Editing Potentiometer (section)

== Theory of operation ==
[[File:Potentiometer with load.svg|left|framed|A potentiometer with a resistive load, showing equivalent fixed resistors for clarity.]]

The potentiometer can be used as a [[voltage divider]] to obtain a manually adjustable output voltage at the slider (wiper) from a fixed input voltage applied across the two ends of the potentiometer. This is their most common use.

The voltage across {{math|''R''<sub>L</sub>}} can be calculated by:
<math display="block">
V_\mathrm{L} = { R_2 R_\mathrm{L} \over R_1 R_\mathrm{L} + R_2 R_\mathrm{L} + R_1 R_2}\cdot V_s.
</math>

If {{math|''R''<sub>L</sub>}} is large compared to the other resistances (like the input to an [[operational amplifier]]), the output voltage can be approximated by the simpler equation:
<math display="block">
V_\mathrm{L} = { R_2 \over R_1 + R_2 }\cdot V_s.
</math>
(dividing throughout by {{math|''R''<sub>L</sub>}} and cancelling terms with {{math|''R''<sub>L</sub>}} as denominator)

As an example, assume <math>V_\mathrm{S} = 10\ \mathrm{V}</math>, <math>R_1 = 1\ \mathrm{k \Omega}</math>, <math>R_2 = 2\ \mathrm{k \Omega}</math>, and <math>R_\mathrm{L} = 100\ \mathrm{k \Omega}.</math>

Since the load resistance is large compared to the other resistances, the output voltage {{math|''V''<sub>L</sub>}} will be approximately:
<math display="block">
{2\ \mathrm{k \Omega} \over 1\ \mathrm{k \Omega} + 2\ \mathrm{k \Omega} } \cdot 10\ \mathrm{V} = {2 \over 3} \cdot 10\ \mathrm{V} \approx 6.667\ \mathrm{V}.
</math>

Because of the load resistance, however, it will actually be slightly lower: {{math|≈ 6.623 ''V''}}.

One of the advantages of the potential divider compared to a variable resistor in series with the source is that, while variable resistors have a maximum resistance where some [[current (electricity)|current]] will always flow, dividers are able to vary the output voltage from maximum ({{math|''V''<sub>S</sub>}}) to [[ground (electricity)|ground]] (zero volts) as the wiper moves from one end of the potentiometer to the other. There is, however, always a small amount of [[contact resistance]].

In addition, the load resistance is often not known and therefore simply placing a variable resistor in series with the load could have a negligible effect or an excessive effect, depending on the load.