# Why does the relationship between the voltage across, and the current through, a light bulb look like it does

I've completed a simple experiment where I progressively turn up voltage and note the strength of the electric current. Afterwards, I created these two graphs... (apparently I can't post more than two images cause I don't have enough reputation, and hence there is only the second graph)

The second graph shows the relationship between current and voltage across and through a light bulb. View circuit diagram for more details.  I(V)≈14V+44

When you anlyse the second graph, a systematic displacement from the trendline is to be seen. This implies that Ohm's law is not applicable in the given sitation, correct?

Furthermore, I wonder what causes this displacement and why it happens with a light bulb while not with a resistor.

My hypothesis is that as the voltage and current increases, the number of electrons that are added to the current progressively become fewer as there are only so many conduction electrons. (But really, I have no clue.)

Vocabulary:

• Glödlampa – light bulb
• Spänning – voltage
• Ström – electrical current
• Note that a linear fit there is a bad idea - your data should be fitted like this (source). – Emilio Pisanty Nov 24 '16 at 13:06
• @EmilioPisanty Thanks. Will make it a polynomial fit instead with the domain 0,5≤V≤ 11 – R. Milky Nov 24 '16 at 13:16
• A polynomial fit of $I$ as a function of $V$ is unlikely to work. In the absence of a physically motivated model, the thing to try there is something like $V=a I + b I^3$. (Why? Well, consider what would happen if you reversed the voltage.) – Emilio Pisanty Nov 24 '16 at 13:22
• from the circuit diagram, I'm surprised your ammeter is measuring so low. An ammeter has a very low internal resistance. If you actually connected yours in parallel with the rest of the circuit, you effectively shorted out the voltage source and should be receiving a massive current across the ammeter, which should mostly not have anything to do with the light bulb at all. Try connecting the ammeter in series with the bulb and then graph that data – Jim Nov 24 '16 at 13:34

## 1 Answer

As more current passes through the light bulb it increases in temperature. This is known as Joule heating. The increase of temperature increases the resistance of the filament.

The reason you see this effect in a light bulb and not a resistor is that the light bulb, by design, has a much greater change in temperature than the resistor.

Whether or not Ohm's Law applies in this case depends on what you include in your statement of Ohm's law. The law is sometimes stated as:

For a conductor in a given state, the electromotive force is proportional to the current produced.

Where a given state would include the temperature. If somehow you could keep the light bulb filament at a constant temperature as you increase the current through it you would probably get a much staighter graph.

• Why does increased temperature lead to increased resistance in the filament? Is it because the atoms that comprise the filament start vibrating more vigorously, hence making the electrons flowing through the current more likely to collide with the atoms? – R. Milky Nov 24 '16 at 13:04
• @R.Milky Yeah, that's essentially correct. – Emilio Pisanty Nov 24 '16 at 13:06