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IBPhysicsSLRevision NotesThe Particulate Nature of MatterCurrent & CircuitsSeries & Parallel Circuits

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Series & Parallel Circuits (SL IB Physics)

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Series & Parallel Circuits

Resistors in Series

  • In a series circuit:
    • The current is the same at any point
    • The potential difference is split across all components depending on their resistance
  • When two or more components are connected in series:

The combined resistance of the components is equal to the sum of individual resistances

  • Three resistors connected in series will have a total resistance of R = R1 + R2 + R3

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

Resistors in series

  • The equation for the total resistance of resistors in series is derived using the above rules for current and potential difference:

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

  • This means the total resistance increases
    • The combined resistance is more than the resistance of any of the individual components
    • For example, if two resistors of equal resistance are connected in series, then the combined resistance will double

5-2-2-resistors-in-series_sl-physics-rn

Connecting more resistors in series increases the overall resistance

Resistors in Parallel

  • In a parallel circuit:
    • The total current is equal to the sum of the currents in each parallel branch of the circuit
    • The potential difference is the same across each loop
  • 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

  • Two resistors connected in parallel will have a total resistance of 1 over R space equals space 1 over R subscript 1 space plus space 1 over R subscript 2

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

Resistors in parallel

  • The equation for the total resistance of resistors in parallel is derived using the above rules for current and potential difference:

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 total 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

  5-2-2-resistors-in-parallel_sl-physics-rn

Connecting more resistors in parallel decreases the overall resistance

Summary of the rules in series and parallel circuits

  • The table below summarises the rules for calculating current, potential difference and resistance within series and parallel circuits

Series and Parallel Circuits Summary

2-5-8-series-and-parallel-circuits-summary-table

Worked example

For the circuit below, state the readings of ammeters A1, A2  and A3.

WE - Kirchoff's first law question image, downloadable AS & A Level Physics revision notes

Answer:

Step 1: Recall the rules for current in series & parallel

  • In a series circuit:  The current is the same at any point I subscript i n end subscript space equals space I subscript 1 space equals space I subscript 2 space equals space I subscript 3
  • In a parallel circuit:   The total current is equal to the sum of the currents in each parallel branch of the circuit I subscript i n end subscript space equals space I subscript 1 space plus space I subscript 2 space plus space I subscript 3

Step 2: Determine the current in ammeter A1

  • Ammeter A1 is in series with ammeter A
  • Therefore, the current in A1 = the current in A

A1 = 0.270 A

Step 3: Determine the current in ammeter A3

  • The current from ammeter A1 enters splits into two branches
  • One branch has a current of 80 mA = 0.080 A
  • The current in the other branch is the reading of ammeter A3

0.270 = 0.080 + A3

A3 = (0.270 – 0.080) = 0.190 A

Step 4: Determine the current in ammeter A2

  • The current of 0.080 A splits into two branches
  • One branch has a current of 27 mA = 0.027 A
  • The current in the other branch is the reading of ammeter A2

0.080 = 0.027 + A2

A2 = (0.080 – 0.027) A = 0.053 A

  • The current readings of the three ammeters are:
    • A1 = 0.270 A = 270 mA
    • A2 = 0.053 A = 53 mA
    • A3 = 0.19 A = 190 mA

Worked example

For the circuit below, state the readings of the voltmeters V1, V2  and V3.

All the lamps and resistors have the same resistance.

series-and-parallel-resistors

Answer:

Step 1: Recall the rules for p.d. in series & parallel

  • In a series circuit:  The potential difference is split across all components (equally if the resistance is equal) V subscript i n end subscript space equals space V subscript 1 space plus space V subscript 2 space plus space V subscript 3
  • In a parallel circuit:  The potential difference is the same across each loop V subscript i n end subscript space equals space V subscript 1 space equals space V subscript 2 space equals space V subscript 3

Step 2: Determine the p.d. in voltmeter V1

  • The potential difference provided by the cell is the total input p.d., so, each loop must sum to 24 V
  • The first loop consists of the 2 V lightbulb, the 12 V lightbulb and resistor V1

2 + 12 + V1 = 24 V

V1 = 24 – 2 – 12 = 10 V

Step 3: Determine the p.d. in voltmeter V2

  • The second loop consists of the 2 V lightbulb, the 8 V resistor, lightbulb V2, and the 8 V lightbulb

2 + 8 + V2 + 8 = 24 V

V2 = 24 – 2 – 8 – 8 = 6 V

Step 3: Determine the p.d. in voltmeter V3

  • The third loop consists of the 2 V lightbulb and resistor V3

2 + V3 = 24 V

V3 = 24 – 2 = 22 V

  • The potential difference readings of the three voltmeters are:
    • V1 = 10 V
    • V2 = 6 V
    • V3 = 22 V

Examiner Tip

The equations for current, potential difference and resistance in series and parallel circuits is given in your data booklet. However, it is much quicker if you remember them!

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    Ashika

    Author: Ashika

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    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.