Batteries are always labeled with their emf, would it also be appropriate to put a label on batteries stating how much current they provide? Why or why not?

Ans: No, a battery does not always produce the same current, no matter what circuit it’s used in. The current in any electric circuit consisting of a cell of emf E and internal resistance r and an external resistance R is given by 

 I = E/(R + r)

 This equation shows that the current that a source of emf produces in a given circuit depends on the external resistance R as well as the internal resistance r of the cell. The greater the resistance, the less current the source will produce. So, however, a battery has a fixed emf, it may not have the same magnitude of current. Hence, it is not appropriate to label with current.