Sequence of running the current conduction simulation:
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1) Create geometry - you have done this
2) Create mesh - you have done this
3) Export mesh from SALOME as UNV
4) convert mesh into Elmer format by ElmerGrid 8 2 your_mesh.unv -autoclean
5) Make sure you have a correct mesh name in current_case.sif
6) Run ElmerSolver current_case.sif
7) Open your_mesh/current.vtu in Paraview, browse the results
8) Try changing material properties and potentials, see how the simulation responds

Things to mind, things to check:
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* In your_mesh/entities.sif, always check the nubering of boundaries and bodies
and make sure they are consistent with the Target Bodies or Target Boundaries entry
in your .sif file.
* Make sure to use the autoclean parameter with ElmerGrid