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.
 A: 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.


A: 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.
