In a direct current circuit, when is a current negative and when is it positive.
Not sure what you mean. Generally, positive or negative is with respect to some direction.
lets say I have a direct current circuit and i have a battery with + and - terminals with a wire between them and i have electrons flowing from the negative terminal to the positive terminal through the wire. Is the current in this case a positive value or a negative value?
and now lets say that this time I have protons going from the positive to the negative through the wire instead. Is the current value in this case positive or negative?
Sorry, but I don't understand what you're asking. The current has a direction, as you indicated. (Conventional current is the direction in which positive charge carriers would flow.) Whether you call the current positive or negative depends on what you are taking as the positive direction.
Do you have a specific example of a problem you are asked to solve that requires the sign of the current?
Current is positive when measured in the direction in which it is flowing. It's negative when it's measured in the opposite direction.
sorry im not very good at this but lets say I have a battery with + and - terminals and I put a wire between them. So now im guessing the electrons flow from the - terminal to the + terminal through the wire. Now lets say I choose the the direction of the flow of the electrons as the positive direction (from - terminal to + terminal) , what is the sign of the current?
Again, the conventional current moves opposite to the direction that the electrons move. That current moves from + to -. Since you defined that as the negative direction, the current will be negative. But it depends on what real question you are trying to answer with the 'sign' of the current.
As PhaseShifter stated, if you are moving from A to B, then that is the nominal positive direction. If the current moves in that direction, consider it positive. (Of course, if you go from B to A, that current will be negative.)
Separate names with a comma.