Step 4: Make the LED Array
Now bend the leads of one set to the side and attach another set between the two bent leads. Repeat this until you have filled out the entire grid.
Note: Always check the polarity of the LED's you are soldering. This configuration creates five parallel blocks of four LED's in series.
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first of all: "this will work, but it's not true." what does that mean?
second, i have no idea what you are trying to say diodes are for, so i'll tell you. they are mainly used to allow current in one direction and not the other.
as for the 1mV thing, i'm not sure what you're trying to say here either. but i am aware that diodes follow ohm's law.
infrared LEDs typically have at least 1.2V required to forward bias. so by putting four of them in series: 1.2 x 4 = 4.8V your voltage drop is around 4.8V. a 9volt battery minus 4.8V = 4.2V. so the LEDs are seeing 4.2V each.
i've measured the internal resistance of two IR LEDs. one had 81ohms, the other had 82ohms. lets even play it safe and say they are only 50 ohms each. 4.2V going in to four 50ohm LEDs in series = 21mA. that's low enough right there. but when you consider that they were closer to 80ohms, you get only 13mA.
in short, you are in absolutely no danger of melting an LED if you follow the instructions that m_jake gives for this project.
as a side note, IR LEDs have the lowest internal resistance. as you move up in hertz, you get higher forward bias, and higher internal resistance. so blue LEDs are the highest. (i've never seen a purple LED.)
have fun
when i say internal resistance i'm including effective resistance as a result of voltage drop. i found it by connecting them to a 4.94V source in series with a 219ohm resistor. current was 16.44mA and 16.41mA.
4.94V / 16.44mA = 300.5ohms.
300.5ohms - 219ohms = 81.5ohms