Potentiometers

You know potentiometers as the volume control knob on almost any audio equipment, until recently when they started to go digital. Above is what's behind the panel, but more interesting is what's inside:

The potentiometer contains a strip of resistive material wrapped almost all the way around the inside of the body. The ends of the strip are connected to the two outer terminals. There is a third terminal, in the middle, which is connected to a wiper. That wiper contacts the curved resistive strip at some point along its length, which you control by turing the knob. In the picture above the wiper is pretty close to the left terminal. The symbol for a potentiometer says it all. (The arrow just represents the wiper, not a current)

You can think of a potentiometer as two resistors in series. Imagine separating the resistive strip at the point that the wiper touches it:

Since the end-to-end resistance of the potentiometer is unchanged, reagrdless of where we physically put the wiper or where we imagine breaking the resistive strip into two parts, we know that the total resistance between terminals 1 and 2 is a constant, which is called the resistance of the potentiometer, R, and that the two parts must add up to R:
R = R1 + R2 
(1) 
As you turn the knob, R1 and R2 change but their sum remains constant. Let's impose a voltage across terminals 1 and 2, using a battery. We'll measure the voltage across terminals 1 and 2 (call it V12) as well as that across terminals 2 and 3 (call it V23)

Remember that no current flows through a voltmeter. To emphasize that, I've drawn the part of the circuit where current flows black, while the "measure only" part is red.

             

The configuration of two resistors shown here is called a voltage divider. This term is usually used when the two resistors are fixed resistors, not part of a single resistor with a "tap" in the middle as they are in the case of a potentiometer. You can think of a potentiometer as an adjustable voltage divider.