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I–V characteristics Why does a filament lamp's I–V graph curve when a resistor's is a straight line?

Foundation and Higher · AQA · 45 minutes

Students slide a resistor's straight line over a filament lamp's curve and find where the two have the same resistance, then take readings in a virtual lamp experiment and work out how its resistance rises. Diodes, thermistors and LDRs follow from their graphs. Slides to present, a vote that shows who's stuck, practice and homework.

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The curve is a filament lamp; the straight line is a resistor of r ohms (across: p.d. in volts, up: current in amps). Move r. Where the line crosses the curve, what is the same for the lamp and the resistor?

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They cross at (0, 0) and (4.24, 0.24)

The idea in one minute

An I–V graph shows the current I through a component at each potential difference V across it. A resistor at a constant temperature gives a straight line through the origin: I is directly proportional to V and its resistance stays the same (it is ohmic). A filament lamp's graph curves: the current heats the filament, and a hotter filament has more resistance, so each extra volt adds less current. A diode lets current through in one direction only. A thermistor's resistance falls as it gets hotter, and an LDR's falls in brighter light, which is why they are used to sense temperature and light. At any point, the resistance is R = V ÷ I, never the gradient of the curve.

The lesson starts with a picture: a resistor's straight line laid over a lamp's curve, moved until they cross, before anyone explains. Students then take their own readings in a virtual experiment (it follows a stated model of a lamp, and is not the required practical or a substitute for it), work out the lamp's resistance at a low and a high p.d., and read the diode, thermistor and LDR from their graphs. It is for Foundation and Higher; the stretch is a temperature-sensing circuit.

By the end, students can

  • sketch and explain the I–V graphs of a resistor, a filament lamp and a diode
  • work out a resistance at a point as R = V ÷ I, not from the gradient
  • explain why a filament lamp's resistance rises as the current heats it
  • say how a thermistor's and an LDR's resistance change, and where they are used

Key words

  • potential difference (p.d.)
  • current
  • resistance
  • I–V characteristic
  • ohmic conductor
  • filament lamp
  • diode
  • thermistor
  • light-dependent resistor (LDR)

Before this lesson

Students should use V = I × R and know how an ammeter and a voltmeter are connected (the lesson on current, potential difference and resistance).

Taught in Current, p.d. and resistance.

The lesson, step by step

60 minutes in total. Each step says what changes for this length.

  1. 1 · Think5 min

    Where do they cross?

    Curve: a filament lamp

    Line: a resistor of r ohms

    x: p.d. V (volts)

    y: current I (amps)

    At the crossing, what is the

    same for lamp and resistor?

    Say what is the same. Then move r.

    Write here

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

    Where do they cross?

    A resistor's straight line moves over a lamp's curve: where they cross, the two have the same V and I, so the same resistance.

    Say

    “The curve is a filament lamp. The straight line is a resistor of r ohms. Where they cross, what is the same for both of them?”

    Ask
    • At the crossing, what is the p.d. across each? The current through each?
    • So what is the lamp's resistance there?
    • As r gets bigger, where does the crossing move? What does that say about the lamp?
    Watch for

    Saying the crossing is where the lamp works best, or where the current is greatest: keep the answer, and ask what V and I are there.

    For the teacher

    Give a minute of silent thinking. Read the axes together first: across is the p.d. in volts, up is the current in amps.

    Move r. At each crossing the lamp and the resistor have the same V and the same I, so the lamp's resistance there is r. At r = 12 they meet only at the origin; at r = 20 the crossing is near 5 V; at r = 32 it is past 10 V.

    Don't explain why yet. The point to keep: the lamp's resistance gets bigger as the p.d. rises. Why is the next step.

    Take a vote with Ask the class: as the p.d. rises, does the lamp's resistance go up, down or stay the same? Then move r from 12 to 32 and read the crossings.

    Shorter: Vote once; move r to three values only (−2 min).

  2. 2 · Watch12 min

    A resistor: a straight line

    x: V (volts), y: I (amps)

    Through the origin: I ∝ V

    4.0 V, 0.20 A: R = 4.0 ÷ 0.20 = 20 Ω

    10 V, 0.50 A: still 20 Ω

    Ohmic, at a constant temperature

    Resistance: R = V ÷ I at the point

    2 · Watch

    A filament lamp: a curve

    More current heats the filament

    Hotter metal: more resistance

    1 V, 0.080 A: R = 12.5 Ω

    12 V, 0.333 A: R = 36 Ω

    I still rises, less for each volt

    Straight line: 12 Ω, the cold lamp

    V ÷ I at the point, never the gradient

    2 · Watch

    Turn the battery round

    Negative p.d.: current the other way

    Resistor: the line carries on

    Lamp: the same curve, turned round

    Both work the same either way

    Predict: what will a diode do?

