Nice project;it's great to see this lad working hands-on on this project. Perhaps a good follow-on project would be to design a switching regulator and avoid the power loss in the resistor bank. Keep up the the good work you've started.
My humble apologies. I just cranked through the numbers (Using E^2/R, 90W across 1-ohm means voltage of ~9.48V, and current of ~9.48V; break that into thirds, carry the zero, hold yer tongue right, etc...) and John (along with the rest of you) is correct! Somehow, 30 years as a BSEE and all, I let my mind take over before doing the (full) analysis.
"it is definately not much more than 3A, or else the LEDs would burn out"
I wonder. They can probably take dobule the nominal current for a while, and BTW, put out considerably over 1000 lumens each while doing so.
This could be explained by looking at a few assumptions. Your battery voltage is probably actually more like 12.6 V or even a bit higher, at full charge, which will drive up both the current the LEDs draw and the resulting power. The I/V curve for these devices increases pretty sharply! And - the LEDs are in series, correct?
As Phil commented, power = heat, and is not dependent upon either voltage or current more than the other. In the case of the 100 kV at 20 mA load, what's the source? It could be that what you are driving with has limited current capbility, and the terminal voltage drops drastically under a 20 mA load. Otherwise, you would be dissipating 5 Megawatts!!
Naw, the power being dissipated IS the heat being given off. Remember that law of thermodynamics? Energy shall neither be created nor destroyed. Here elecrtrical energy (the power x the time it is applied to the resistor) is entirely converted to heat.
It's actually even less than that, and it's 90W of power handling. The Cree XM-L datasheet puts 2.5A at 3.25V. (12-(3.25*3))V^2/1Ohm=5W. 5W/9=1/2W per. Better get those resistors some airflow John. You got them wrapped in insulation or something?
@laserdudephil, thanks, but I generally, (except on DX), can only really buy stuff from stores, and constant current switching supplies arent exactly cheap or common. I just used resistors becasuse radioshack carries them for about $1 each.
As for the power dissipation of the resistors, they are sinking a lot more than 1.6W each, and it is definately not much more than 3A, or else the LEDs would burn out. Also, I'm not sure if heat is solely dependent on wattage, I believe current is generally more important (not sure though...) since high voltage at low current (estimated 100,000V@~20mA) should be about 2000W, but the resistor didn't break a sweat.
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