What happens to batteries connected together with a resistor?
Assuming we are talking about the circuit below:



...then the voltage across the resistor is indeterminate. If we assume the batteries are mathematically ideal voltage sources, then the circuit is like saying 5 = 1. It can't be solved because it's inconsistent to begin with.

Just because ideal batteries create a mathematical problem doesn't mean building the circuit with real batteries breaks any physics (but it will quickly break the batteries themselves, wire used to connect them, and/or the experimenter). Actual batteries and the wire used connect them have some a small but nonzero series resistance. If we model the internal resistances of the batteries then the circuit to analyze looks like this:



For a typical battery, R1 and R2 will be under an ohm. The series resistance makes the circuit solvable.