Resistor Power Rating: What Does It Mean?

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quantum13
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i have a question about resistors. i thought they were described by their resistance - 20 ohm, 40 ohm, 2 Megaohm, etc.

how come I see "power" values on resistors? for example my lightbulb says 40 watts. but i thought the power is simply P = V^2/R and that would depend the voltage of my power outlet whatever that happens to be. The power would only be partially determined by the lightbulb. so what does it mean to see a power value on a resistor?
 
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Q, If you put too much current through your resistor it will get too hot. There are different resistor types intended for different degrees of power they need to dissipate. Maybe P=I^2 * R, so it's a current limiting rating.