# 5.3.1 Resistors in Series & Parallel

### 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

Resistors connected in series

• To calculate the total resistance of resistors in series:

#### Worked Example

The combined resistance R in the following series circuit is 60 Ω.

What is the resistance value of R2?

A.     100 Ω               B.     30 Ω               C.     20 Ω               D.     40 Ω

#### Resistors in Parallel

• When two or component are connected in parallel:
• The reciprocal of the combined resistance is the sum of the reciprocals of the individual resistances

Resistors connected in parallel

• To calculate the total resistance of resistors in parallel:

• 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

#### Exam Tip

The most common mistake in questions about parallel resistors is to forget to find the reciprocal of RT (1/RT) instead of RT. 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

The reciprocal of a number is 1 ÷ number

• 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)

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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