>> Question: When did electricity become common knowledge?
>>
> I would say early to mid 1800's ... 1800 Volta (battery) or ... 1831
> Faraday (electric dynamo)

 From what I can gather from Wikipedia, Babbage's Analytical Engine was 
1837. It seems clear that at that data, some scientists at least were 
aware of the existence of electricity. But I can't find any word on when 
electricity came to be "useful", nor when it became "widely known".

And, obviously, no mention on whether Babbage himself knew it existed. ;-)

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