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Series and parallel circuits Why does adding a resistor in parallel lower the resistance?

Foundation and Higher · AQA · 45 minutes

Students predict what a second resistor does to the current, then measure it: three ammeters and two voltmeters in a series loop, then a parallel circuit with a switch on one branch. The rules come from their own readings. Slides to present, a vote that shows who's stuck, practice and homework.

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The idea in one minute

In a series circuit there is one path: the same current flows through every component, the supply's potential difference is shared between them, and the total resistance is the sum, R = R1 + R2. In a parallel circuit each branch has the full p.d. of the supply, the branch currents add up to the current from the supply, and the total resistance is less than the smallest branch: each new branch is another path, so the same p.d. drives more current.

Students first predict what a second resistor does to the current, in series and in parallel. Then they measure: a virtual series loop with three ammeters and a voltmeter across each resistor, then a parallel circuit with a switch on one branch, so closing it shows the current from the cell rising. The rules are said only once their readings show them, then used in calculations. It is a virtual experiment, not a substitute for the required practical.

By the end, students can

  • say how current and potential difference behave in series and in parallel, and show it from readings
  • work out the total resistance of resistors in series, and the current and each p.d. in a series circuit
  • find a branch current or the total current in a parallel circuit
  • explain why adding a resistor in series raises the total resistance and adding one in parallel lowers it

Key words

  • series, parallel
  • branch, junction
  • total resistance
  • shared potential difference
  • current (I, amps, A)
  • potential difference (V, volts, V)

Before this lesson

Builds on the lesson on current, p.d. and resistance: students should use V = I R and place an ammeter in series and a voltmeter in parallel.

Taught in Current, p.d. and resistance.

The lesson, step by step

45 minutes in total. The stretch is optional.

  1. 1 · Think4 min

    Add a second resistor

    A 6 V cell and one 10 Ω resistor: 0.6 A.

    Add a second 10 Ω resistor.

    In series, one after the other: the current?

    In parallel, side by side: the current?

    Predict both before we measure.

    Write here

    4 min 1 · Hook · students think · the slides say “Think”

    Add a second resistor

    Students predict what a second resistor does to the current, in series and in parallel.

    Say

    “A 6 V cell and one 10 Ω resistor: the current is 0.6 A. I add a second 10 Ω resistor. First in series, one after the other; then in parallel, side by side. Write down the current from the cell each time.”

    Ask
    • Does a second resistor always make it harder for the current?
    • In parallel, does each resistor still get 6 V?
    Watch for

    'More resistors, less current' said for both: keep the prediction for the parallel circuit.

    For the teacher

    Give a minute of silent thinking, then gather predictions for each: more, less or the same as 0.6 A, and by how much.

    Leave them unanswered: the readings will settle both.

    Collect predictions with Ask the class; don't settle them. The virtual circuits do.

    Shorter: Series prediction only; parallel is predicted at the practical (−2 min).

  2. 2 · Your turn12 min

    The virtual circuits

    Series: one path. Parallel: branches.

    Series: change the cell and R2; 3 readings.

    Compare A1, A2 and A3; add V1 and V2.

    Parallel: change the cell; open and close S1.

    Compare A1 with A2 + A3. What does S1 do to A1?

    Virtual experiments, not the required practical.

    Answer each question from your readings.

    12 min 2 · Your turn · students write

    Measure them: series, then parallel

    Two virtual circuits, series then parallel: students find the rules in their own readings, before anyone states them.

    Say

    “Series means one path; parallel means branches that split at a junction and join up again. Open the virtual circuits. Series first: change the cell and R2 and record three readings. Then parallel: try the switch open and closed. Answer each question from your own readings.”

    Ask
    • Series: what is V1 + V2 every time?
    • Parallel: what do A2 and A3 add up to?
    • What did closing S1 do to A1?
    Watch for

    Reading A1 as the current in each branch: A1 is the current from the cell.

    Virtual experiments: the circuits follow a model, and they are not the required practical. Record your readings first, then answer the questions about them.

