# What does the current vs voltage graph of a halogen look like?

I have a halogen light with a tungsten filament. It is rated 500w at 130v but I am running it from an inverter in my car that is putting out 110v. I would like to know what the actual power usage of this lamp is at 110v.

When I was a Sophomore in high school I had a physics lab where I calculated the temperature of a tungsten filament by measuring the current and then doing some calculation-which I can't pull out of my brain at the moment.

I am guessing that I am not the first person to do this and there must be some sort of curve that plots the current vs voltage of a halogen. If anyone knows of such a graph - or better yet some equations I could use to solve for an exact number, I would appreciate it.

EDIT: Ok, so I answered my original question, but if someone can give me actual equations instead of the mediocre graphs I found, I would be happy.

## 2 Answers

After posting this I poked around the internet and found a PDF all about halogens that included some graphs. None of the graphs were voltage vs current, but I did find a graph that was voltage vs flux, as well as power vs flux. Using those two graphs I was able to find that find the actual power of my light.

Here are the two graphs that I found. I drew some lines on them (the black lines) to help me find the values I was looking for because it was hard to read them. Using the data from these graphs, assuming it's accurate, my halogen is using about 88% of it's 500w rating which is 440w.  • Resistivity of Tungsten is highly dependent on operating temperature. When you reduce your voltage, temperature of the filament also drops, and thus lamp impedance, which messes the possibility of using any simple formula. I am afraid you are going to have to go with your graphs. – Jaime Jan 7 '13 at 7:38

See here https://en.wikipedia.org/wiki/Lamp_rerating for simplified formulae.

If you want a closed form, you may solve https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law against P=U^2/R and probably assume R ~ T for 300-3000K (the usual tungsten filament temperatures).

p.s. be aware that production tolerances of the halogen lamps are probably more than 130v/110v change. Be also aware that these lamps fade a lot with time (say, down to 1/3 of the initial luminous flux) before one starts to notice.