Potentiometer

Spirit level shows same height or 2 points of the same gravitational potential . Potentiometer shows same electric potential has reached by indicating zero reading on a galvonometer at balance length. When two points have the same potential , no current flows and that explains the galvanometer reading. Since no current flows from one circuit to the other, these two circuits can be taken to be undisturbed (ie current constant within each circuit) and therefore solved separately.