    1. Virtual practical, series. R1 and R2 are in one loop with three ammeters, A1, A2 and A3; V1 is across R1 and V2 across R2. Change the cell's p.d. (B1) and R2, and record at least 3 readings, each at different settings.They set up a virtual circuit and record its meters' readings, each checked.
    2. Series: compare A1, A2 and A3 in each of your readings. What do they show?
      1. A1 is the biggest and A3 the smallest: each resistor uses some current up
      2. All three read the same: the current is the same all the way round
      3. A2 is the biggest: the current builds up between the resistors
      4. They add up to the current from the cell
    3. Set the cell to 12 V and R2 to 20 Ω. What does V2 read, in volts?
    4. Series: in each of your readings, what is V1 + V2?
      1. Less than the cell's p.d.: some is used up in the wires
      2. Twice the cell's p.d.: each resistor gets the cell's p.d.
      3. The cell's p.d.: the supply's p.d. is shared between the resistors
      4. It depends on R2: sometimes more than the cell's p.d.
    5. At 12 V with R2 = 20 Ω, the current is 0.40 A. Use total resistance = p.d. of the cell ÷ current. What is the total resistance, in ohms?
    6. Virtual practical, parallel. R1 and R2 are in two branches; A1 measures the current from the cell, A2 the current in R1's branch and A3 in R2's. Change the cell's p.d. (B1) and click the switch S1 to open and close R2's branch. Record at least 3 readings, each at different settings, with S1 open in at least one.They set up a virtual circuit and record its meters' readings, each checked.
    7. Parallel, with S1 closed: how does A1 compare with A2 and A3?
      1. A1 = A2 + A3: the branch currents add up to the current from the cell
      2. A1, A2 and A3 all read the same, as in series
      3. A2 and A3 are each half of A1: the current splits equally
      4. A1 is less than A2 + A3: some current is used up in the branches
    8. Parallel: set the cell to 6 V with S1 closed. What does A1 read, in amps?
    9. Use that reading: total resistance = 6 V ÷ the current from the cell. What is the total resistance of the two branches, in ohms?
    10. Closing S1 adds R2 in parallel with R1. From your readings, what happens to the current from the cell (A1), and so to the total resistance?
      1. A1 goes up, and the total resistance goes up too
      2. A1 goes down, so the total resistance goes up: more resistors, more resistance
      3. A1 stays the same; A2 goes down to make room for A3
      4. A1 goes up, so the total resistance goes down
    For the teacher

    The series circuit: a cell B1 (2 to 12 V), A1, R1 (10 Ω), A2, R2 (10, 20 or 30 Ω), A3 in one loop, with V1 across R1 and V2 across R2. Three readings at different settings, each checked against the circuit. The questions: what the three ammeters show, V2 at one setting, what V1 + V2 comes to, and the total resistance from a reading.

    The parallel circuit: a cell B1 (3 to 12 V) with A1 beside it; branch 1 is A2 and R1 (10 Ω) with V1 across R1; branch 2 is A3, R2 (15 Ω) and the switch S1, with V2 across R2. With S1 open no current flows in R2, so V2 reads 0 V. The questions: A1 against A2 and A3, the current and total resistance at 6 V, and what closing S1 does.

    Say plainly that this is a virtual experiment, not the required practical: real meters, wires and cells have some resistance, so real readings are close to these, not equal.

    Don't give the rules yet: the readings say them. Once most have their parallel readings, go back to the hook's predictions and ask who would change theirs, and why. Then the rules.

  3. 3 · Watch10 min

    Series: one path

    Drawn: a cell, then R1 and R2.

    The same current through each.

    The p.d. is shared: V = V1 + V2

    Total resistance: R = R1 + R2

    9 V; 5 Ω and 10 Ω: R = 15 Ω

    I = 0.6 A; V1 = 3 V, V2 = 6 V

    One path: each resistor adds to the total.

    3 · Watch

    Parallel: branches

    Drawn: a cell; R1, R2 side by side.

    Each branch: the full supply p.d.

    Branch currents add: I = I1 + I2

    12 V: 30 Ω takes 0.4 A, 60 Ω 0.2 A

    From the cell: 0.4 + 0.2 = 0.6 A

    R = 12 ÷ 0.6 = 20 Ω: under 30 Ω

    Less than the smallest branch.

    3 · Watch

    Why parallel lowers R

    Along: the second resistor, in Ω.

    Up: the total resistance, in Ω.

