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Physics · Electricity

Series and parallel circuits

Describe and calculate current, potential difference and resistance in series and parallel circuits.

  • 6 key terms
  • All boards
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Warm-up

Answer each one, then check.

  1. 1

    What is the same everywhere in a series loop?

    Show answerHide answer

    The current

  2. 2

    What does an ammeter measure?

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    Current

  3. 3

    How is a voltmeter connected?

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    In parallel

  4. 4

    What is the equation linking V, I and R?

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    \(V = IR\)

  5. 5

    Add \(4 + 8\).

    Show answerHide answer

    12

Learning Objectives

  1. 1Describe the differences between series and parallel circuits.
  2. 2Use \(R_{total} = R_1 + R_2\) for resistors in series.
  3. 3Calculate currents, pds and resistances in series circuits.
  4. 4Explain why adding resistors in series increases and in parallel decreases the total resistance.

SERIES AND PARALLEL

Series: same current, pd shared, \(R_{total} = R_1 + R_2\). Parallel: same pd, currents add, \(R_{total}\) is less than the smallest resistor.

You are not required to calculate the total resistance of two resistors in parallel.

Series or Parallel?

Series

  • One loop for the current.
  • The same current through each component.
  • The supply pd is shared between components.
  • Total resistance = R1 + R2.

Parallel

  • More than one loop.
  • The same pd across each branch.
  • The currents in the branches add to the total current.
  • Total resistance is less than the smallest resistor.

Series Circuit

A 12 V battery is connected in series with resistors of 4.0 Ω and 8.0 Ω. Calculate the current and the pd across each resistor.

Show the solutionHide the solution
  1. 1 Total resistance \(R = 4.0 + 8.0 = 12\ \Omega\)
  2. 2 Current \(I = V \div R = 12 \div 12 = 1.0\) A
  3. 3 Pd across 4.0 Ω \(V = IR = 1.0 \times 4.0 = 4.0\) V
  4. 4 Pd across 8.0 Ω \(V = 1.0 \times 8.0 = 8.0\) V
  5. 5 Check \(4.0 + 8.0 = 12\) V

AnswerCurrent 1.0 A; pds 4.0 V and 8.0 V.

Parallel Circuit

Two lamps are connected in parallel to a 6.0 V supply. A1 reads 1.2 A and A2 reads 0.80 A. What does A3 in the main wire read?

Show the solutionHide the solution
  1. 1 Currents in the branches add \(I_{total} = 1.2 + 0.80\)
  2. 2 Answer \(I_{total} = 2.0\) A

Answer2.0 A; each lamp has 6.0 V across it.

Why Resistance Changes

Explain it in words.

  • In series

    The current has to pass through each resistor one after another, so the total opposition is greater.

  • In parallel

    There are more paths for the current, so more charge can flow: the total resistance is less than any single resistor.

  • Uses of series circuits

    Measurement and testing, for example a circuit with a thermistor and an ammeter.

  • Uses of parallel circuits

    House lighting: each lamp has the full supply pd and can be switched on separately.

Circuit Puzzle

A 9.0 V cell is connected to two resistors in series, 6.0 Ω and 12 Ω. (a) Find the total resistance. (b) Find the current. (c) Find the pd across the 12 Ω resistor.

1. Add the resistances.

2. Find I, then V across each.

A good answer shows: (a) 18 Ω (b) \(9.0 \div 18 = 0.50\) A (c) \(0.50 \times 12 = 6.0\) V

Can I...?

  1. 1Describe series and parallel circuits.
  2. 2Add resistors in series.
  3. 3Find the current in a series circuit.
  4. 4Find the pd across each resistor.
  5. 5Add branch currents in parallel.
  6. 6State that pd is the same across parallel branches.
  7. 7Explain why total resistance changes.
  8. 8Draw a circuit diagram.

Summary & Exam Focus

  • Series: \(R_{total} = R_1 + R_2\), same current, shared pd.
  • Parallel: same pd, currents add, total resistance less than the smallest.
  • Ammeters in series, voltmeters in parallel.
  • Household circuits use parallel wiring.

Exam focus

A 12 V battery is connected in series to resistors of 4.0 Ω and 8.0 Ω. Calculate the current. (3 marks) (3 marks)

Add the resistances first, then use V = IR.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Series
Components connected one after another in a single loop.
Parallel
Components connected on separate branches.
Equivalent resistance
The single resistance that could replace the combination.
Branch
One of the paths in a parallel circuit.
Total resistance
The resistance of the whole circuit.
Shared pd
The supply pd divides between series components.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Calculate 3 marks

    The diagram shows a 12 V battery connected to two resistors in series. Calculate (a) the total resistance and (b) the current in the circuit.

