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ASPhysicsCIERevision Notes10. D.C. Circuits10.2 Kirchhoff’s LawsResistors in Parallel

Resistors in Parallel (CIE AS Physics)

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Ashika

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Ashika

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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 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:

10-1-2-5-derivation-of-resistors-in-parallel-1

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

Resistors in parallel

  • When two or components are connected in parallel:

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

Resistors in parallel

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

Resistors connected in parallel have the same voltage

 

  • The equation for the combined resistance, R  of resistors in parallel is:

1 over R space equals space 1 over R subscript 1 space plus thin space 1 over R subscript 2 space plus thin space 1 over R subscript 3...

  • 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 fraction numerator 1 over denominator v a l u e end fraction
  • For example, the reciprocal of a whole number such as 2 equals 1 half
    • The reciprocal of 1 half is 2

  • If the number is already a fraction, the numerator and denominator are ‘flipped’ round

Reciprocals

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 over R. To get the value of R from 1 over R, you must calculate fraction numerator 1 over denominator y o u r space a n s w e r end fraction
  • You can also use the reciprocal button on your calculator (labelled either x-1 or 1 over x, depending on your calculator

 

Worked example

The circuit below shows 3 resistors connected in parallel. 

Which value gives the combined resistance of all the resistors in this circuit?

A. fraction numerator 5 R over denominator 2 end fraction      B. fraction numerator 2 over denominator 5 R end fraction     C. fraction numerator 5 over denominator 2 R end fraction      D. fraction numerator 2 R over denominator 5 end fraction

10-2-4-we-resistors-in-parallel--cie-new

Answer: D

Step 1: Resistors in parallel equation

1 over R space equals fraction numerator space 1 over denominator R subscript 1 end fraction space plus thin space 1 over R subscript 2 space plus thin space.... space equals space 1 over R subscript 1 space plus thin space 1 over R subscript 2 space plus thin space 1 over R subscript 3

Step 2: Substitute in the values given from the equation

1 over R subscript T space equals fraction numerator space 1 over denominator R end fraction space plus thin space fraction numerator 1 over denominator 2 R end fraction space plus fraction numerator space 1 over denominator R end fraction space equals space open parentheses 1 space plus thin space 1 half space plus thin space 1 close parentheses space 1 over R space equals space fraction numerator 5 over denominator 2 R end fraction

Step 3: Calculate the total resistance

1 over R subscript T space equals fraction numerator space 5 over denominator 2 R end fraction

R subscript T space equals fraction numerator space 2 R over denominator 5 end fraction

Examiner Tip

The most common mistake is to leave the answer as 1/RT. Remember to calculate fraction numerator 1 over denominator a n s w e r end fraction to get the value of RT.

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    Ashika

    Author: Ashika

    Expertise: Physics Project Lead

    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.