The shape of the lesson
By the end of the lesson, learners can
- Trace the characteristic: Sweep the voltage and plot the I-V characteristic for a metal conductor, a filament lamp and a diode, and see why only the first is a straight line through the origin.
- Shape the wire: resistivity: The I-V sim treats resistance as a fixed number; here you see where that number comes from.
- Resistance and the material: One relation for the component, one for the material.
- Reading I-V graphs: The shape of the characteristic reveals the component.
- Resistance: R = V/I.
- Material: R = ρL/A.
- Ohmic: straight I-V line.
One picture every idea returns to
Resistance is defined by R = V / I. A component obeys Ohm law if the current is proportional to the voltage (a straight-line I-V graph through the origin) at constant temperature. The resistance of a uniform wire is R = ρL / A, where ρ is the resistivity of the material. A thermistor (NTC) and a light-dependent resistor (LDR) both fall in resistance, with rising temperature and rising light level respectively.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Opposition to the flow.. Resistance measures how hard a component makes the charge work to get through. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 11 min | Teach and check: Trace the characteristic | Sweep the voltage and plot the I-V characteristic for a metal conductor, a filament lamp and a diode, and see why only the first is a straight line through the origin. Project tab 3 of the lab (I-V characteristics) and let a student drive it while the class predicts. | Whole class, then pairs |
| 11 to 17 min | Teach and check: Shape the wire: resistivity | The I-V sim treats resistance as a fixed number; here you see where that number comes from. Project tab 4 of the lab (Resistivity) and let a student drive it while the class predicts. | Pairs |
| 17 to 23 min | Teach and check: Resistance and the material | One relation for the component, one for the material. | Pairs |
| 23 to 30 min | Teach and check: Reading I-V graphs | The shape of the characteristic reveals the component. | Cooperative Concept Mapping |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 14 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Reading I-V graphs, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Cooperative Concept Mapping
Teams receive the key terms on cards and arrange them on a large sheet, drawing and labelling the links. Compare maps between teams before showing the model map.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Resistance R = V/I is the value at a point, found from the coordinates, not the gradient, on a curved I-V graph. | A filament lamp is not Ohmic: its resistance rises as it heats, so the graph curves. In R = ρL/A the resistance is proportional to length and inversely proportional to area, so a longer, thinner wire has more resistance. |
Resistance and resistivity: worksheet
6 questions, 14 marks. Written in the style of the papers; no past paper question is reproduced.
State Ohm law and the condition under which it applies.
A potential difference of 9.0 V drives a current of 0.30 A through a resistor. Find its resistance.
A wire of length 10 m and cross-sectional area 2.0 × 10⁻⁷ m² is made of material of resistivity 1.7 × 10⁻⁸ Ω m. Find its resistance.
A 2.0 m wire of cross-sectional area 1.0 × 10⁻⁷ m² has a resistance of 4.0 Ω. Find the resistivity of the material.
Describe and explain the shape of the I-V characteristic of a filament lamp.
State how the resistance of a light-dependent resistor (LDR) changes as the light intensity increases, and how a thermistor (NTC) changes as it warms.
Answer key and marking notes
- The current is proportional to the potential difference ✓
- provided the temperature (and other physical conditions) stays constant ✓
- R = V/I = 9.0/0.30 ✓
- R = 30 Ω ✓
- R = ρL/A = (1.7 × 10⁻⁸ × 10) / (2.0 × 10⁻⁷) ✓
- R = 0.85 Ω ✓
- ρ = RA/L = (4.0 × 1.0 × 10⁻⁷) / 2.0 ✓
- ρ = 2.0 × 10⁻⁷ Ω m ✓
- It is an S-shaped curve that bends away from a straight line as the voltage rises ✓
- because the filament heats up and its resistance increases, so the current rises less steeply ✓
- The LDR resistance decreases as the light gets brighter ✓
- The NTC thermistor resistance decreases as the temperature rises ✓
14 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
The resistance of a component is defined by:
- AR = V / I
- BR = I / V
- CR = VI
- DR = V²I
A component obeys Ohm law if, at constant temperature, the current is:
- Ainversely proportional to the voltage
- Bconstant
- Cproportional to the voltage
- Dzero
The resistance of a uniform wire is given by:
- AR = ρA / L
- BR = ρL / A
- CR = ρLA
- DR = L / (ρA)
A 12 V supply drives 3.0 A through a resistor. Its resistance is:
- A36 Ω
- B0.25 Ω
- C9.0 Ω
- D4.0 Ω
The unit of resistivity is the:
- Aohm metre
- Bohm
- Cohm per metre
- Dmetre per ohm
For a wire of fixed area and material, a greater length gives a:
- Asmaller resistance
- Bunchanged resistance
- Cgreater resistance
- Dzero resistance
For a wire of fixed length and material, a greater cross-sectional area gives a:
- Agreater resistance
- Bsmaller resistance
- Cunchanged resistance
- Dinfinite resistance
As an NTC thermistor gets hotter, its resistance:
- Aincreases
- Bstays constant
- Cbecomes infinite
- Ddecreases
As the light on an LDR gets brighter, its resistance:
- Adecreases
- Bincreases
- Cstays constant
- Dbecomes infinite
The I-V graph of a filament lamp is:
- Aa straight line through the origin
- Ba horizontal line
- Ca curve, because its resistance rises with temperature
- Dzero everywhere
A semiconductor diode:
- Aconducts equally both ways
- Bconducts in one direction only
- Cnever conducts
- Dhas constant resistance
A wire has ρ = 2.0 × 10⁻⁸ Ω m, length 4.0 m and area 2.0 × 10⁻⁷ m². Its resistance is:
- A2.5 Ω
- B4.0 Ω
- C0.10 Ω
- D0.40 Ω
Halving the length of a wire (same material and area) changes its resistance to:
- Ahalf
- Bdouble
- Ca quarter
- Dunchanged
At constant temperature, the I-V graph of a metal conductor is:
- Aa curve that flattens
- Bflat
- Ca straight line through the origin
- Donly in the positive quadrant
Quiz key
R = V/I.
Ohmic: I ∝ V.
R = ρL/A.
R = V/I = 12/3.0 = 4.0 Ω.
Resistivity ρ is measured in Ω m.
R ∝ L, so a longer wire has more resistance.
R ∝ 1/A, so a thicker wire has less resistance.
An NTC thermistor falls in resistance as temperature rises.
An LDR falls in resistance in brighter light.
A filament lamp is non-Ohmic; heating raises its resistance, curving the graph.
A diode conducts when forward biased above a threshold and blocks reverse current.
R = ρL/A = (2.0 × 10⁻⁸ × 4.0)/(2.0 × 10⁻⁷) = 0.40 Ω.
R ∝ L, so halving the length halves the resistance.
A metal at constant temperature is Ohmic, giving a straight line through the origin.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.