Kt Kingtronics Potentiometer Theory of Operation

7 Jan 2011

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 the most common use of them.

The voltage across RL can be calculated by:

$V_\mathrm{L} = { R_2 R_\mathrm{L} \over R_1 R_\mathrm{L} + R_2 R_\mathrm{L} + R_1 R_2}\cdot V_s.$

If RL is large compared to the other resistances (like the input to an operational amplifier), the output voltage can be approximated by the simpler equation:

$V_\mathrm{L} = { R_2 \over R_1 + R_2 }\cdot V_s.$

As an example, assume

$V_\mathrm{S} = 10\ \mathrm{V}$ , $R_1 = 1\ \mathrm{k \Omega}$ , $R_2 = 2\ \mathrm{k \Omega}$ , and $R_\mathrm{L} = 100\ \mathrm{k \Omega}.$

Since the load resistance is large compared to the other resistances, the output voltage VL will be approximately:

${2\ \mathrm{k \Omega} \over 1\ \mathrm{k \Omega} + 2\ \mathrm{k \Omega} } \cdot 10\ \mathrm{V} = {2 \over 3} \cdot 10\ \mathrm{V} \approx 6.667\ \mathrm{V}.$

Due to the load resistance, however, it will actually be slightly lower: ≈ 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 will always flow, dividers are able to vary the output voltage from maximum (VS) to 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.

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Kt Kingtronics Potentiometer Theory of Operation

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