The Lamp That Refused to Obey Ohm's Law
During a first-year practical in a Madurai school laboratory, students are asked to verify Ohm's law using a 230 V, 60 W tungsten lamp, a variac, an ammeter and a voltmeter. The teacher insists that the lamp is a resistor. The readings recorded are: at 40 V the current is 0.090 A; at 120 V it is 0.170 A; at 200 V it is 0.240 A. A student computes V/I for each reading and obtains 444 Ω, 706 Ω and 833 Ω. He concludes that Ohm's law has failed and that the ammeter must be faulty. The teacher asks the group to resolve the contradiction before the practical record is written. The variac and meters are known to be accurate; the lamp is new and rated 230 V, 60 W.
1. Calculate the resistance of the lamp at its rated 230 V, 60 W condition. Compare it with the three measured values and explain, in terms of filament temperature, why the ratio V/I changes.
Read the worked answer
At rated conditions the lamp resistance is R = V²/P = 230²/60 = 881.7 Ω, and the rated current is I = P/V = 60/230 = 0.261 A. The measured values are 40/0.090 = 444 Ω, 120/0.170 = 706 Ω and 200/0.240 = 833 Ω. The resistance is not constant; it rises steeply as the filament becomes hotter. Tungsten has a positive temperature coefficient, about 0.0045 per kelvin, so V/I at each setting is the resistance at that particular filament temperature. Ohm's law is still obeyed at every instant, but the component is non-ohmic because its resistance depends on temperature. The measured 833 Ω at 200 V agrees with the rated 881.7 Ω because at 200 V the filament is already close to normal operating temperature. At 40 V the filament is much cooler, so its resistance is only about half the hot value.
2. The student proposes to use the 40 V reading, 444 Ω, to predict the current the lamp will take at 230 V. Calculate that predicted current and power, and explain why the prediction is both wrong and unsafe.
Read the worked answer
Using R = 444 Ω gives a predicted current I = 230/444 = 0.518 A and a predicted power P = 230 × 0.518 = 119 W. That is nearly twice the lamp's 60 W rating. A real lamp does not behave this way: as the current tries to rise, the filament heats up, its resistance increases towards about 882 Ω, and the current settles near 0.26 A. The calculation is unsafe because it treats a temperature-dependent resistance as a fixed constant. The same effect explains the high inrush current when a lamp is switched on: the filament is cold, its resistance is low, and the initial current can be several times the running value. The correct approach is to use the rated hot resistance for normal running and the cold resistance only for estimating the brief starting surge, not for steady-state power.
3. What experimental change would make V/I nearly constant, and how should the students present the results so that the difference between an ohmic and a non-ohmic conductor is clear?
Read the worked answer
Replace the lamp with a fixed resistor of low temperature coefficient, such as a metal-film or a wire-wound resistor operated well below its power rating. If a wire-wound resistor is used, keep P = VI below about half its rating so self-heating is small; otherwise its resistance will again drift. Take readings quickly and allow the resistor to cool between readings. Present a table of V, I and V/I, and plot V against I. A fixed resistor gives a straight line through the origin, so V/I is constant. The lamp gives a curve whose slope increases with V, showing that resistance rises with temperature. Conclude that Ohm's law is not a universal statement about all conductors; it is a relationship that holds for a conductor maintained at constant temperature. The lamp is a valid non-ohmic device, not a faulty one.