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The physical size of the resistor determines how much power(wattage), or heat can be dissipated. The larger the resistor the more power it can dissipate. Resistance is the opposition to current flow(electrons) and this opposition causes heat to be generated when current flows through it.
The AMOUNT of Heat dissipated per unit of time is measured in watts.
example if P=I X E (power formula)
P=Power(watts)
E=Voltage
I=Current
ohm's law-->E=I X R
say you are using a 1/2 w 100 ohm resistor and you put 12VDC thru the resistor to ground.
determine the current: I=E/R
I=12V/100 ohms
I=120 ma.
Plug in value into ohms law formula.
P=I X E
P=.120 x 12
P=1.44 watts (resistor will be dissipating 1.44 watts at 12v with 120 milli amps flowing thru it.
Resistors come in different wattage values( 1/8w, 1/4w, 1/2w, 1w etc) usually printed on them. So for this case you would need at least a 2 WATT resistor and still be safe and NOT BURN and destroy it to a crisp.
If the resistance has not changed then your resistor passed the required safe amount of current.
If the resistance has changed you may have burned the resistor with too much current and thus you have overpowered it.
You can also use a wattmeter and measure the wattage as voltage and current is applied to the resistor at a given resistance.
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