# What type of Math do I use to to describe this situation

### What type of Math do I use to to describe this situation

Everyone has heard the question, "When will I use _________ in real life?", when referring to math topics. I have the opposite question, what kind of math can I use to describe this real life phenomenon. I feel like it has something to do with series, convergence, and divergence, probably with calculus and perhaps a natural log thrown in somewhere. I don't know what to search for in google, but I haven't had luck so far with the searches I've tried.

Here is a sample situation:

A lighting unit connected to a power supply by a long cable draws a constant amount of electrical Power ( [P]ower = [I]Current * [V]olts ) after it stabilizes. The power supply provides a constant [V]oltage, and the cable has (for our purposes) a constant [R]esistance. The voltage from the supply to the light will drop along the cable based on how much current is drawn (Ohm's law V = I * R). With the light off it draws no current, so there is no drop across the cable, and the voltage at the light will be the same as at the supply.

Once the light starts drawing current, there will be a voltage drop along the cable, which will cause the voltage at the light to drop, which in turn causes the light to draw more current to maintain constant power. But now the light is drawing more current, which causes a larger voltage drop, which causes the light to draw more current, which causes a larger voltage drop, which causes . . . .

I can easily work out what current draw the light will stabilize by setting this up in the lab and testing it, and I can do it in software using loops, but I'd like to know what tools I need to work this out mathematically.

Another good example would be maintaining constant brightness on an LED. LEDs get dimmer as they warm up, they warm up as you supply more current, and you need to supply more current to maintain constant brightness because they are dimming.

Thanks!
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