    2 · Watch

    A diode: one way only

    x: V (volts), y: I (milliamps)

    Reverse: almost no current

    (a very high resistance)

    Forward: almost none until ~0.6 V,

    then the current rises steeply

    Current: the way its arrow points

    Why might a circuit need one?

    2 · Watch

    Thermistor: hotter, lower R

    x: temperature (°C)

    y: resistance (kΩ)

    Not an I–V graph: R against T

    Used in thermostats: a fridge,

    an oven, a heating system

    Hotter, less resistance

    2 · Watch

    LDR: brighter, lower R

    Light-dependent resistor

    x: light intensity (lux)

    y: resistance (kΩ)

    Dark: high R. Bright: low R

    Used to switch lights on at dusk

    Brighter, less resistance

    12 min 2 · Explain · you explain · the slides say “Watch”

    Five components, five graphs

    A resistor's straight line, a lamp's curve and why it curves, a diode's one-way graph, then the thermistor and the LDR.

    Say

    “Read the axes first, then the shape: a straight line through the origin is a constant resistance; a bend means the resistance changes.”

    Ask
    • The resistor: double the p.d. What happens to the current?
    • The lamp at 1 V and at 12 V: work out V ÷ I at each. Which is bigger?
    • Reverse the battery. What does the lamp's graph do? The diode's?
    Watch for

    Working out the resistance from the gradient: with current up the gradient is 1 ÷ R, and a curve's gradient changes anyway. Read V and I at the point and divide.

    A resistor: the same R everywhere

    At 4.0 V: 0.20 A

    R = V ÷ I = 4.0 ÷ 0.20 = 20 Ω

    At 10.0 V: 0.50 A, still 20 Ω

    A lamp: R rises

    At 1.0 V: 0.080 A, R = 12.5 Ω

    At 12.0 V: 0.333 A, R = 36 Ω (2 s.f.)

    The hotter filament resists more

    For the teacher

    Resistor: a straight line through the origin. Double V and I doubles; V ÷ I is 20 Ω at every point. That is an ohmic conductor, and it stays one only at a constant temperature.

    Lamp: the current heats the filament until it glows. In a hotter metal the ions vibrate more and get in the electrons' way, so the resistance rises. The current still rises with V, by less each volt: the curve flattens. Reversed, the lamp behaves the same, so the graph is the same shape upside down on the left.

    Diode: in reverse almost no current flows (a very high resistance); forward, almost none until about 0.6 V, then the current rises steeply. Draw the arrow of its symbol: current goes the way it points.

    Thermistor: its resistance falls as it gets hotter (thermostats, fridge and oven sensors). LDR: its resistance falls as the light gets brighter (lights that come on at dusk). Both graphs here are resistance against temperature or light, not I–V: say so.

    Ask the class before the diode slide: what will its graph look like if it only lets current through one way?

    Shorter: Skip the reversed lamp slide; say the LDR beside the thermistor (−4 min).

  3. 3 · Your turn15 min

    The virtual lab

    A virtual experiment: it follows a stated model,

    and doesn't replace the practical in the lab

    1. A resistor: 5 readings, then V ÷ I

    2. A filament lamp: 6 readings, 0 to 12 V

    3. The lamp's R at 2 V and at 12 V

    Model: R = R₀(1 + 0.5P), R₀ = 12 Ω

    Open the Lab quiz. Record, then answer.

    3 · Your turn

    Worked, then yours

    I do: 6.0 V, 0.30 A: R = 6.0 ÷ 0.30 = 20 Ω

    You do: 9.0 V, 0.36 A. The resistance?

    I do: 1.5 V, 50 mA = 0.050 A: R = 30 Ω

    You do: 2.4 V, 80 mA. The resistance?

    Volts ÷ amps. Milliamps into amps first.

    Write here

    Its answers' slide comes with your copy.

    15 min 3 · Your turn · students write

    The virtual lab, then yours

    Students take readings in a virtual experiment, a resistor first and then a filament lamp, and work out the lamp's resistance from their own readings.

