CIE A Level Physics (9702) 2019-2021

Revision Notes

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:

Derivation of resistors in parallel (1), downloadable AS & A Level Physics revision notes
Derivation of resistors in parallel (2), downloadable AS & A Level Physics revision notes

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 in parallel diagram, downloadable AS & A Level Physics revision notes

Resistors connected in parallel

 

Resistors in parallel equation, downloadable AS & A Level Physics revision notes

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

Reciprocals, downloadable AS & A Level Physics revision notes

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

 

Worked example

Worked example - resistors in parallel, downloadable AS & A Level Physics revision notes

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

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