Let say for example, that I want to use in a 12 V lighting system. I will need : 1 K ( the base resistor ), TIP 31 , LuxLED, 13 ohms @ 6 Watt ( the limiting resistor ) , Heatsink - DIY type will do. ( for the LED, the transistor and the limiting resistor ). Make sure the PSU can supply at least 1.5 A. My imaginary system use a car battery. My 2 cent.
Your lamp circuit -- http://itp.nyu.edu/physcomp/Tutorials/HighCurrentLoadsYou see 3.2? You can ditch the Arduino and transistor amd the wires that connect to them.External power goes to power and ground directly since it's the -only- power left.The yellow wire on the lamp goes to the middle leg of the pot and the green wire goes to ground.Turn the pot adjusts the lamp.