    For this length: Plot the class's lamp readings on the board and sketch the reversed half

    Say

    “This is a virtual experiment: it follows a model of a lamp, not a real one, and it doesn't replace the practical in the lab. Change the cell's voltage, read both meters, record each reading.”

    Ask
    • Where is the ammeter? The voltmeter? Why is each connected that way?
    • Your lamp at 2 V and at 12 V: what is V ÷ I at each?
    Watch for

    Dividing the current by the p.d. (I ÷ V): resistance is volts per amp, V ÷ I.

    Resistance at a point on a curve

    At 6.0 V a lamp takes 0.30 A

    R = 6.0 ÷ 0.30 = 20 Ω

    Then theirs

    At 9.0 V the same lamp takes 0.36 A. Its resistance?

    Milliamps first into amps

    At 1.5 V: 50 mA = 0.050 A

    R = 1.5 ÷ 0.050 = 30 Ω

    Then theirs

    At 2.4 V: 80 mA. The resistance?

    This is a virtual experiment: it follows the model written under it and is not the required practical, or a substitute for it. Change the cell's voltage, then record each reading. Give resistances in ohms (Ω), to the significant figures asked.

    1. A resistor's I–V. Change the cell's voltage and record the current (ammeter A1) and the p.d. across the resistor (voltmeter V1): at least 5 readings at different voltages. Look at the graph of your readings: what shape is it?They set up a virtual circuit and record its meters' readings, each checked.
    2. Use any one of your resistor readings: what is the resistor's resistance, in ohms?
    3. A filament lamp's I–V. Change the cell's voltage from 0 to 12 V and record the current through the lamp (A1) and the p.d. across it (V1): at least 6 readings at different voltages, including 2 V and 12 V. Why does the graph curve?They set up a virtual circuit and record its meters' readings, each checked.
    4. From your reading at 2 V: what is the lamp's resistance, in ohms, to 2 significant figures?
    5. From your reading at 12 V: what is the lamp's resistance now, in ohms, to 2 significant figures?
    6. Why is the lamp's resistance bigger at 12 V than at 2 V?
      1. The current gets smaller at higher voltages
      2. The lamp is brighter, so its resistance is lower
      3. The battery's own resistance gets bigger
      4. A bigger current heats the filament more, and a hotter metal filament has more resistance
    For the teacher

    The model is said under the experiment: wires and the ammeter have no resistance, the voltmeter takes no current, and the lamp's resistance rises with the power in it, R = R₀(1 + 0.5P) with R₀ = 12 Ω. It is a model, honestly said: a real filament's resistance rises far more.

    First the resistor: five readings, then V ÷ I from any of them. Then the lamp: six readings from 0 to 12 V. The page draws their I–V graph from the readings.

    Then the questions on their readings: the lamp's resistance at 2 V and at 12 V, and why it changed. Work the two examples aloud while the slower ones finish recording; the twins check they divide the right way and turn mA into A.

    In the real practical you would also reverse the supply to get the left half of the graph, and switch off between readings so a resistor stays at a constant temperature. The virtual cell here goes one way only: say that the left half is the same curve turned round.

    Students open the Lab quiz on their own devices; they record readings at different voltages and each is checked against the circuit. Open the answers slide once most have done the twins.

    Shorter: Skip the resistor experiment; do the lamp only (−4 min).

    Longer: Plot the class's lamp readings on the board and sketch the reversed half (+3 min).

  4. 4 · Vote and practise20 min

    Vote first

    A lamp's I–V graph at 4.0 V: 0.25 A.

    The curve's gradient there: 0.025 A per volt.

    Its resistance at 4.0 V?

    A: 40 Ω

    B: 0.0625 Ω

    C: 16 Ω

    D: 0.025 Ω

    Choose on your own, then say why.

    4 · Vote and practise

    Practise: show your working

    1. 6.0 V, 0.30 A: the resistance?

    2. Sort: lamp, thermistor, LDR, diode

    3. Which is a diode's graph?

    4. 3.0 V, 150 mA: the resistance?

    5. 2 V 0.4 A, 4 V 0.8 A, 6 V 1.2 A: which component?

    Stuck on 4? Milliamps into amps first.

    Write here

    4 · Vote and practise

    Reason it out

    6. "The lamp's current goes down at high V"?

    7. Dusk: what does the LDR's resistance do?

    8. Diode and lamp in series, battery reversed?

    9. 3.0 V 0.20 A, 9.0 V 0.36 A: the rise in R?

