A potential divider a voltage and reduces it to another voltage.It does this using a series circuit in which the voltage across eachresistor is divided in the ratio of their resistances.
The total resistance in the circuit above is
sincethese resistances are in series. Then 
Now apply
to
The power dissipated by
ismaximum when
Apotentiometer has the same arrangement, with the difference that theresistances are continuously variable. One such is shown below.
By moving the point of contact A, the ratio x:y and R-1 : R-2 canbe changed continously. Equation (1) becomes 