The Filament Lamp and the Non-Ohmic Judgement
A student is investigating whether a small filament globe obeys Ohm's law. They connect the globe in series with a variable DC supply, an ammeter and a voltmeter, and record: at 1.0 V the current is 0.10 A; at 2.0 V it is 0.14 A; at 3.0 V it is 0.17 A; at 4.0 V it is 0.19 A. The student plots V against I and finds the graph curves upward (concave up), then concludes 'the globe is non-ohmic because the graph is not a straight line through the origin.' A second student argues that the globe is ohmic because 'at each point V = IR holds, so R is defined.' The teacher asks the class to resolve the disagreement using the data.
1. Calculate the resistance at each data point and use the values to judge whether the globe is ohmic. State the criterion you are applying.
Read the worked answer
Resistance at each point from R = V/I:
- 1.0 V, 0.10 A → R = 10 Ω
- 2.0 V, 0.14 A → R = 14 Ω
- 3.0 V, 0.17 A → R = 18 Ω
- 4.0 V, 0.19 A → R = 21 Ω
The resistance rises from 10 Ω to 21 Ω as the current increases. The criterion for an ohmic conductor is that resistance is constant (equivalently, the V–I graph is a straight line through the origin) over the range tested. Since R is not constant, the globe is non-ohmic over this range.
The second student's argument is a definitional confusion: V = IR defines resistance at any instant, but 'ohmic' requires that this ratio be the same at every current. The first student's conclusion is correct, though the reason should be stated as 'resistance changes with current' rather than simply 'the graph is not straight.'
2. Explain, in terms of the microscopic behaviour of charge carriers in the filament, why the resistance increases with current. Then predict qualitatively what would happen to the resistance if the globe were immersed in liquid nitrogen while operating at 2.0 V.
Read the worked answer
As current increases, the power dissipated in the filament (P = VI) increases, so the filament temperature rises. In a metal, the ions of the lattice vibrate with greater amplitude at higher temperature, so conduction electrons collide more frequently with the lattice and are scattered more strongly. This reduces the drift velocity for a given applied field, which is equivalent to increased resistivity and therefore increased resistance. The V–I curve is therefore concave upward, as observed.
If the globe is immersed in liquid nitrogen (about 77 K), the filament is held at a much lower temperature even while dissipating power. Lattice vibrations are reduced, electron scattering is weaker, and the resistance at 2.0 V would be lower than 14 Ω. The globe would draw a larger current at the same voltage, and the V–I curve would be closer to linear over the measured range. This is a prediction from the temperature-dependence of metallic resistance, not a memorised fact about the globe.