> I know that this is basic Ohm's law stuff..., but what is the formula to calculate the series resistor to ground for a phantom power LED?
R=V/I
What I (current) do you want? Most LEDs are rated 20mA (0.020A) max, but they all work on less, and most are pretty bright at 5mA.
What is your available voltage? 48V? The LED eats some of that: 1.7V for red LEDs and more for other colors, maybe over 3V for Blue? In a 5V circuit, that makes a difference, so you better check the specs. In a 48V circuit, 1.7V or 4V makes very little difference: 48V-1.7V= 46.3V, 48V-4V=44V, only 5% difference, and the current is not at all critical.
So given about 48V-2V= 46V, and say 5mA (0.005A) current, 46V/0.005A= 9,200Ω. Sort of an odd value. I find a 10K on the floor, will that work? 46V/10,000= 0.004,6A or 4.6mA. This is safely below the 20mA maximum (even if the 10K 10% resistor is really 9K or 11K) and reasonably close to the 5mA operating current that we picked out of thin air.
Or hey: we have a baggie of 6.8K resistors left over from Phantom wiring. 46V/6K8= 6.76mA, more than our thin-air 5mA figure but lower than the typical 20mA rating of an LED. Try it. If too bright, try two 6K8 in series for 46V/13K6= 3.4mA.
Ah, you learn that your particular LED is 4V, not 1.7V or my rounded 2V. So 48V-4V is 44V. 44V/6K8 is 6.47mA, a fine current. In general, if the supply voltage is much more than the LED voltage, and you are not desperate for all the bright you can get, these calculations can be very rough.
You need to check heat. When things are well, this will be just volts times amps. Say 46V*0.0067A= 0.31 Watts. A 1/4 Watt resistor will run VERY hot, drift in value, and generally be no good. Use a 1/2 Watt resistor and let it get plenty of air.
As an extreme case: you work in the sunlight (ugh!), you need all the bright you can get. You want to run the LED up to 19.9999mA. 46V/20mA= 2K3 resistor. This is an odd value, but you can't use the nearest 2K2 value: 46V/2K2= 20.91mA. The LED might live forever with 5% abuse, but it seems like a bad plan. In 10% standard values, you are stuck with 2K7. 46V/2K7= 17mA. Less than max, but you will hardly notice a 15% change in brightness (the eye is logarithmic like the ear). Now we have 46V*0.017A= 0.78 watts, and even a 1 Watt resistor will run hot.