Suppose we have a bulb or a forward-biased LED (or any other component) which needs no more than say 3 V across it to operate. And we want to connect it in series with a voltage source of say 12 V, and a resistor. So without this resistor, the LED would quickly burn out and be destroyed. I've edited a diagram to illustrate the situation: [PLAIN]http://img225.imageshack.us/img225/6515/circt2.jpg [Broken] How can we calculate the value of this resistor in series with the LED and the battery, that limits the current flow through the LED to a safe value, and reduce the 12 V to 3 V? I know that there many websites and softwares that can calculate the value of the resistor, but I just want to know how engineers would do the calculation without using them. Is there a quick method or a formula? And what if there are two (or more) LEDs instead of just one? I couldn't find any methods for this in my physics textbook so any guidance is greatly appreciated.