The ballast resistor can be calculated using the formula: R = V −V LED I = 12− 2 0.03 = 333Ω R = V − V L E D I = 12 − 2 0.03 = 333 Ω. The resistor must have a resistance of 333 Ω. If the precise value is not available, choose the next higher resistance value to keep the current below the LED limits. The LED voltage drop depends on their colour (1.8 - 4.0V), to make them 12V compatible they need a series resistor which is built into '12V LEDS'. There's not really such thing as a "12V LED". Anything labeled and/or sold as such is really a 'normal' LED with a series resistor 'built-in'. \$\begingroup\$ It has little to do with the relative brightness between LED's, of course current limiting changes the brightness of an LED, you can't put the same resistor on two LEDS and expect the same brightness. The other reason why you current limit, is to protect the LED from a supply that has a much higher voltage than the LED's current. If you put more than 3V across a red LED without
Part of a larger circuit? Series? Parallel? Playing with LEDs is supposed to be fun, and figuring out the answers to these questions is actually part of the fun. There's a simple formula that you use for figuring it out, Ohm's Law. That formula is V = I × R, where V is the voltage, I is the current, and R is the resistance.
Let's assume you have a supply voltage of 12v dc. The chosen LED is rated at a Max forward current (Shown as IF) of 20Ma and its working avearage voltage is 2.2v. The sum is then supply V - LED v / forward current. Or 12v - 2.2 divided by 0.20. (12-2.2=9.8/0.02 = 490) Therefore a resistor of at least 490 ohms is required.
Dimming an LED light is, add a resistors to the connection or even several resistors, to ensure you get the right brightness, this is called analog dimming. There is probably already a resistor in the line to drop the 12V, so the actual value you need is probably less than 10K. Now, we get to the tricky part: some LEDs will begin to dim

For example, I know the "12 volt" power supply to my old slot-car track put out considerably more than 12V, especially with a capacitor across the terminals. A 12 volt car battery charges on something like 14 volts, so in a car it might need to withstand that voltage, but by itself it's 12.6 volts fully charged, which I'm sure is close enough.

Uuot.
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    • do 12v leds need resistors