    Stretch: a thermistor's sensing circuit

    V ÷ I at each point, not the slope.

    20 min 4 · Who's stuck? · students vote · the slides say “Vote and practise”

    Vote, then practise

    One question shows who's stuck on resistance from a graph; then practice in levels, and a sensing circuit as the stretch.

    For this length: The stretch: the thermistor's sensing circuit, in the virtual lab

    Say

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

    Ask
    • What are V and I at that point? So what is V ÷ I?
    Watch for

    Answering before reading the point off the graph: ask for V and I there first.

    Show your working on paper. Give resistances in ohms (Ω) and currents in amps (A); turn milliamps into amps first. The stretch is optional.

    The question that shows who's stuck

    1. On a filament lamp's I–V graph (current up, p.d. across), the point at 4.0 V shows 0.25 A, and the curve's gradient there is 0.025 A per volt. What is the lamp's resistance at 4.0 V?
      1. 40 Ω
      2. 0.0625 Ω
      3. 16 Ω
      4. 0.025 Ω
    In your Classroom, as they answer (an example)
    • A6
    • B5
    • C10
    • D4

    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 resistor at a constant temperature has 6.0 V across it and 0.30 A through it. What is its resistance, in ohms?
    2. Put each component with what is true of it.They sort 4 items into Resistance rises as it heats up and Resistance falls as it heats up and Resistance falls in brighter light and Lets current through one way only.
    3. Which describes a diode's I–V graph?
      1. A straight line through the origin, both ways
      2. A curve that flattens as the p.d. rises, the same shape both ways
      3. Almost no current in reverse; forwards, almost none until about 0.6 V, then a steep rise
      4. The current falls as the p.d. rises
    4. A component has 3.0 V across it and a current of 150 mA through it. What is its resistance, in ohms?
    5. A component's readings: 2.0 V, 0.40 A; 4.0 V, 0.80 A; 6.0 V, 1.20 A. Which is it most likely to be?
      1. A filament lamp
      2. A resistor at a constant temperature
      3. A diode in reverse
    6. Ali says: "A filament lamp's I–V graph curves over because the current goes down at high voltages." What is wrong with that?
      1. Nothing: the current does go down
      2. The current still goes up, by less for each volt, because the resistance rises
      3. The current goes up because the resistance falls
    7. A street lamp uses an LDR to switch itself on at dusk. As the sky gets darker, what happens to the LDR's resistance?
      1. It falls
      2. It rises
      3. It stays the same
    8. A diode, a lamp and a 6 V battery are in series, and the lamp lights. The battery is turned round. What happens?
      1. The lamp goes out: the diode now blocks the current
      2. The lamp lights the same: the lamp works both ways
      3. The lamp gets brighter
    9. A lamp takes 0.20 A at 3.0 V and 0.36 A at 9.0 V. By how many ohms does its resistance rise between the two? (Whole number.)
    10. Stretch, a temperature sensor. T1 is a resistor standing in for a thermistor (100 Ω when hot to 2000 Ω when cold); R1 is a fixed 500 Ω resistor and V1 reads the p.d. across it. Set T1 as the thermistor warms up, from 2000 Ω down, and record at least 4 readings.They set up a virtual circuit and record its meters' readings, each checked.
    11. Stretch: a fan switches on when V1 reaches 3.0 V. At what resistance of the thermistor, in ohms, does that happen?

    Support · For the thermistor and the LDR, say it as a sentence first: hotter, lower resistance; brighter, lower resistance. For the sensing circuit: a smaller resistance in series takes a smaller share of the battery's p.d.

    For the teacher

    Everyone chooses before anyone explains. Then ask three things in turn: what are V and I at that point? What is V ÷ I? Is that the same as the gradient of the curve there?

    Questions 1–3 build fluency; 4–5 change the look (milliamps, a table); 6–8 ask for reasons; 9 is exam-style. The stretch is a virtual sensing circuit, with a resistor standing in for a thermistor.

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

    If many chose an answer from the gradient, draw a straight line from the origin to the point on the lamp's curve, as in the hook: its resistance is that line's resistor, V ÷ I, before they practise.

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

    Longer: The stretch: the thermistor's sensing circuit, in the virtual lab (+8 min).

  5. 5 · Show what you know8 min

    Which component is it?

