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Heres what I have:

12VDC Supply Voltage
3VDC Voltage Drop
20ma LED Current

I used to think that the Total LED Voltage Drop should equal the Supply Voltage. But after doing some research I found that the Total Voltage Drop should be less than 80% of the Supply Voltage.

So the correct circuit would look like this:
3 LED's in series with a 150ohm resistor and a 12VDC Supply Voltage.

My questions are this: does the resistor actually lower the voltage? and what would be the problem if 4 leds with the same Voltage Drop were used?

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LEDs operate from current. If you connect an LED to a voltage supply then it will burn out because the current will be unlimited.

The resistor in series with the LED or in series with a few LEDs in series limits the current according to Ohm's Law.

Most ordinary small LEDs have a max allowed current of 30mA. If an LED has a voltage drop of 3.0V (it is a range of voltages, it could be 2.5V or 3.5V) and a 12V supply is used then for 25mA the resistor is calculated as (12V-3.0V)/25mA= 360 ohms. 25mA was selected so that if the LED voltage is 2.5V and the 360 ohms resistor is actually 5% low then the current won't be high enough (more than 30mA) to burn out the LED.

If you connect four 3.0V LEDs in series and connect them to a 12V battery without a current liniting reasistor then they will immediately burn out, seem to operate fine or they won't light.
If they are actually 2.5V then the current will be unlimited.
If they are exactly 3.00V then they will work until the battery voltage runs down a little.
If they are actually 3.5V then they need at least 3.5V x 4= 14V to light.

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Okay, so If I use a 12VDC power supply with a 450 Ohm resistor (using 20mA) in series with one 3V LED everything will be fine then?

(12V-3V)/20mA = 450 ohms (or the next highest standard resistor)

See, for some reason, I have always thought that the 3V was all the LED could handle. But now its clear that current is the main thing to worry with. Voltage is important when considering how many LEDs in series you want to have. For instance if I wanted to max the amount of LEDs I could have in series on a 12V power supply I would take 80% to be the max amount of volts I should spent LED wise.

12V * .8 = 9.6V

With 3V LEDs only three could be in series. Is this correct?

(I used this as a reference: http://www.theledlight.com/LED101.html)

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