Superbright leds and potential dividers

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I'm trying to feed a voltage to my superbright leds. I am not sure how many voltages they require to work(6v?)

I have a 12V dc supply from my computer's power supply unit, which i connect to the potentialmeter(500K, 1M). I then tap the voltage and pass it directly to my LED. However, when I connect my multimeter to the LED to check the voltage, some LEDs do not light up, but when I remove the multimeter, the LED lights up. Other LEDs do not face such problem. What is happening here? How then do i measure the voltage?

Also, I realize that the LEDS burn out way before they turn bright. Am i doing something wrong?
 
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If you have access to a bench power supply (i.e. a power supply with adjustable voltage and current limiting), here's a trick you can use:

1) set the current limit to a few (10-ish) mA
2) test the current limit by (briefly!) shorting out the test leads
3) adjust the voltage upwards until the LED turns on--note the voltage at which this occurs
4) assuming your current limit is properly set, adjusting the voltage upwards should result in the current limit kicking in quite shortly (the current-voltage curve should be pretty steep in the forward-active region)
5) turn the current limit to zero, and set the voltage to a volt or so above the LED turn-on voltage
6) very carefully adjust the current limit upwards, and figure out the "sweet spot" for current versus brightness--don't get greedy, and don't exceed more than a few dozen mA (unless we're talking about the really big multi-watt LEDs here)

If you have done this, you'll have (crudely) done what a curve tracer does.

However, as Redbelly98 says, the usual practice is to choose a current-limiting resistor based on the numbers above. It's possible to cheat and not use a resistor, but only when you can guarantee the voltage going to the LED (or that the current is limited properly), which is why it's not frequently done (at least not by amateurs and hobbyists).

If you don't have access to a bench supply, you can do as Redbelly98 suggests, and then use the DMM to figure out what the diode voltage is, and then choose a more appropriate resistor value to increase (decrease) current (the steepness of the voltage-current curve means that you're probably pretty close to the design voltage of the LED).

EDIT: If all the talk of curves doesn't ring a bell:
http://en.wikipedia.org/wiki/Diode#Current.E2.80.93voltage_characteristic
 
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