To interpret a current-voltage (I-V) graph, pick a point, read its V and I, and calculate R = V ÷ I for that point. A straight line through the origin means constant resistance. A curve means the resistance changes.
This lesson follows current in series and parallel branches and belongs to potential difference, resistance and circuits. The graph-reading habit is shared with motion and graphs.
What do the common shapes mean?
- Fixed resistor (at constant temperature): a straight line through the origin. Double the p.d. and the current doubles.
- Filament lamp: a curve that flattens as p.d. rises. The filament heats up and its resistance increases.
- Diode: almost no current in one direction, and a sharp rise after a small forward p.d. in the other.
For a straight line through the origin with I on the vertical axis, the gradient is I ÷ V, which equals 1 ÷ R. For a curve, the gradient at a point is not the resistance.
How do I work through a question?
- Check the axes. Which quantity is on the vertical axis, and what are the units?
- Pick the point the question asks about, and read V and I accurately.
- Convert units (mA to A) if needed.
- Calculate R = V ÷ I at that point.
- Describe the trend by comparing R at two or more points.
Worked example
The table shows invented readings for a small lamp.
| V (V) | 0 | 2.0 | 4.0 | 6.0 |
|---|---|---|---|---|
| I (A) | 0 | 0.50 | 0.80 | 1.00 |
Find the resistance at each non-zero point and describe the trend.
Step 1, at 2.0 V: R = 2.0 ÷ 0.50 = 4.0 Ω.
Step 2, at 4.0 V: R = 4.0 ÷ 0.80 = 5.0 Ω.
Step 3, at 6.0 V: R = 6.0 ÷ 1.00 = 6.0 Ω.
Step 4, trend: the resistance rises from 4.0 Ω to 6.0 Ω as the p.d. increases. This is consistent with a filament that gets hotter as more current flows.
Step 5, check: 0.80 × 5.0 = 4.0 V and 1.00 × 6.0 = 6.0 V, both matching the table.
The mistake to watch for
A common slip is to read resistance from the gradient of a curve, or from the change between two points.
Mistaken answer: R = (6.0 − 4.0) ÷ (1.00 − 0.80) = 2.0 ÷ 0.20 = 10 Ω
The student used the change in V divided by the change in I. That is not the resistance, and 10 Ω is larger than any value in the table.
The correction is to use V ÷ I at one point, with both values measured from zero. The resistance at 4.0 V is 5.0 Ω, not 10 Ω.
Check yourself
Try these, then open each answer.
1. A straight line through the origin passes through the point (6.0 V, 0.30 A). Find the resistance.
Show answer
R = 6.0 ÷ 0.30 = 20 Ω. Check: 0.30 × 20 = 6.0 V.
2. A filament lamp has 3.0 V and 0.60 A at one point, and 6.0 V and 0.90 A at another. Does its resistance increase or decrease? Give the values.
Show answer
At 3.0 V: R = 3.0 ÷ 0.60 = 5.0 Ω. At 6.0 V: R = 6.0 ÷ 0.90 ≈ 6.7 Ω. The resistance increases, because the filament is hotter.
3. Why does a diode graph show almost no current when the p.d. is reversed?
Show answer
In the reverse direction a diode has a very high resistance, so almost no current flows even though there is a p.d. across it.
Where this leads next
The next lesson separates the definition of resistance from Ohm’s law, which explains why the lamp above still obeys R = V ÷ I. The graph-model and residual explorer helps you practise reading lines, and the practice set includes table-based questions.
If graphs still feel like pattern-matching, our teachers can work through them with you in online one-to-one Physics tuition.