What is the difference between electric and electrical and their usage?
For example, what is the difference between "electrical machine" and "electric machine"?
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These two words have a large semantic overlap, but at the edges there are a few key differences.
Electric is used to describe things pertaining to electricity. It can also be used metaphorically: "the evening was electric".
Electrical can be used nearly everywhere that electric is used when pertaining to electricity (aside from some set phrases). It is not generally used metaphorically in the way electric is. The word electrical can also be used in an additional domain: things concerning electricity. So, generally, people do not say "electric engineer" unless the engineer runs on electricity; instead they say "electrical engineer".
So, in the case of "electric(al) machine" from your question, since you are talking about something that runs on electricity, the two words are essentially identical in meaning.
Here's a simple distinguishment which I hope will help:
Electric refers to anything that runs on electricity, i.e. “electric kettle”
Electrical refers to something related to electricity, i.e. “electrical faults”, “electrical component”.
"Electric" is used in front of a device or machine that runs on electricity. It is used when the object has been specified.
"Electrical" is used in a more general sense, as in referring to ambiguous nouns. (By ambiguous, I mean unspecified, e.g. machine, appliance). "electrical" is also used when the object is specified, but the object is not run on electricity, but is related to electricity, i.e. Electrical engineer.
Electric means "of, worked by, charged with, or producing electricity."
It can be used figuratively, as in "the atmosphere was electric;" to refer to a musical instrument, as in electric guitar; or to refer to a color, as in electric blue.
Electric cannot be always replaced with electrical; you don't say electrical guitar, or "the atmosphere was electrical" (if not to mean something else than the phrase using electric).
In addition to what has been said so far, "electric," unlike "electrical," can be used as a noun for an electrically powered machine or vehicle.
Electric used about something that works using electricity, for example, electric cooker , electric guitar, electric kettle. Electrical used about things in general that use electricity, or people whose job is to make or repair these things: a company manufacturing electrical goods|, an electrical engineer electronic used about equipment such as computers and televisions that work by using extremely small electrical parts, or about systems that work using computers: Most kids love electronic games.|Email is the short word for electronic mail.