My question is about the LED connection through a resistor ?

You do not use a resistor to rectify, you use a resistor to change the amount of current flowing.

For a 12V power supply there will be a 2V drop across the resistor. The LED is a maximum of 50mA but should be lower at about 20mA and typically 10 ~ 15mA is even better. So for a 10mA current flow with the 10V remaining, you would need 10 V / 0.01 Amps = a 1,000 resistor for EACH LED.

[If you want it brighter, then use 20mA or 0.02 so 10 V / 0.02 Amps = 500 ohms. The power rating of the resistor is P = I^2 * R so (0.02)^2 * 500 = 0.2 watts or roughly 1/4 watt, which is close to the maximum rating which you should not go any closer.]

Keep in mind that a tricolor LED which has RED GREEN & BLUE LEDS has (3) LEDS, so if you want all three on you need (3) 1,000 or 500 ohm resistors for each LED.

The way you designed things the resistor has to dissipate 5 times the amount of power as the LED.

The heat has to get out of the resistor somehow.

10 volts X 0.05 amps = 0.5 watts

>the resistor gets too hot and it even melts my insulating rubber.

That's because the wattage rating for resistors is based on them being in open air. When you insulate the resistor the amount of wattage they can dissipate drops.

>Solution...?

-Redesign things so that the heat can get out of the resistor.

For example, thermally couple it to a metal housing using non-conductive heat sink goop.

or

-Use power resistors and design the surroundings for them to run hot.

-use a string of lower ohm resistors to spread the heat around.

-use a buck converter to not waste so much energy (which ends up as heat).

Resistors do get hot, you need to use a higher wattage rated resistor

200 Ohm is fine, you may want to use a 0.8 W resistor

http://www.hebeiltd.com.cn/?p=zz.led.resistor.calc...