Filament Lamp I–V Data: Resistance, Ohm's Law and a Curved Graph
During a required practical on electrical characteristics, students use a 12 V supply, a 12 V 24 W filament lamp, a 100 Ω resistor, an ammeter and a voltmeter. Group A records for the lamp: (1.0 V, 0.30 A), (2.0 V, 0.55 A), (4.0 V, 0.95 A), (6.0 V, 1.30 A), (8.0 V, 1.60 A), (10.0 V, 1.85 A), (12.0 V, 2.00 A). For the resistor at 6.0 V they record 0.060 A. A student calculates R = V/I at each lamp point and reports that resistance rises from 3.3 Ω to 6.0 Ω, concluding that 'the lamp is not ohmic, so Ohm's law does not apply to it, and resistance is not a real property.' Another student says the lamp's resistance should be constant because resistance depends only on material and dimensions. The teacher has a data projector and pre-prepared graph axes. The scheme of work expects students to distinguish ohmic and non-ohmic behaviour and explain temperature effects.
1. Evaluate the two students' claims using the data. Include the physical reason for the lamp's changing resistance and a precise statement of what Ohm's law says.
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Calculating R = V/I gives approximately 3.3, 3.6, 4.2, 4.6, 5.0, 5.4 and 6.0 Ω. The resistor gives 100 Ω at 6 V, constant within the data's precision. The lamp's resistance rises because its filament temperature rises with electrical power; for a metal, resistivity increases with temperature. The first student is right that the lamp is non-ohmic but wrong that Ohm's law 'does not apply' in an absolute sense. Ohm's law, V = IR for a metallic conductor at constant temperature, is a condition-dependent relationship. The second student is wrong because resistance depends on temperature as well as material and dimensions. A more precise conclusion is: the lamp is non-ohmic because its temperature changes during the measurement, so R is not constant.
2. The teacher wants to use the graph to confront the misconception that a curved I–V graph means the component has no resistance. Draft the key questions and the expected student reasoning.
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Ask: 'At 6 V, what single resistance value would you use to predict the current if the voltage changed slightly?' Students should calculate R = V/I = 4.6 Ω from the chord from the origin to the point. Then ask: 'Why is the graph curved?' Expected reasoning: the filament temperature rises as current increases, so resistivity and resistance increase. A curved graph means R is not constant; it does not mean R is zero or undefined. Follow with a compare–contrast table for the resistor and lamp: straight line through origin means constant R at constant temperature; curve means R changes with operating conditions. Have students annotate one graph with 'chord gives static resistance' and 'tangent gives dynamic resistance'.
3. One group plots V on the x-axis and I on the y-axis and draws a tangent at 6 V, then uses the tangent gradient as resistance. Explain why this is incorrect and what they should do instead.
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On an I–V graph with V on the x-axis, the tangent gradient is dI/dV, not R. Its reciprocal is the dynamic resistance dV/dI, which describes the response to a small change in voltage. At 6 V the static resistance is the chord from the origin: R = V/I = 6.0/1.30 = 4.6 Ω. The tangent gradient is steeper than the chord, so using it gives a different value and does not answer 'what is the resistance at this operating point?' Students should draw the chord from the origin to the point and use R = V/I. If they need dynamic resistance, they should take the reciprocal of the tangent gradient and state that choice explicitly.