My textbook says, that across a battery or a cell there should be a potential drop equal to its e.m.f. Now consider a simple circuit with a cell of e.m.f 9 V. Let us assume a point on the negative terminal side of the cell to be of 0 potential. Then any point on the other side of the cell must be of electric potential 9 v. Now I've also learnt from sites that the potential at all points connected by a wire (or simply a conductor) remains same. Now consider any point on the wire and it is connected with the part having 9 v (with the positive terminal) and the 0 v part (the side close to negative terminal). This means that particular point must have both 9 v and 0 v at the same time instant. Unfortunately, I also read that potential at any point at any instant is unique - a point cannot have 2 potentials at the same time - implies - this circuit cannot exist.
Does this mean there will be no potential difference because two potentials cannot exist here? If that is true then no current should be flowing through the battery implying that the battery doesn't spend any of its chemical energy. But even when battery is simply connected by a wire into a complete circuit it slowly dies - it spends chemical energy by converting it to electrical energy to create the potential difference but from my assumption that shouldn't happen. How do I solve this confusion? -- There should be a potential difference but there shouldn't be a potential difference.
(note: potential difference means or is the alternative term for voltage) (assume the wire has zero resistance)