    2.0 V, 0.10 A

    4.0 V, 0.20 A

    6.0 V, 0.25 A

    Its resistance at 6.0 V?

    Resistor, filament lamp or thermistor?

    V ÷ I for each reading first.

    Write here

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

    Which component is it?

    Three readings: a resistance at a point, and which component behaves that way.

    For this length: Sketch its I–V graph, both halves, and explain the bend

    Say

    “Work out V ÷ I for each reading before you decide what it is.”

    Watch for

    Seeing the current rise and calling it ohmic: it must rise in proportion.

    Work out V ÷ I for each reading first.

    1. A component's readings: 2.0 V, 0.10 A; 4.0 V, 0.20 A; 6.0 V, 0.25 A. What is its resistance at 6.0 V, in ohms?
    2. Which component could it be?
      1. A resistor at a constant temperature
      2. A filament lamp, warming up at the highest reading
      3. A thermistor, warming up at the highest reading
    For the teacher

    Readings: 2.0 V, 0.10 A; 4.0 V, 0.20 A; 6.0 V, 0.25 A.

    Work out the resistance at each, then decide which component it is.

    Those who name the component but get the resistance wrong need R = V ÷ I again next lesson; set the homework.

    Longer: Sketch its I–V graph, both halves, and explain the bend (+4 min).

One to one: at every point you read off a graph, ask for V and I aloud before any resistance, and ask whether the component is hotter or colder there; let the student drive the virtual experiment while you only ask what each meter shows.

Homework: graphs and resistance

Show your working, with units. For each resistance, write V and I first, then V ÷ I.

  1. A resistor has 12 V across it and a current of 0.40 A. Find its resistance.
  2. A filament lamp takes 0.16 A at 2.0 V and 0.32 A at 8.0 V. Find its resistance at each, and explain the change.
  3. Sketch the I–V graph of a diode, both directions. Describe what it shows.
  4. A thermistor is used in a fridge's thermostat. What happens to its resistance as the inside of the fridge warms up?
  5. An LDR has 600 Ω in bright light and 15 000 Ω in the dark. With 6.0 V across it, find the current in each, in amps.
  6. In the practical, why should a student switch the circuit off between readings of a resistor? And why can't they find a lamp's resistance from the gradient of its I–V graph?

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

Teaching i–v characteristics: common questions

Why isn't the resistance the gradient of the I–V graph?

Resistance is defined as V ÷ I at a point. With current up the axis, a straight line through the origin has gradient I ÷ V, which is 1 ÷ R, and a curve's gradient changes from point to point and is neither. Drawing a straight line from the origin to the point, as the hook does, shows the resistance at that point: the resistor whose line it is.

Is the virtual experiment the required practical?

No. It follows a stated model (ideal meters and wires, a lamp whose resistance rises with the power in it) and says so under the experiment. It is good for practising readings, tables and graphs before or after the real practical, which students should still do with a real lamp, resistor and diode.

How realistic is the lamp in the virtual experiment?

The shape is right: the curve flattens because the resistance rises with the power in the filament. The size of the rise is not: the model goes from 12 Ω cold to about 36 Ω at 12 V, while a real filament's resistance can rise ten times or more as it heats from room temperature to glowing.

Do students need to draw thermistor and LDR I–V graphs?

AQA asks students to know that a thermistor's resistance falls as its temperature rises and an LDR's falls as the light gets brighter, with uses for each. The graphs on the slides are resistance against temperature and against light, which is how those facts are usually shown; a tutor can say that at a fixed temperature or light level their I–V graphs are straight lines through the origin, steeper when the resistance is lower.

Is this Foundation or Higher?

Both. The graphs, the facts about each component and R = V ÷ I are for every student. The sensing circuit in the stretch, where the thermistor shares the battery's p.d. with a fixed resistor, leans towards Higher.

Can I use the lesson without creating an account?

Yes. Read the lesson, print the worksheet and open its slides without signing in; nothing you draw there is kept. A free teacher account keeps the whole lesson in your Library to change and teach, with the virtual experiments, the quizzes, the answers and the answer slides.

Curriculum reference: AQA GCSE Physics 8463: 4.2.1.4 (resistors: ohmic conductors, filament lamps, diodes, thermistors and LDRs; I–V characteristics) and required practical 4 (I–V characteristics of a filament lamp, a diode and a resistor at constant temperature), with 4.2.1.3 (current, resistance and potential difference: V = I × R).

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