To explain a curved I-V graph, calculate V ÷ I at several points, show that the ratio changes, and link the change to the rising temperature of the filament.
This lesson follows comparing potential difference readings and belongs to electrical reasoning from diagrams and measurements.
Worked example: a fictional filament lamp
This is an original table of readings, not a real experiment.
| V (V) | I (A) | R = V ÷ I (Ω) |
|---|---|---|
| 1.0 | 0.10 | 10.0 |
| 2.0 | 0.17 | 11.8 |
| 3.0 | 0.22 | 13.6 |
| 4.0 | 0.26 | 15.4 |
| 5.0 | 0.29 | 17.2 |
The resistance rises from 10.0 Ω to 17.2 Ω as the voltage increases. The current still rises, but each extra volt adds less current than the one before.
How do I write the explanation?
Use three short statements.
- Data: V ÷ I increases from 10.0 Ω at 1.0 V to 17.2 Ω at 5.0 V, so the lamp is not ohmic.
- Reason: a larger current heats the filament, so its temperature rises.
- Link: a hotter filament has a higher resistance, so each extra volt produces less extra current and the graph curves towards the V-axis.
Each statement ties to evidence or to a physical idea, which is what the marks reward.
The mistake that costs marks
The common slip is to treat the gradient of the curve as the resistance.
| Claim | Why it fails |
|---|---|
| “Resistance equals the gradient of the curve” | The gradient is a change in I for a change in V. It does not give V ÷ I at a point |
| “Resistance is constant because current increases” | Constant resistance needs V ÷ I constant, and here it changes |
| Correct: “V ÷ I rises, so the filament’s resistance rises with temperature” | Uses the ratio and the physical cause |
The safe method is to divide V by I at a point. Use the gradient only to describe how steep the curve is.
Check yourself
A second component gives V = 1.0, 2.0, 3.0 V with I = 0.20, 0.30, 0.36 A. Is it ohmic? Give evidence.
Answer
Resistance values: 1.0 ÷ 0.20 = 5.0 Ω, 2.0 ÷ 0.30 = 6.7 Ω, 3.0 ÷ 0.36 = 8.3 Ω.
V ÷ I is not constant, so the component is not ohmic. The resistance increases with voltage, so the graph would curve, like the filament lamp.
For comparison, V = 2, 4, 6 V with I = 0.05, 0.10, 0.15 A gives 40 Ω each time, which is ohmic.
What to study next
The last reasoning lesson is separating electrical energy from power in a fictional appliance table. Then try the section practice set and log faulty explanations in the mistake log and paper-error review.
For a teacher to go through your graph explanations, see online one-to-one Physics tuition or try the one-hour trial class (from RM50).