Translation:Please turn on the light.
Depends on context really. In most contexts indoors it means electric light. However if you were to go outside and talk about a street light it would be referred to as something different: 外灯 (がいとう, outside light), although you would still be understood if you said でんき. If you were in a science class talking about electricity then 電気 (でんき) would be used.
Quite honestly, I was thinking about turning the electricity on in a house, as one does when one moves in or after one has cut off fuses or circuit breakers to do repairs. I am not a particularly DIY person, but I have several times had to ask my daughter to turn the electricity back on after I had fixed something in a lighting fixture. The light itself, however, might very well be in the off position.
Hmm in that situation you could say "ブレーカーを上げてください", "bureekaa o agete kudasai". Literally "please raise the breaker". Although I'm sure you would be understood if you said something like いえの電気 there are more... colloquial ways to say it.
The hover hint for "電気" shows only "electricity", yet "Please turn on the electricity," is marked incorrect. Perhaps "light" should be added to the hover hint?
Prepositions are entirely abitrary and culturally specific. The definition of things like "on" and "above" is not at all consistent between cultures. English is terrible for this because we have so many hundreds of commonly used prepositional phrases/phrasal verbs. Think about the difference between "shut down" and "shut up". How many different contexts they have and whether any thing is actually moving down or up.
Is there any relation between this phrase and 気をつけて (often translated as "be careful" or "take care")?
I'm pretty sure that only the kanji are related, but because there aren't spaces in Japanese, I'm pretty sure Duolingo sees "気をつけて" when you are hovering over "電気をつけて". If you were to say "be careful", it would be pronounced differently as the kanji would be isolated and in a different context (it would be "kiwotsukete").
what about the case where something needs to be turned on. In my Australian I would say 'turn the power on' (to a computer/tool/appliance etc) I thought this was the Japanese phrase - obviously not!
I hear 起動する (kidou suru) for booting up a computer. I think 電気をつける is used mostly just for turning on lights.
This is similar to the Hungarian sentence: Kapcsold fel a villanyt! :) Kapcsold fel: Turn on villany: electricity, but also the electric light in a room