power dissipation
When current is forced through a resistor, the resistor fights back, and that struggle turns electrical energy into heat, exactly like rubbing your hands together turns motion into warmth. Power dissipation is the rate at which that heat is produced, measured in watts (W). Every resistor in a real circuit gets at least a little warm, and your job as a designer is to make sure it never gets too warm.
Power is voltage times current: P = V times I. Using Ohm's law you can rewrite that two handy ways for a resistor: P = I^2 times R (current squared, times resistance) and P = V^2 / R. The squared terms are a warning, because doubling the current quadruples the heat. A concrete case: 5 V across a 100 ohm resistor carries 50 mA, so P = V^2/R = 25/100 = 0.25 W, a quarter of a watt. That part runs hot, and you would not put it in a tiny resistor rated for one-eighth of a watt.
This is why resistors come with a power rating, commonly 1/8 W, 1/4 W, or 1/2 W for small ones, and tens of watts for chunky wirewound types. Good practice is to pick a rating with comfortable margin, often twice the calculated power or more, a habit engineers call derating. Push a resistor past its rating and it drifts in value, discolours, and eventually chars or burns open. Heat is the silent killer of electronics, so estimating dissipation early is not optional.
A 12 V supply drives a 10 ohm load resistor. Current is 12/10 = 1.2 A, and dissipation is P = I^2 times R = 1.2^2 times 10 = 14.4 W. That demands a big wirewound resistor on a heat sink, not a tiny axial part.
The I^2 R term grows fast, so high-current resistors need surprisingly large power ratings.
A resistor's value tells you nothing about how much heat it can take. Always check P against the part's power rating and leave margin, because exceeding it shifts the value and can start a fire.