calculation of current in a resistor
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. (a) The circuit redrawn with + at the top and - at the bottom. (b) A real-world setup with internal resistance.

The redrawn circuit of Figure 1 clearly shows that the voltage sources are shorted out. 

A theoretical ideal analysis can't be performed because an ideal voltage source can't have an output voltage and both its terminals at the same potential.

In the real case with two identical batteries there would be no voltage across R2.