


A battery of voltage 6V is connected to
two resistors in series, as shown here. 
Let the voltage across R_{1} be V_{1} and across R_{2}
be V_{2} 
As they are in series, the two resistors have the same current,
I. 
From the definition of resistance we have 

It therefore becomes clear that in a circuit such as this, the two resistors
"share" (or divide) the voltage of the supply in the same ratio as their
resistances. 

This shows why circuits of this type are called potential
dividers (or voltage dividers). 


A variable potential divider can be made if we use all three connections
of a variable resistor. 

A typical variable resistor is shown here. 



This is the type of
variable resistor used in (non digital) volume controls etc). 

The
sliding contact is on an axle which can be rotated. 




This circuit shows the variable resistor used as a variable potential
divider. 

Here, the two resistors are formed by the two parts of the
variable resistor. 

This can
be very useful but it must be remembered that this is not a stable
variable voltage supply. If any significant amount of current is
allowed to flow between S and B (or S and A) the voltage will change. 

See here for more on using of variable resistors. 
