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Potential Dividers
   
A battery of voltage 6V is connected to two resistors in series, as shown here.
Let the voltage across R1 be V1 and across R2 be V2
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.
 
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