This is a very basic general guide for people who don’t know much about LEDs or Electronics at all, we make some generalised assumptions to simplify matters and don’t go into details, if you want to know more details, start with learning about Ohm’s Law.
So you have yourself some LEDs, and you want to connect them to some power supply.
An LED has a “Forward Voltage”, this is the “number of volts” that it will “use up” in order to light, a Blue led for example has a forward voltage around 3.2 Volts, so the LED will “use up” 3.2 Volts to produce light.
The number of volts an LED “uses up” does not change (significantly) no matter it’s brightness. But the amount of current (milliamps) does, and most importantly, too many milliamps and the led will burn out instantly. Most standard LEDs have a maximum recommended current around 20 or 30 mA.
So what we have to do is limit the current, the easiest way to do this is to use a suitably sized resistor.
How do you work out what resistor you need ?
Here is a rough ballpark formula for you for 1 or more led's in series which will get you around 20mA through them (give or take!)
First, we define how many volts your power supply puts out;
VSupply = 12
Then we add together the voltages of the LEDs you will have in series, we group these into red, green, yellow and blue, white.
Vf1 = (R+G+Y)*2.1Vf2 = (B+W)*3.1
Now we know how many volts the leds will “use up” we find out how many volts are “remaining”
Vremaining = VSupply - Vf1 - Vf2
And finally we can calculate the Resistor we require
ResistorOhms = Vremaining / 0.02
Note that if the Vremaining is negative, you have too many led's in series, there are not enough volts to power them (in which case you can make more than one smaller series string each with it’s own resistor, and join those strings in parallel).
Here is an example string of 2 Red, 1 Green and 1 Blue in series ( Supply+ > R > R > G > B > Supply- )
VSupply = 12Vf1 = (2+1+0) * 2.1 = 6.3Vf2 = (1+0) * 3.1 = 3.1Vremaining = VSupply - Vf1 - Vf2 = 12 - 6.3 - 3.1 = 2.6Resistor = 2.6 / 0.02 = 130 Ohms
Finally, remember that unlike a light bulb LEDs only work in one direction, the Positive voltage must be applied to the Anode (long leg on standard 5/3mm leds), and the Negative voltage must be applied to the Cathode (short leg on standard 5/3mm leds), and when chaining “in series”, you connect the Cathode of the first to the Anode of the second… and so forth.