AQA GCSE Physics Physics Paper 1 (Higher), November 2020: Question 8

9 marks · Standard Demand difficulty · Short Answer

Calculate missing data, evaluate precision, analyze inverse proportionality from a graph, and explain the effect on total resistance when adding resistors in parallel.

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Question

Question text

08 A student investigated how the total resistance of identical resistors connected in

parallel varied with the number of resistors.

The student used an ohmmeter to measure the total resistance of the resistors.

Figure 11 shows the student’s circuit with 3 resistors.

Figure 11

The student repeated each reading of resistance three times.

Table 1 shows some of the results for 3 resistors in parallel.

Table 1

Number of Total resistance in ohms

resistors

Reading 1 Reading 2 Reading 3 Mean

3 15.8 15.3 X 15.7

08.1 Calculate value X in Table 1.

[2 marks]

X = Ω

08.2 The student thought that taking a fourth reading would improve the precision of the

results.

The fourth reading was 16.2 Ω.

Explain why the student was wrong.

[2 marks]

Figure 12 shows the results from the investigation.

Figure 12

08.3 The student concluded that the number of resistors in parallel was inversely

proportional to the mean total resistance.

Explain why the student was correct.

Use data from Figure 12 in your answer.

[3 marks]

08.4 Explain why adding resistors in parallel decreases the total resistance.

[2 marks]

Mark scheme

Show the mark scheme

Question 8

AO /

Question Answers Extra information Mark

Spec. Ref.

08.1 AO2

15.8 + 15.3 + X 1 4.2.1.3

15.7 = RPA 3

X = 16.0 (Ω)

08.2 precise results show little 1 AO3

variation 4.2.1.3

RPA 3

the 4th result was further away allow the range of values has 1

from the mean than the other increased

values

ignore the 4th result was an

anomaly

08.3 two pairs of values of n and R eg 2 × 24 = 48, 3 × 16 = 48 1 AO3

showing that n × R = constant 4 × 12 = 48, 5 × 9.5 = 47.5 4.2.1.3

6 × 8 =48 RPA 3

third pair of values of n and R 1

showing that n × R = constant

(so) n × R = constant (showing 1

the student was correct)

allow 1 mark each for two

statements relating the change

in number of resistors to the

change in (mean total)

resistance

allow 1 mark for use of data

from graph to confirm at least

one statement

08.4 multiple paths for charge / allow current for charge 1 AO1

electrons to flow 4.2.1.3

RPA 3

total current is greater (for the 1

same potential difference when

more resistors are added)

Total 9

How to answer it

Resistance of Resistors in Parallel Study Guide

📌 What this question tests

This question assesses your understanding of electrical circuits (specifically resistors in parallel), working with experimental data, calculating means, understanding precision, analyzing graphical relationships (inverse proportionality), and explaining current flow.

Part 08.1: Calculating Missing Data

Calculate value X in Table 1. [2 marks]

📐 Step-by-Step Calculation

State the formula for a mean: Mean = (Sum of all values) / (Number of values)
Rearrange the formula to find the total sum: 15.7 × 3 = 47.1
Add the known readings together: 15.8 + 15.3 = 31.1
Subtract from the total sum to find X: 47.1 - 31.1 = 16.0

✅ Correct Answer

X = 16.0 (Ω)

Awarded 1 mark for correct method/substitution and 1 mark for the final correct answer.

Part 08.2: Precision and Anomalies

Explain why taking a fourth reading of 16.2 Ω would not improve precision. [2 marks]

💡 Key Knowledge

Precision refers to how close repeated measurements are to each other (showing little variation). It is not the same as accuracy.

✅ Correct Answer

Precise results show little variation.
The 4th reading (16.2 Ω) is further away from the mean than the other readings, meaning it increases the range of values rather than clustering tightly.

2 marks total (1 mark for defining/identifying what precise results show, 1 mark for noting the 4th result increased spread/variation).

Part 08.3: Inverse Proportionality Analysis

Explain why the student was correct that number of resistors is inversely proportional to resistance. Use data from Figure 12. [3 marks]

🧠 Exam Technique

To prove inverse proportionality using graph data, pick pairs of values for n (number of resistors) and R (resistance) and show that multiplying them together gives a constant value (or roughly the same product).

✅ Correct Answer

Select pairs of coordinates from Figure 12: e.g., at 2 resistors, resistance = 24 Ω ( 2 × 24 = 48 ).
Pick a second pair: e.g., at 3 resistors, resistance = 16 Ω ( 3 × 16 = 48 ).
Pick a third pair: e.g., at 6 resistors, resistance = 8 Ω ( 6 × 8 = 48 ).
Conclusion: Since n × R = constant (48), the student was correct.

3 marks total (1 mark for each correct pair showing constant product, up to 3 marks).

Part 08.4: Circuit Theory Explanation

Explain why adding resistors in parallel decreases the total resistance. [2 marks]

❌ Common Errors

Students often lose marks by simply stating "current increases" without explaining why. You must mention multiple paths for charge.

✅ Correct Answer

Adding resistors in parallel provides multiple pathways for charge (or electrons) to flow.
Therefore, the total current is greater for the same potential difference, which means overall resistance decreases (since R = V / I ).

2 marks total (1 mark for mentioning multiple paths for charge/current, 1 mark for stating total current increases for the same potential difference).

Topics

Physics · Required Practicals · P2: Electricity · Required Practicals

Question and mark scheme from the AQA GCSE Physics examination, Physics Paper 1 (Higher), November 2020. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.