    A 12 V battery connected in series with a 4.0 ohm and an 8.0 ohm resistor and an ammeter.
    Show answerHide answer

    Model answer

    (a) \(R = 4.0 + 8.0 = 12\ \Omega\). (b) \(I = 12 \div 12 = 1.0\) A

    Mark scheme

    • Adds resistances — 1 mark
    • 12 Ω — 1 mark
    • 1.0 A — 1 mark
  2. Question 2 Calculate 3 marks

    Use your answer to the previous question to calculate the potential difference across the 8.0 Ω resistor. The current is 1.0 A.

    Show answerHide answer

    Model answer

    \(V = IR = 1.0 \times 8.0 = 8.0\) V

    Mark scheme

    • Correct equation — 1 mark
    • Correct substitution — 1 mark
    • 8.0 V — 1 mark
  3. Question 3 Use the diagram 3 marks

    The diagram shows two lamps connected in parallel to a 6.0 V supply. Ammeter A1 reads 1.2 A and A2 reads 0.80 A. (a) Calculate the reading on A3. (b) State the pd across each lamp.

    Two lamps in parallel from a 6 V battery, with ammeters A1 reading 1.2 A, A2 reading 0.80 A and A3 in the main wire.
    Show answerHide answer

    Model answer

    (a) 1.2 + 0.80 = 2.0 A. (b) 6.0 V across each lamp.

    Mark scheme

    • Adds the branch currents — 1 mark
    • 2.0 A — 1 mark
    • 6.0 V — 1 mark
  4. Question 4 Explain 2 marks

    Explain why the lights in a house are connected in parallel rather than in series.

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    Model answer

    In parallel each lamp has the full supply potential difference across it, and each lamp can be switched on and off independently of the others.

    Mark scheme

    • Each lamp gets the full supply pd — 1 mark
    • Lamps can be switched independently or one failing does not stop the others — 1 mark
  5. Question 5 Explain 3 marks

    Explain, in terms of the flow of current, why adding a second resistor in series increases the total resistance but adding a second resistor in parallel decreases the total resistance.

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    Model answer

    In series the current must pass through both resistors so the opposition is greater. In parallel there are two paths, so more current can flow for the same potential difference, so the total resistance is less.

    Mark scheme

    • Series: current passes through both, so resistance is greater — 1 mark
    • Parallel: two paths — 1 mark
    • More current for the same pd, so total resistance is less — 1 mark
  6. Question 6 Calculate 4 marks

    A 9.0 V cell is connected to a 6.0 Ω resistor and a 12 Ω resistor in series. Calculate the potential difference across the 12 Ω resistor.

    Show answerHide answer

    Model answer

    \(R = 18\ \Omega\); \(I = 9.0 \div 18 = 0.50\) A; \(V = 0.50 \times 12 = 6.0\) V

    Mark scheme

    • Total resistance 18 Ω — 1 mark
    • Current 0.50 A — 1 mark
    • Correct substitution — 1 mark
    • 6.0 V — 1 mark

Quick check

  1. In a series circuit the total resistance is...

    1. Athe sum of the resistances
    2. Bthe smallest resistance
    3. Cthe average
    4. Dzero
    Show answerHide answer

    A: the sum of the resistances

    \(R_{total} = R_1 + R_2\).

  2. In a parallel circuit, the pd across each branch is...

    1. Ashared
    2. Bthe same
    3. Czero
    4. Dalways different
    Show answerHide answer

    B: the same

    Each branch is connected directly to the supply.

  3. Two branches carry 0.5 A and 0.3 A. The main current is...

    1. A0.2 A
    2. B0.15 A
    3. C0.8 A
    4. D1.5 A
    Show answerHide answer

    C: 0.8 A

    Branch currents add.

  4. Resistors of 5 Ω and 10 Ω in series give...

    1. A3.3 Ω
    2. B5 Ω
    3. C50 Ω
    4. D15 Ω
    Show answerHide answer

    D: 15 Ω

    Add the resistances.

  5. Adding a resistor in parallel...

    1. Adecreases the total resistance
    2. Bincreases the total resistance
    3. Cdoes not change it
    4. Dstops the current
    Show answerHide answer

    A: decreases the total resistance

    There are more paths for the current.

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