Resistance in Series & Parallel (Edexcel A Level Physics)

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Deriving Equations for Resistance 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 in series diagram, downloadable AS & A Level Physics revision notes

Resistors connected in series

  • The equation for combined resistors in series is derived using the electric current rule and the electrical voltages rule
  • These rules describe that for a series circuit:
    • The current is the same through all resistors
    • The potential difference is  split between all the resistors

3-6-derivation-resistors-in-series_edexcel-a-level-physics-rn

  • The equation for the combined resistance of resistors in series is therefore: 

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

Resistors In Parallel

  • In a parallel circuit, the combined resistance of the components requires the use of reciprocals
    • The reciprocal of the combined resistance of two or more resistors 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

  • The equation for combined resistors in parallel is derived using the electric current rule and the electrical voltages rule
  • These rules describe that for a parallel circuit:
    • The current is the split at the junction (and therefore between resistors)
    • The potential difference is the same across all resistors

3-6-derivation-resistors-in-parallel-edexcel-a-level-physics-rn

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

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

  • This means the combined resistance decreases
    • The combined resistance 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

Using Equations for Resistance in Series & Parallel

Series Circuits

Worked example

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

Wich of the following is the value of R2?

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

WE - Resistors in series answer image, downloadable AS & A Level Physics revision notes

Parallel Circuits

Worked example

WE - Resistors in parallel question image, downloadable AS & A Level Physics revision notes

WE - Resistors in parallel answer image, downloadable AS & A Level Physics revision notes

Examiner Tip

The most common mistake is to forget to find the correct value for RT in parallel. Remember to do 1 over answer to get the correct value.

Reciprocals can be considered in the following way:

  • The reciprocal of a value is 1 over value 
    • 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, downloadable AS & A Level Physics revision notes

The reciprocal of a number is 1 ÷ number

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

 

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Joanna

Author: Joanna

Expertise: Physics

Joanna obtained her undergraduate degree in Natural Sciences from Cambridge University and completed her MSc in Education at Loughborough University. After a decade of teaching and leading the physics department in a high-performing academic school, Joanna now mentors new teachers and is currently studying part-time for her PhD at Leicester University. Her passions are helping students and learning about cool physics, so creating brilliant resources to help with exam preparation is her dream job!