# 12.1.8 Resistors in Parallel

### Deriving the Equation for Resistors in Parallel

• In a parallel circuit, the reciprocal of the combined resistance of two or more resistors is the sum of the reciprocal of the individual resistances
• In a parallel circuit:
• The current is the split at the junction (and therefore between resistors)
• The potential difference is the same through all resistors
• The equation for combined resistors in parallel is derived using Kirchhoff’s laws:

### 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 Combined resistance of two or more resistors in parallel equation

• This means the combined resistance decreases and is less than the resistance of any of the individual components
• For example, If two resistors of equal resistance are connected in parallel, then the combined resistance will halve

#### Maths tip

• The reciprocal of a value is 1 / value
• For example, the reciprocal of a whole number such as 2 equals ½
• 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 for the resistance R, this becomes 1/R. To get the value of R from 1/R, you must do 1 ÷ your answer
• You can also use the reciprocal button on your calculator (labelled either x-1 or 1/x, depending on your calculator

#### Exam Tip

The most common mistake is to forget to find 1/RT and not RT . Remember to do 1 / answer to get this value ### 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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