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I was looking at a datasheet for a transistor here, but I didn't know what Collector Power Dissipation meant. It's value is 1 watt.

Does this mean that this part is rated 1 watt? They already have the maximum voltage and amperage, so that makes me question what this means. I couldn't find anything on Google either so I am confused as to what this is.

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You have to obey all the limits. The maximum power is a lot less than maximum voltage * maximum amperage.

Remember, dissipating power is what makes the transistor hot.

For bipolars, the absolute max values are not as useful as the safe-operating-area plot:

enter image description here

You'll notice one of the bounds is the maximum voltage, one is the maximum amperage, and one is the maximum wattage. Stay within the bounds to keep your transistor happy. (Also you need to avoid overheating: look at the Pc-Ta plot, or derive it yourself with the junction-to-ambient thermal resistance.)

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Well the part does have maximum current and maximum voltage, but that doesn't mean that you can run maximum current at maximum voltage.

What you should do instead is to switch to the page with graphs. That's the only safe way to determine how you can use the transistor. For example from top left graph on page two we can see that the 1 W rating only applies to temperatures below 20 and bit degrees Celsius.

You can also "simplify" things a bit and say that the part is rated at 1 W. The emitter current is base current plus collector current. We generally consider base current to be negligible (and therefore have very little impact on power dissipation), so collector current is used for power calculation.

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