## 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.

• In the symbol for battery, the broad side is positive. If the battery is a 6 volt battery, what does voltmeter V12 read? (Easy question, but get the sign right)

• What is the current i that flows in the circuit? For this you can treat R1 and R2 as a pair of resistors in series, or you can treat them as a single resistor R.

• Given that the current through R2 is i as you calculated it above, what is the voltage measured by V23? Use the constitutive law of R2

• When the wiper is moved all the way toward terminal 1, what is V23? (Ask first, what is R1?)

• When the wiper is moved all the way toward terminal 2, what is V23?

• When the wiper is half way, what is V23?

• Your answers above reflected a constant voltage V12 from a battery. If V12 had been instead an audio signal from a CD player, and V23 were the audio signal going into your amplifier, what would be the effect of turning the knob all the way toward terminal 1? All the way toward terminal 2?

• Given that the knob would be above the body in the picture, and that we want full-clockwise to be loudest, should we use the left terminal as terminal 2, or the right terminal? Terminal 2 is called the common terminal, because it is involved with both the input and the output.

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.

• Draw a schematic diagram of the circuit below. (You can click on the battery, the battery holder , or the circuit board to see detail, and you may need the resistor color code) Calculate the current running through the three resistors, and then the voltage across the one that is being measured. What does the voltmeter read? Note carefully the polarity of the voltmeter.