Yes, transmission lines have known losses which need to be accounted

for and factored into their designs, but that has nothing to do with

the current discussion. There are no long distance transmission lines

in a residential or even commercial property, so the losses from such

lines are irrelevant to the current discussion. I suspect the reason

you were never taught that is because this is far outside your area of

expertise, which I believe is what you said in a previous post.

Take your example of the electric dryer. If you have two dryers, one

designed for 120v and the other designed for 240v, the 120v model will

draw twice as many amps as the 240v model. Both dryers will use the

same number of Watts, (because P=IE), assuming the only differences

between the two models are the voltages they are designed to operate

with.

If we're having a technical discussion, then P (power) is expressed in

Watts, not amps. Current draw refers to amps, but power refers to

Watts. Watts are the product of amps times voltage. (P=IE)

If you're saying that "P equals IE" is wrong, and should be restated

as "P is approximately equal to IE", well we better get the textbooks

updated with this new formula. In the meantime, yes, if E is doubled

then I will be halved and P will remain unchanged. It doesn't just

work that way in the textbooks, it works that way in the field, too.

Not a bad idea to dust off the books now and then.