AQA AS Level Physics Paper 2, June 2024: Question 13

1 mark · Medium difficulty · Multiple Choice

Calculate the potential difference across a resistor when the power is 32 W, given that a current of 4.0 A produces a power of 8.0 W.

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Question

Multiple choice question 13 stating: A current of 4.0 A in a resistor produces a power of 8.0 W. What is the potential difference across this resistor when the power is 32 W? Four options are given: A 2.0 V, B 4.0 V, C 8.0 V, and D 16 V.
Question text

13 A current of 4.0 A in a resistor produces a power of 8.0 W.

What is the potential difference across this resistor when the power is 32 W?

[1 mark]

A 2.0 V

B 4.0 V

C 8.0 V

D 16 V

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer for question 13 is option B, which corresponds to 4.0 V.

13 B 4.0 V

How to answer it

Power, Current, and Potential Difference Relations

What this question tests:
This question assesses your understanding of electrical power equations (P = IV and P = V² / R), your ability to manipulate constants like resistance under changing conditions, and proportional scaling reasoning required at AS Level Physics.
Question Part 1.3

Determining Potential Difference from Changed Power

✅ Correct Answer

Option B: 4.0 V

Mark Allocation: 1 mark for selecting B.

💡 Key Knowledge

  • Electrical power formulas: P = IV and P = V² / R and P = I²R .
  • Assuming the resistor is ohmic (constant resistance R ), power is proportional to the square of the potential difference ( P ∝ V² ).
  • Alternatively, find R first using initial conditions, then calculate V for the new power.

🧠 Exam Technique

Since this is a multiple-choice question worth 1 mark, avoid lengthy working out if a proportional scaling method can get you there faster and safer.

❌ Common Errors

  • Assuming current remains constant even though power changed (forgetting that changing power in a fixed resistor requires changes to both V and I ).
  • Failing to take the square root when scaling V² to V .

📐 Step-by-Step Calculation

Method 1: Finding Resistance First

  1. Find the resistance R of the component using P = I²R :
    8.0 = (4.0)² × R
    8.0 = 16 × R ⇒ R = 8.0 / 16 = 0.50 Ω
  2. Use the new power ( 32 W ) and the resistance to find new potential difference via P = V² / R :
    32 = V² / 0.50
    V² = 32 × 0.50 = 16
    V = √16 = 4.0 V

Method 2: Proportional Scaling (Faster)

  1. Notice the power increases by a factor of 4 (from 8.0 W to 32 W ).
  2. Since P ∝ V² , scaling factor for V is the square root of the power scale factor: √4 = 2 .
  3. Multiply the original current-implied or proportional voltage step, or recognize that initial V = P / I = 8.0 / 4.0 = 2.0 V . Scaling by 2 gives 2.0 V × 2 = 4.0 V .

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.