To find a filament lamp’s resistance at an operating point, divide its voltage by its current at that same point. On a curved current–voltage graph, a tangent shows how the current changes locally. The resistance at the point comes from V/I.
The 2027 SEC G3 Physics K323 syllabus covers interpreting the current–voltage characteristic of a filament lamp. This guide compares two operating points and explains how to read the axes.
- Read the axis labels and units.
- Take voltage and current from the same point.
- Convert milliamps to amps before calculating ohms.
- Compare resistance values before explaining the curve.
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Read an operating point
If voltage is on the horizontal axis and current is on the vertical axis, a point on the graph gives a pair of readings. Use the voltage from the horizontal coordinate and current from the vertical coordinate.
Resistance at that point is V/I. On this set of axes, the slope of the line joining the origin to the point is I/V. The reciprocal of that line’s slope gives V/I.
The tangent to a curved line generally has a different slope. Use the tangent only when the question asks for a local gradient.
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Worked example | Compare two lamp readings
A graph for a lamp shows 200 mA at 2.0 V and 300 mA at 6.0 V. Find the resistance at each point.
| Voltage | Current in amps | Resistance |
|---|---|---|
| 2.0 V | 0.200 A | 2.0 ÷ 0.200 = 10 Ω |
| 6.0 V | 0.300 A | 6.0 ÷ 0.300 = 20 Ω |
The voltage triples but the current increases by a factor of 1.5. The ratio V/I therefore doubles. In the usual lamp model, the filament gets hotter as current increases, and its resistance rises.
Avoid dividing the difference in voltage by the difference in current for this question. That would use changes between points, while the requested resistance uses the pair of readings at one point.
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CHAPTER 3 OF 4 · Back to contents
Practise reading swapped axes
Suppose a new graph puts current on the horizontal axis and voltage on the vertical axis. At 0.25 A the lamp has 4.0 V across it. Its resistance is 4.0 ÷ 0.25 = 16 Ω.
On these swapped axes, the slope from the origin to the point is V/I. Read the axes before connecting any slope to resistance.
For an ohmic conductor at constant temperature, the straight graph through the origin gives the same V/I at each non-zero point.
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CHAPTER 4 OF 4 · Back to contents
Frequently asked questions
What if the graph passes through the origin?
At the origin, V and I are both zero and their ratio is undefined. Use a suitable non-zero point for V/I.
How do I convert 300 mA?
Divide by 1,000 to get 0.300 A.
Why can the lamp have more than one resistance value?
Its filament temperature changes as it operates. Different points on the characteristic can therefore give different values of V/I.
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