    Series, the line: always above 10.

    Parallel, the curve: always below.

    A new branch is a new path:

    the same p.d. drives more current.

    Why can't the curve pass 10 Ω?

    3 · Watch

    The rules side by side

    Current: series, the same; parallel, branches add up.

    P.d.: series, shared; parallel, the same on each branch.

    Resistance: series, R1 + R2; parallel, less than either.

    Both: current is never used up.

    Series: one path. Parallel: branches.

    10 min 3 · Explain · you explain · the slides say “Watch”

    The rules, from the readings

    The rules for current, p.d. and total resistance in each, named from the readings, and why parallel lowers the total.

    Say

    “Your readings showed the rules. Series: one path, so one current through everything, and the p.d. shared. Parallel: each branch across the cell, so each has its full p.d., and the branch currents add up.”

    Ask
    • In series, what was the same on every meter: current or p.d.?
    • In parallel, what did each branch get from the cell?
    • Closing S1 added a branch: more current from the cell, or less?
    Watch for

    Swapping the rules: 'p.d. is the same in series'. Ask which one has a single path.

    Series: total resistance, current, each p.d.

    9 V cell, 5 Ω and 10 Ω in series

    R = 5 + 10 = 15 Ω, so I = 9 ÷ 15 = 0.6 A

    V1 = 0.6 × 5 = 3 V, V2 = 0.6 × 10 = 6 V: 3 + 6 = 9 V

    Parallel: branch currents and the total

    12 V cell, 30 Ω and 60 Ω in parallel

    Each branch has 12 V: 12 ÷ 30 = 0.4 A and 12 ÷ 60 = 0.2 A

    From the cell: 0.4 + 0.2 = 0.6 A, so R = 12 ÷ 0.6 = 20 Ω

    For the teacher

    Series (the readings: three equal ammeters, V1 + V2 the cell's p.d.): one path, so the same current flows through each component. The supply p.d. is shared: V = V1 + V2. Total resistance R = R1 + R2: the charge goes through both, so adding a resistor in series always raises the total.

    Parallel: each branch is connected across the supply, so each has the same p.d. as the supply. The current splits at a junction: the branch currents add up to the current from the supply, I = I1 + I2, and the smaller resistance takes the bigger current.

    Why parallel lowers the total: a new branch is another path. The p.d. across the first branch doesn't change, so its current doesn't either; the new branch adds its own current. More current from the same p.d. means less resistance: the total is less than the smallest branch.

    AQA GCSE asks for the reason, not a calculation of the parallel total; R = V ÷ I from the readings shows it.

    The graph slide: the line is the total in series, the curve the total in parallel, as the second resistor changes. Ask why the curve never gets above 10 Ω.

    Shorter: Leave out the graph slide; one worked example (−4 min).

  4. 4 · Your turn5 min

    Worked, then yours

    I do: 12 V, 4 Ω and 8 Ω in series.

    R = 12 Ω, I = 1 A; V1 = 4 V, V2 = 8 V

    You do: 9 V, 10 Ω and 20 Ω in series. I?

    I do: 1.2 A from the cell; one branch 0.8 A.

    The other branch: 1.2 − 0.8 = 0.4 A

    You do: 2.0 A from the cell; one branch 1.5 A. Other?

    Series or parallel? Then the rule.

    Write here

    Its answers' slide comes with your copy.

    5 min 4 · Your turn · students write

    Worked, then yours

    Worked examples, series and parallel, each beside the twin students solve.

    Say

    “Say first whether it is series or parallel, then which rule. I do one; you do its twin straight after.”

    Ask
    • Series or parallel? How can you tell?
    • Which rule did you use, and why that one?
    Watch for

    Using a series rule on a parallel circuit: ask whether the current has one path or several.

    Series

    I do: 12 V cell, 4 Ω and 8 Ω in series

    R = 12 Ω, I = 12 ÷ 12 = 1 A; V1 = 4 V, V2 = 8 V

    Then theirs

    You do: 9 V cell, 10 Ω and 20 Ω in series. I?

    Parallel

    I do: 1.2 A from the cell; one branch 0.8 A

    Other branch: 1.2 − 0.8 = 0.4 A

    Then theirs

    You do: 2.0 A from the cell; one branch 1.5 A. Other?

