If
then at some point between A and B the potential will be equal to
If the potentiometer wire between A and B is uniform, then the potential at C will be proportion to the distance
When the potentiometer contact is at C, the potential difference across AC due to
is
and this is the voltage across the cell with EMF
so that no current flows. We have
These equation assumes that the contacts all have zero resistance and that the potentiometer wire is uniform. These conditions can be closely approached.