Question

how rheostat work as potential divider

Answer 1

Rheostat is a large resistance which can be used as a variable resistance.  A very long coil made of a resisting material (conductor) is wound around a cylinder made of non conducting material.  The two ends T1 and T2 of the rheostat are connected between the source of potential E (battery).

Suppose we want a voltage/potential  V =  x * E   in our circuit , that varies from 0 to E , between two points A and B.      So x varies from 0 to 1.

We connect B to the negative terminal of the battery or to the ground.  The other end A is connected to third metallic terminal T3 of the rheostat.  T3 is touched up on the top of the cylindrical surface anywhere along its length. Thus only the potential difference in the wire wound between the T3 and T2 is available to the external circuit in AB.

By moving the position of the terminal T3 from one end to the other end of rheostat, we get voltage from 0 to E (max).