The Bulb That Wouldn't Obey Ohm's Law
Mr. Delgado's physics class is testing a small incandescent bulb labeled 6.0 V. Each lab group connects the bulb in series with a variable resistor, an ammeter, and a 6 V battery, and uses a voltmeter across the bulb. One group's data: 1.0 V, 0.080 A; 2.0 V, 0.140 A; 3.0 V, 0.190 A; 4.0 V, 0.230 A; 5.0 V, 0.260 A; 6.0 V, 0.290 A. A student computes R = V/I at 1.0 V and 6.0 V and gets about 12.5 Ω and 20.7 Ω. The group writes, 'The resistance changes, so this bulb disobeys Ohm's law. Ohm's law is only a theory and doesn't apply to real devices.' Two students want to know whether they did something wrong. Mr. Delgado also has on hand a 20 Ω ceramic resistor rated 5 W, and the lab has an infrared thermometer that cannot safely read the filament directly.
1. Compute the resistance at each data point and describe the trend. What does the trend imply about what is happening inside the bulb?
Read the worked answer
Using R = V/I:
- 1.0 V / 0.080 A = 12.5 Ω
- 2.0 V / 0.140 A = 14.3 Ω
- 3.0 V / 0.190 A = 15.8 Ω
- 4.0 V / 0.230 A = 17.4 Ω
- 5.0 V / 0.260 A = 19.2 Ω
- 6.0 V / 0.290 A = 20.7 Ω
Resistance is not constant; it rises by about 66% across the range. The trend is smooth and monotonic, which is what you expect from a real device rather than a wiring mistake. Current still increases with voltage, so the bulb is conducting; it simply requires proportionally more voltage per ampere at higher currents. The physical interpretation is heating: power dissipated rises from 0.08 W at 1.0 V to 1.74 W at 6.0 V, the tungsten filament heats toward incandescence, and the resistivity of tungsten increases with temperature. The 20.7 Ω value is the hot resistance, not the resistance you would measure with an ohmmeter on a cold bulb.
2. Explain what Ohm's law actually claims and why the bulb's behavior does not refute it. Include the role of temperature in your answer.
Read the worked answer
Ohm's law is V = IR, which defines resistance as the ratio V/I. Its testable, empirical content is that for many conductors R is approximately constant over a range of currents when temperature is held constant - those are the ohmic cases. The law is not a claim that every device has a fixed resistance.
The bulb is non-ohmic because its operating temperature changes as current changes. At low currents the filament is cool and R approaches a roughly constant cold value; at higher currents the filament is hot, tungsten's resistivity rises, and R rises with it. That is fully consistent with V = IR - the definition holds at every point - but the material does not meet the constant-R condition.
'Only a theory' is also a misuse. Ohm's law is an empirical regularity with stated conditions, not a guess. When a device departs from it, the productive conclusion is 'this device is non-ohmic and something (here, temperature) is changing R,' not 'the law is false.' The group has not made an error; they have found a real material effect.
3. Propose an additional measurement or experiment using the available equipment that would support the temperature explanation, and predict the result.
Read the worked answer
A good test separates 'the circuit is wrong' from 'the filament heats.'
- Swap in the 20 Ω, 5 W resistor. Collect V–I data at the same voltages. If R stays near 20 Ω across the range (within the resistor's tolerance and power rating), the meters and wiring are fine and the bulb itself is the non-ohmic element. The resistor is a strong control because its resistance is nearly independent of temperature at these power levels.
- Take rapid, low-duty-cycle readings. Switch on briefly, read V and I, and switch off to let the filament cool between points. If R at a given current is lower than in the steady-state run, heating is the cause.
- Plot R versus power and extrapolate to zero power. The extrapolated cold resistance should be lower than the lowest measured value (the 1.0 V point), consistent with a positive temperature coefficient.
Prediction: the resistor shows constant R; the bulb shows R increasing with power; quick, cool measurements give lower R at the same current than steady-state measurements. Together these support the temperature explanation without touching the filament.