Simple Circuit analysis of potentiometer problem

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Really simple problem but:

If you have a circuit with a power supply, a potentiometer and an output voltage taken from midway down the potentiometer and just after it; would this act like a potential divider with the potentiometer acting as two resistors?
 
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Yes, It will act like a two resistors voltage divider.
But only without the load resistor.
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Keep in mind that is only true if the potentiometer wiper is connected to a high impedance. If there is a finite input impedance to the circuit that follows the wiper, then that impedance needs to be included in the circuit analysis to figure out the wiper voltage.

Also, it is not good design practice to connect a high impedance to a potentiometer wiper. There is a minimum wiper current needed to keep the potentiometer reliable. This is a good reference for using potentiometers:

http://www.google.com/url?q=http://www.bourns.com/pdfs/trmrpmr.pdf&sa=U&ei=vLOFT5nRKsSQiAK8vIH3BA&ved=0CBAQFjAA&usg=AFQjCNFDFeeCAZLuimBWRSHq48nFEuHt3Q

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Yes, this circuit can be analyzed as a potential divider with the potentiometer acting as two resistors. The potentiometer can be thought of as two resistors in series, with the adjustable wiper acting as a variable connection point between them. The output voltage taken from midway down the potentiometer would be equivalent to the voltage at the junction between the two resistors in a typical potential divider circuit. The ratio of the two resistors, determined by the position of the wiper, would determine the output voltage. This concept is commonly used in circuit analysis and can be applied to this simple potentiometer problem.