A LevelPhysicsAQARevision NotesElectricityCircuits & The Potential DividerResistors in Series & Parallel

Resistors in Series & Parallel (AQA A Level Physics): Revision Note

Exam code: 7408

Resistors in series & parallel

Resistors in series

When two or more components are connected in series:
The combined resistance of the components is equal to the sum of individual resistances

Circuit diagram showing three resistors, R1, R2 and R3, connected in series along the top wire. Voltmeters V1, V2 and V3 are connected in parallel across R1, R2 and R3 respectively. — **The total resistance of resistors in series is the sum of their resistances**

To calculate the total resistance of resistors in series:

$R_{T} = R_{1} + R_{2} + R_{3} + \dots$

Worked Example

The combined resistance R in the following series circuit is 60 Ω. What is the resistance value of R₂?

Series circuit containing a cell and three resistors connected in a single loop. R1 is 30 ohms, R2 has an unknown resistance, and R3 is 10 ohms.

A. 100 Ω B. 30 Ω C. 20 Ω D. 40 Ω

[1]

Answer:

The total resistance of resistors in series is given by:

$R_{T} = R_{1} + R_{2} + R_{3}$

Rearrange for the unknown resistance:

$R_{2} = R_{T} - R_{1} - R_{3} = 60 - 30 - 10 = 20 Ω$

Therefore, the correct answer is C [1 mark]

Resistors in parallel

When two or more components are connected in parallel:

The reciprocal of the combined resistance is the sum of the reciprocals of the individual resistances

Circuit diagram showing two parallel branches between the same pair of junctions: resistor R1 on the upper branch and resistor R2 on the lower branch, with connecting wires at the left and right. — **Adding resistors in parallel lowers the total resistance**

To calculate the total resistance of resistors in parallel:

$\frac{1}{R_{T}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \dots$

This means as more resistors are added, their combined resistance decreases and is, therefore, less than the resistance of the individual components
- For example, if two resistors of equal resistance are connected in parallel, then the combined resistance will halve

Worked Example

Question showing a cell with three resistors labelled R, 2R and R connected in parallel. It asks which value gives the combined resistance of all the resistors in the circuit, with options A 5R/2, B 2/(5R), C 5/(2R) and D 2R/5.

[1]

Answer:

The total resistance of resistors in parallel is given by:

$\frac{1}{R_{T}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}$

$\frac{1}{R_{T}} = \frac{1}{R} + \frac{1}{2 R} + \frac{1}{R} = \frac{5}{2 R}$

Calculate the total resistance from the reciprocal of the sum:

$R_{T} = \frac{1}{\frac{1}{R_{T}}} = \frac{2 R}{5}$

Therefore, the correct answer is D [1 mark]

Examiner Tips and Tricks

The most common mistake in questions about parallel resistors is to forget to find the reciprocal of R_T (1/R_T) instead of R_T. Here is a maths tip to rejig your memory on reciprocals:

The reciprocal of a value is 1 / value
For example, the reciprocal of a whole number such as 2 equals ½
- Conversely, the reciprocal of ½ is 2
If the number is already a fraction, the numerator and denominator are ‘flipped’ round

$Examples show reciprocal arrows between 2 and one-half, three-quarters and four-thirds, and R and one over R. Each arrow is labelled “reciprocal”, showing that fractions are flipped.$

In the case of the resistance R, this becomes 1/R
To get the value of R from 1/R, you must calculate 1 ÷ your answer
You can also use the reciprocal button on your calculator (labelled either x^-1 or 1/x, depending on your calculator)

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

I would just like to say a massive thank you for putting together such a brilliant, easy to use website.I really think using this site helped me secure my top gradesin science and maths. You really did save my exams! Thank you.

Beth
IGCSE Student

This website is soooo useful and I can’t ever thank you enough for organising questions by topic like this. Furthermore, the name of the website could not have been more appropriate as it literally did SAVE MY EXAMS!

Fathima
A Level Student

Incredible! SO worth my money, the revision notes have everything I need to know and are so easy to understand. I actually enjoy revising! It makes me feel a lot more confident for my GCSEs in a few months.

Kate
GCSE Student

Absolutely brilliant, both my girls used it for A levels and GCSE. It's saves on paper copies, also beneficial exam questions ranked from easy to hard. It's removed a lot of stress from the exams.

Sameera
Parent

Just to say that your resources are the best I have seen and I have been teaching chemistry at different levels for about 40 years

Mark
Chemistry Teacher

Excellent