Oh, and I will concede the point that this thread was not placed in the Homework Help forum (which I really didn't even realize since I just click the e-mailed links to come straight here and have long since forgotten that it wasn't) and so adding additional information is much more appropriate here than if it had been located in Homework Help. By posting here, the OP basically forfeits the nice, constrained world of what is appropriate for their level in the learning process.

 

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So please explain how giving an example of how it is possible to EXCEED the 1/4 W rating of a resistor somehow gets the point across that the resistor can't always be relied up to be safely operate even when it is NOT exceeding the 1/4 W rating?
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I think the mistake you made in the logic is to assume a resistor's "1/4 watt rating" is the same thing as "1/4 watt".

"1/4 watt" is a simple quantity and won't be exceeded, so you are correct there.

But a "1/4 watt rating" must be respected in real word use as a resistor size and type, and a "1/4 watt rated resistor" must be run at less than 1/4 watt under certain circumstances.

 

You're missing the point of my question. How does showing an example in which the 1/4 W rating IS exceeded in anyway inform anyone that there are times when it may not be safe to operate the resistor even when the 1/4 W rating ISN'T exceeded.

It's like if someone where to give an example that said that a particular airplane, with a particular engine, could never exceed the Never Exceed airspeed. Someone else then points out that, well, it could exceed it if it were in a steep dive. They then use that case as the basis for saying that is shows how sometimes you can run into trouble even if you stay below the Never Exceed airspeed. While this might be -- in fact is -- a true statement, how does it follow from the case offered?