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Virginia
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I have a project whereby I am using 5mm Clear LED Extra Bright 20,000mcd.

What resistor should I use to gain the most brightness without burning out the LEDs?  I currently have 10-kohm .25 Watt carbon filters and some resistors that came with my Arduino (22O-ohm and 27O-ohm).  I noticed there is a big difference in brightness.

Thanks!
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As always you want to look to the datasheet of the specific part, if available, for the standard operation and maximum ratings.  Then you can use that information to determine the current through the LEDs you want to set using the resistors.   First total the voltage drop of the LEDs (if you are using more than one) and subtract from 5 VDC, that's the voltage drop that will be across the current limiting resistor.  Then use Ohm's Law, VR = IR * R, to figure the resistance that will get you closest to the desired current.

Of course if you are powering the LED directly from the Arduino's I/O pins, this current should always be below 40 mA.  I'd suggest keeping it below 35 mA or even 30 mA if the LED will be on for prolonged periods to be more certain you won't damage the I/O pin.
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For more on how to use the datasheets...

http://www.arunet.co.uk/tkboyd/ele1led.htm
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LEDs have a voltage drop across them.
Red ~2.5V, Green/Blue ~3.3V.
Measure the drop across yours using a 270 ohm resistor.

Then, most LEDs are rated for 20mA for being on continuously.
So the resistor needed would  be:
(5V - Vled)/.02 = resistor in ohms
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Well...I appreciate the info but I am still stuck.

According to DipMicro they even say refer to the manufacturers datasheet. LOL the only problem is that I do not see it.  The manufacturer is listed as generic.

According to the product page it gives the Forward Voltage and Current Rating (http://screencast.com/t/Pzl0Xnz7)

The product page is here http://dipmicro.com/store/LED5W

Is there a way to use my tester?  I can measure volts perfectly (well for me that is).  But I cannot quite figure out how to test Ohms.
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You don't test ohms - you calcute how many ohms are needed to meet your current goal/requirement.
If you know the Forward Voltage, and you know the current you want, and you know the voltage of your source, then you can calculate the resistance needed:

(Vsourse - V(LED forward voltage))/current desired = resistance

So
(5V - 3.2V)/20mA = 90 ohm
I think both 91, 100 are standard, go with those.
20,000mCD is VERY bright, do not look directly at the light.
You may find you have to increase the resistance a LOT and only run at 3-4mA to make the brightness bearable depending on where the LED is being used.
(5-3.2)/.003 = 1.8K
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Arduino for Teens available at Amazon.com.

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Thanks Crossroads!

You added greater clarity to that formula that makes PERFECT sense to me.

As far as looking at the light...I figure I need a really bright light to walk into in case my Arduino electrocutes me.  lol
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