    For the teacher

    Each worked example aloud, its twin straight after. Students write the rule they use before the numbers.

    Each worked example aloud, its twin straight after; open the answers slide when most have finished the twins.

    Shorter: No worked examples: go straight to the vote (−5 min).

  5. 5 · Vote and practise9 min

    Vote first

    A 6 V cell: 10 Ω and 30 Ω in parallel.

    The 10 Ω branch carries 0.6 A.

    What is the current in the 30 Ω branch?

    A: 1.8 A

    B: 0.6 A

    C: 0.2 A

    D: 0.15 A

    Choose on your own, then say why.

    5 · Vote and practise

    Practise: series or parallel?

    1. 5 Ω and 15 Ω in series. Total, in Ω?

    2. 9.0 V, two in series; one has 3.5 V. The other?

    3. Parallel: 0.9 A from the cell, one branch 0.5 A.

    4. 12 V, 8 Ω and 16 Ω in series. Current, in A?

    5. In 4, the p.d. across the 16 Ω, in V?

    Stuck on 3? The branches add up.

    Write here

    5 · Vote and practise

    Reason it out

    6. 20 Ω and 30 Ω in parallel: the total is …?

    7. Sort the rules: series, parallel or both.

    8. 6.0 V; 10 Ω and R in series; 0.20 A. R?

    Stretch: 12 V; 20 Ω and R in parallel; 1.0 A.

    What is R?

    8: the total resistance first.

    Write here

    9 min 5 · Who's stuck? · students vote · the slides say “Vote and practise”

    Vote, then practise

    One question shows who's stuck; then practice in levels.

    Say

    “Choose an answer on your own. Nobody talks until everyone has chosen.”

    Ask
    • What is the p.d. across each branch?
    • Which branch should take the bigger current, and why?
    Watch for

    Who checks first whether the circuit is series or parallel before choosing a rule.

    Show your working on paper: say first whether it is series or parallel, then which rule you use. The stretch is optional.

    The question that shows who's stuck

    1. A 6 V cell has two branches in parallel: a 10 Ω resistor and a 30 Ω resistor. The current in the 10 Ω branch is 0.6 A. What is the current in the 30 Ω branch?
      1. 1.8 A
      2. 0.6 A
      3. 0.2 A
      4. 0.15 A
    In your Classroom, as they answer (an example)
    • A4
    • B8
    • C9
    • D5

    Each wrong answer is a different mistake. While they answer, your Classroom shows who chose which, so you know in seconds whom to help with what.

    1. A 5 Ω resistor and a 15 Ω resistor are in series. What is their total resistance, in ohms?
    2. A 9.0 V battery is connected to two resistors in series. The p.d. across one is 3.5 V. What is the p.d. across the other, in volts?
    3. In a parallel circuit, the current from the cell is 0.9 A. One branch carries 0.5 A. What current is in the other branch, in amps?
    4. A 12 V supply is connected to an 8 Ω resistor and a 16 Ω resistor in series. What is the current, in amps?
    5. In question 4, what is the p.d. across the 16 Ω resistor, in volts?
    6. A 20 Ω resistor and a 30 Ω resistor are connected in parallel. Their total resistance is:
      1. 50 Ω
      2. less than 20 Ω
      3. between 20 Ω and 30 Ω
      4. 25 Ω, the average
    7. Sort each statement: is it always true of series circuits, of parallel circuits, or of both?They sort 7 items into Series and Parallel and Both.
    8. A 6.0 V cell is connected in series with a 10 Ω resistor and a resistor R. The current is 0.20 A. What is the resistance of R, in ohms?
    9. Stretch: a 12 V cell has a 20 Ω resistor and a resistor R in parallel. The current from the cell is 1.0 A. What is the resistance of R, in ohms?

    Support · For question 3: the branch currents add up to the current from the cell. Take the branch you know away from the total.

    For the teacher

    Everyone chooses before anyone explains. Ask for a reason for each option, then settle it together: what is the p.d. across each branch, and so its current?

    Questions 1–2 are series fluency; 3–5 change the look; 6–7 are reasons and sorting the rules; 8 is exam-style; the stretch is a parallel circuit worked backwards.

    Students show their working on paper or the board; the quiz keeps their final answers.

