How do you know if a resistor will burn out?

All resistors have a rating called 'maximum power dissipation', usually referred to as simply 'power'. Typical values are 1/8 watt, 1/4 watt, 1/2 watt, 1 watt, etc. up to many hundreds of watts for specialized resistors. Basically, if you exceed the power rating for a given resistor, it will fail. If you run it right at maximum power, it will work for a while, but will have a fairly short lifespan and will eventually fail (this is true for all electronic components for the most part). If you run it well below its maximum rating, it will pretty much last forever. Take a 10 ohm, 1 watt resistor and connect it to a 12 volt battery (hypothetically, that is, don't try this at home!) The current through the resistor will be: I=E/R I=12/10 I= 1.2 amperes The power dissipation will be: P=I^2 * R P=1.2^2 * 10 P=14.4 watts A 1 watt resistor that is dissipating 14.4 watts will fail in seconds, accompanied by smoke and quite possibly fire! Now connect a 270 ohm, 1 watt resistor to the 12 volt battery. The current: I=12/270 = 0.044 amperes (44 ma.) The power: P=0.044^2 * 270 = 0.52 watts This resistor will certainly get warm, but is operating well within its power rating and will last a long time.