That's fantastic; like I said, I'm a total beginner, so I think I'm just about following it - if the resistor is less than 150 ohms I guess that means that the LED is getting too much current and burns out? And the resistor has to be 60mW because that's how much power is in the circuit? Does that mean that the LED also has a power rating of 60mW? Sorry if my questions are too basic, I'm trying to learn this stuff myself and finding the right steps on the internet takes a LOT of searchingHere's an example. A typical LED load is about 20 mA. For a 3 volt battery, you'd need a load resistance of (3 volts)/(0.02 A) = 150 ohms. The power rating of the resistor needs to be more than the current through the resistor times the voltage across it. Here, that's minimal at 3(0.02) = 60 mW. If the battery was unable to keep a voltage of around 3 volts across a 150 ohm resistor, it's time to put a tag on its toe and send it to the morgue.