    If many chose the same wrong option, ask a student who chose it to explain, then work out the p.d. across each branch together before they practise.

    Shorter: After the vote, questions 1–5 only (−4 min).

    Longer: The exam-style question and the stretch, gone through together (+10 min).

  6. 6 · Show what you know5 min

    Show what you know

    1. 6.0 V, 4 Ω and 8 Ω in series. Current?

    2. Why does adding a resistor in parallel

    make the total resistance smaller?

    Say what happens to the current from the cell.

    Two or three sentences for question 2.

    Write here

    5 min 6 · Exit · students show · the slides say “Show what you know”

    Show what you know

    A series calculation and an explanation of why parallel lowers the resistance.

    Say

    “Answer the two exit questions on your own: one calculation, then two or three sentences.”

    Watch for

    Explanations that say only 'more paths': ask what happens to the current from the cell, and so to V ÷ I.

    One calculation, then two or three sentences.

    1. A 6.0 V cell is connected to a 4 Ω resistor and an 8 Ω resistor in series. What is the current, in amps?
    2. Explain, using what happens to the current from the cell, why adding a resistor in parallel makes the total resistance of a circuit smaller.
    For the teacher

    A series calculation (total resistance, then current), then why adding a resistor in parallel makes the total resistance smaller, using current.

    The explanations show who can give the reason, not just the rule: start the next lesson with two of them. Set the homework.

    Longer: Why are the lights in a house wired in parallel? (+5 min).

One to one: before each new setting in the virtual circuits, ask the student to predict every meter. When a prediction is wrong, ask which rule the reading shows, and write the rule in their words.

Homework: the rules in use

Say first whether each circuit is series or parallel, and which rule you use. Show the equation, the numbers and the answer with its unit.

  1. A 3 Ω, a 5 Ω and a 12 Ω resistor are in series. What is their total resistance?
  2. A 12 V battery is connected to a 20 Ω and a 40 Ω resistor in series. Find the current, and the p.d. across each resistor.
  3. A 6.0 V cell is connected to a 12 Ω resistor and a 6 Ω resistor in parallel. Find the current in each branch and the current from the cell.
  4. Use your answer to question 3 to find the total resistance of the two branches. Compare it with each resistor on its own.
  5. Explain why the lights in a house are wired in parallel, not in series. Give two reasons.
  6. A student says the current always splits equally between two parallel branches. A 10 Ω and a 40 Ω resistor are in parallel across 8.0 V. Find both branch currents to show whether she is right.

Print the worksheet with working space and homework. Teacher answers come with your Library copy.

Teaching series and parallel circuits: common questions

Do students need to calculate resistors in parallel for AQA GCSE?

No. AQA GCSE Physics asks students to explain why adding a resistor in parallel lowers the total resistance, and to know the total is less than the smallest branch, but not to calculate it with a formula. This lesson finds the total from readings (V ÷ I) instead, which also shows why.

Can the virtual circuits replace the required practical?

No. They follow an exact model (ammeters and wires with no resistance, voltmeters that take no current, resistors that never warm up), which suits seeing the rules clearly. Students must still build real circuits for the required practical on resistance, where readings are close to the rules rather than equal.

Why does adding a branch not take current away from the other branches?

Because the cell keeps the p.d. across each branch the same (in this model, with no internal resistance). The first branch has the same p.d. and resistance as before, so the same current; the new branch adds its own. Students who think the cell gives a fixed current expect the current to be shared out: the switch in the parallel circuit tests exactly that.

Is this lesson for Foundation or Higher?

Both: none of AQA's 4.2.2 is Higher only. Foundation students can stop at the standard questions; the exam-style question and the stretch, working a circuit backwards, suit Higher.

Can I use the lesson without creating an account?

Yes. Read the lesson, print the worksheet and open its slides without signing in. A free teacher account keeps the whole lesson in your Library to change and teach, with the virtual circuits, the quizzes, the answers and the answer slides.

Curriculum reference: AQA GCSE Physics 8463: 4.2.2 (series and parallel circuits: current, potential difference and total resistance in each, and why adding resistors raises or lowers the total), using 4.2.1.3 (V = I R). Links to required practical 3 (combinations of resistors in series and parallel).

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