Struggling to understand series connections based on experiment

I'm having some issues understanding how series connections work based on an experiment I did at school.

I took two lamps, and then connected them in series so the power initially goes to the first then the second. My book tells me that in series connection, the current stays constant throughout the system, which is also what I measured (1,86A), and the voltage potential should split between the two lamps, which I could also see (6,55V + 5,16V almost equals the total potential of the system at 11,86).

This I could also see, as one of the lamps (the one closest to + on my power supply) were shining much brighter than the other one. What I don't understand is, given how the resistance of the lamps are the same, how does this make sense?

According to Ohm's Law, U=I*R, this doesn't make sense. Given both a constant I and the same R across each lamp, U should really stay the same too?

To be honest I'm surprised they were that similar. Putting two bulbs in series has some strange effects that can be confusing when you first see them.

No two lamps are going to be identical, one will be a tiny bit higher resistance than the other. Current is the same in both lamps and power = resistance * current which means one of the lamps will have a very very slightly higher power dissipation.

This is where the weird stuff starts to happen.

Power dissipation in a lamp = heat.

The resistance of (most) metals increases with temperature.

So the slightly higher resistance lamp has a slightly higher power which means it gets slightly hotter. If it gets hotter it's resistance will increase more. Which means the difference in resistance increases and a higher proportion of the power goes into that one lamp. You get a positive feedback effect, the lamp with the higher resistance ends up significantly brighter, far more than you would expect based on their resistance differences when cold.

You can check this easily:

You measured the voltage and current for each lamp when they were on. That means you can calculate their on resistance. Use a meter to measure the resistance of them when they are out of the circuit and cold, you'll get a very different number.

Light intensity for incandescent lamps is related to temperature and area of the filament (and probably a couple more factors).

Small differences in the length and diameter of the filaments can lead to slightly different resistances (which you saw in your voltage measurement).

That, in turn, can lead to a somewhat different power consumption (P = I * U), and you end up with a noticably different filament temperature, light intensity and color temperature.

TLDR: The lamps are identical only in theory.

Have you measured the resistance across both lamps? I think you will find if you actually measured them, you will see they are slightly different, hence one being brighter than the other. You can see this is true because if they were both the same, you would see half the supply voltage in between them, which according to your results, you did not see.

Fun experiment: Use Ohm's Law to try and calculate what the resistances SHOULD be using the results you have so far, then measure with a multimeter to compare.

• I'm having some issues meassuring the resistance though. With a multimeter set to Ohms at the very lowest setting gives 0 ohms, which can't be true? Could this have something to do with the other answers that say the resistance have to do with the temperature, and since the lightbulb isn't on when testing via multimeter, it gives wrong results? – jsmnbom Jun 13 '17 at 9:11
• It shouldn't stop you getting a reading.... you can always wait for them to cool down and try again? To be sure, make sure you take it out of the circuit and measure it just as an extra precaution – MCG Jun 13 '17 at 9:22
• It's possible my multimeter is broken then. Course I'm getting nothing... I tried calculating the resistance using Ohm's law however, where they are indeed different. I guess I could do the same just for single lightbulbs too? – jsmnbom Jun 13 '17 at 9:38