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Using a high brightness LED, two calculator batteries, a little piece of wire, and an SD card case, I created this really spiffy little pocket flashlight in about 2 minutes flat.
Step 1Connect the batteries
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Using electrical tape (I chose white) and about 3/4 inch of wire, connect the two batteries in series. Using a longer piece of tape on the back side, I also taped the positive lead of the LED to the first battery, laying the other lead (the fuzzy line in the second pic) over the negative terminal on the second one.
If the batteries are 1.5v each, then you don't need a resistor for the 3v total because the white LED wants to see 3.4v. Funny thing about white and blue LEDs, they have a "threshold" where they run up to full brightness only between 3.2v-3.4v. When they are fed from 2.5v-3v they tend to just "glow" at around 1/2 brightness - but the LED will last forever, and so will the battery with such a low current draw (somewhere around 5mA at this voltage).
If the batteries are 3v each (which is most likely here), then you have a 6v total and you should use a resistor.
There are two ways of looking at this scenario however.
1- do you want to run this thing for the next decade reliably? If so, a 100 Ohm resistor would see that it lasts good and long.
2- do you want lots of light for short periods of time and don't care about living past a year or two? Then don't bother with the resistor. BUT - even with the batteries' internal resistance, you will still get 60mA to 80mA across the LED which will make it get warm. Heat is what kills LEDs, so if you use the circuit wisely with minimum on-time (or provide heatsinking for the leads as close to the LED base as possible) you will still get fairly good lifetime...and lots of bright light.
* for what it's worth - one way of "heatsinking" a bare LED is to make a bead of epoxy (the good stuff that hardens like "glass") across the leads at the base of the LED, which can also serve to cement the LED into its enclosure.
I like the way you think. ;)