V and an

internal resistance of 4.0 Ω.

What is the terminal pd?

[1 mark]

A 0.50 V

B 0.75 V

C 1.30 V

D 1.50 V

Mark scheme

Show the mark scheme Mark scheme indicating the correct answer is D (AO2), corresponding to 1.50 V.

31 D (AO2) 1.50 V

How to answer it

Calculating Terminal Potential Difference

What this question tests

This question assesses your understanding of electromotive force (emf), internal resistance, and terminal potential difference in a single-loop DC circuit. You must apply Ohm's law and potential divider concepts to calculate how voltage drops across internal resistance affect the output pd of a cell.

Question 3.1 — Multiple Choice [1 Mark]

Cell Terminal Potential Difference Calculation

✅ Correct Answer

Option D: 1.50 V

Awarded for selecting option D (AO2 - Application of knowledge).

💡 Key Knowledge

  • Emf formula: ε = I(R + r) or ε = V + Ir
  • Terminal pd ( V ): The potential difference across the external load resistor ( V = IR ).
  • Potential Divider view: The emf splits proportionally between the load resistance and internal resistance.

📐 Step-by-Step Calculation

  1. Identify given values:
    Emf ( ε ) = 2.0 V
    Load resistance ( R ) = 12 Ω
    Internal resistance ( r ) = 4.0 Ω
  2. Find total circuit resistance:
    R_total = R + r = 12 + 4.0 = 16 Ω
  3. Calculate total circuit current ( I ):
    I = ε / R_total = 2.0 / 16 = 0.125 A
  4. Calculate terminal pd ( V ):
    V = I × R = 0.125 × 12 = 1.50 V
    Alternative shortcut (Potential Divider ratio):
    V = ε × [R / (R + r)] = 2.0 × [12 / (12 + 4)] = 1.50 V

❌ Common Errors & Examiner Traps

  • Using internal resistance only: Calculating I × r ( 0.125 × 4 = 0.50 V ). This gives Option A, which represents the "lost volts", not the terminal pd!
  • Forgetting internal resistance in total: Dividing emf by just the load resistor 2.0 / 12 , leading to incorrect rounding/distractors.
  • Misinterpreting definitions: Confusing emf with terminal pd when no current flows (they are only equal when I = 0 ).

🧠 Exam Technique & Top Tips

For quick multiple-choice questions involving sources with internal resistance, using the potential divider ratio formula ( V = ε × (R / (R + r)) ) saves precious time and bypasses calculating current entirely. Always double-check whether the question asks for terminal pd (voltage across R ) or lost volts (voltage dropped across r ).

Topics

Physics · 3.5 Electricity

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2022. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.