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There is a chapter on this very question in a wonderful little book
entitled "Similarities in Physics" by John Shive and Robert Weber.
(That's the same Shive that gave us the Shive Wave Machine, which has
become a staple in lecture demonstrations.) In general, if you
regard impedance as the ratio of cause to effect [and let's NOT get
into cause/effect arguments here], then in electrical circuits the
ratio would be the applied voltage to resulting current and the power
is their product.
Shive and Weber give examples from many areas, whether they be wave
physics or mechanics, etc. and talk about impedance matching devices
(transformers) in all of these situations for maximum transfer of
power. The book is a lot of fun.