That woke up a few brain cells. It has been a few decades since I went through electronics school but I do remember the power factor being important in the equation. The heat comparison is probably the sanest way to look at it.
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This brought back memories for me. Many years ago when I was in the early years of getting my EE degree, I had this class that covered basic electricity, power factors, etc. The class was fine, but the lab was unique. It was 4 hours long, and during it, no student was allowed to speak with any other student. Each week, the teacher would bring in some type of apparatus into the room, maybe with inductors or capacitors, or maybe just a bunch of light bulbs, or a motor. He would do "something" like unscrew a light bulb, and something unusual and unexpected would occur demonstrating something he had taught.
If you could figure it out, you could go up to the teacher and whisper it to him, and you were right, you could leave and you got an "A." If you were wrong, you had to go back to your seat and rethink it. If you were still in the lab after 4 hours, you received an "F."
I can't say I always got A's, but usually if you took the common sense approach, you could guess it. If you were one of those people that just crunched the numbers in their scientific calculator and just spit out the answer, they were almost always wrong. I guess it was at that point I learned, that sure, start with a calculator if you want, but before finishing, see if the answer makes sense. Does that bulb use 30 watts or 30,000 watts because you screwed up the decimal? Over the years this approach has saved me lots of problems.