AQA AS Level Physics Paper 2, November 2021: Question 30

1 mark · Easy difficulty · Multiple Choice

Calculate the total resistance of three resistors with resistances R, R, and 3R connected in parallel.

Practise this question

Question

Multiple choice question 30 shows a circuit diagram with three resistors connected in parallel, two with resistance R and one with resistance 3R. Below the diagram, four possible combined resistance values are listed: A (3R/7), B (7R/3), C (5R/6), and D (6R/5), each with an answer box next to it.
Question text

30 Resistors of resistance R, R and 3R are connected as shown.

What is the resistance of the arrangement?

[1 mark]

3R

A

7R

B

5R

C

6R

D

Mark scheme

Show the mark scheme The mark scheme table shows question number 30 with the correct answer A and the corresponding value 3R/7.

3R

30 A

How to answer it

Combined Resistance in Parallel Circuits

AQA AS Level Physics • Electricity • Multiple Choice

What this question tests

This question assesses your ability to apply the standard formula for resistors connected in parallel ( 1/R_total = 1/R_1 + 1/R_2 + ... ) when algebraic expressions involving a common resistance variable ( R ) are used instead of numerical values.

Question 30

Determining Total Resistance of Three Parallel Resistors

✅ Correct Answer

Option A: 3R / 7

Worth 1 mark. Fully derived by calculating the reciprocal sum for parallel resistors.

💡 Key Knowledge

  • For any number of resistors in parallel, combine them using: 1/R_total = 1/R_1 + 1/R_2 + 1/R_3
  • Always remember to take the final reciprocal ( R_total = 1 / (sum) ) at the very end of the calculation.

📐 Step-by-Step Calculation

  1. Identify individual resistances: R₁, R₂, and R₃ are given as R , R , and 3R .
  2. Set up the parallel formula:
    1/R_total = (1/R) + (1/R) + (1/3R)
  3. Find a common denominator:
    The common denominator is 3R .
    1/R_total = (3/3R) + (3/3R) + (1/3R)
  4. Add the fractions:
    1/R_total = (3 + 3 + 1) / 3R = 7 / 3R
  5. Invert to find R_total:
    R_total = 3R / 7

🧠 Exam Technique

In multiple-choice questions involving algebraic fractions, do not waste time converting into decimals. Work cleanly with common denominators, combine numerators carefully, and make sure you don't forget the final inversion step.

❌ Common Errors

  • Forgetting to invert: Students often calculate 7 / 3R correctly as the sum of reciprocals, but forget to flip the final fraction, leading them to incorrectly select Option B ( 7R / 3 ).
  • Treating them as series: Incorrectly adding R + R + 3R = 5R , leading to confusion.

Topics

Physics · 3.5 Electricity

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, November 2021. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.