Electrical Circuits?

Is there ever a use for having both the white and black wire hot, or would that in all cases a mistake made somewhere earlier in the circuit.

Would wires of different circuits (operating from different jumpers), ever be connected together.

Answers:
yes it can be most often for a light from a switch (single leg run). Not the right way but, acceptable

Other answers:
It depends...what country are you in? In the US, the NEC requires AC voltage cables be wired:

Black - Hot, White - Neutral, and Green - Ground.

Other countries have different standards.

If you're in the US, and you see a difference in potential between the Green and White wires, there may be a short circuit somewhere.

I don't follow the second part of your question. Please elaborate. If you're asking whether it's acceptible to wire multiple circuits off of one breaker, then the answer is "No". NEC states one wire under each lug in the breaker box. No exceptions.
It depends...what country are you in? In the US, the NEC requires AC voltage cables be wired:

Black - Hot, White - Neutral, and Green - Ground.

Other countries have different standards.

If you're in the US, and you see a difference in potential between the Green and White wires, there may be a short circuit somewhere.

I don't follow the second part of your question. Please elaborate. If you're asking whether it's acceptible to wire multiple circuits off of one breaker, then the answer is "No". NEC states one wire under each lug in the breaker box. No exceptions.
Quite frequently in home wiring, the white and black wire would go to a switch, since a switch can only be placed on the HOT wire, and they don't make cable with 2 black wires in it. The white SHOULD be reidentified with black or red tape or marker.

One of the wires to the switch would be always hot, the other would be hot only when the light is on, and it should go to the light/whatever is being switched.

I can't think of a reason why two circuits would be connected together.
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