# Potentiometer

A potentiometer is a variable tapped resistor that can be used as a voltage divider. The same term is applied both to an electrical component and to a measuring instrument.

As an electrical component, a potentiometer is a three-terminal resistor with a sliding contact that forms an adjustable voltage divider [1]. If all three terminals are used, it can act as a variable voltage divider. If only two terminals are used (one side and the wiper), it acts as a variable resistor or rheostat. Potentiometers are commonly used as controls for electrical devices such as a volume control of a radio. Potentiometers operated by a mechanism can be used as position transducers, for example, in a joystick.

A potentiometer instrument for measuring the potential (or voltage) in a circuit taps off a fraction of a known voltage from a resistive slide wire and compares it with the unknown voltage by means of a galvanometer. The sliding tap of the potentiometer is adjusted and the galvanometer briefly connected to both the sliding tap and the unknown potential; the deflection of the galvanometer is observed and the sliding tap adjusted until the galvanometer no longer deflects. At that point the galvanometer draws no current from the unknown source, and the magnitude of voltage can be calculated from the position of the sliding contact. This null balance method is a fundamental technique of electrical metrology.

## Potentiometer as measuring instrument

File:Pot schem.svg
Schematic symbol for a potentiometer. The arrow represents the moving terminal, called the wiper.

Before the introduction of the moving coil galvanometer, potentiometers were used in measuring voltage, hence the '-meter' part of their name. Today this method is still important in standards work. The null-balance principle of measurement is also used in other areas of electronics.

The potentiometer used for measurement is a type of bridge circuit for measuring voltages by comparison between a small fraction of the voltage which could be precisely measured, then balancing the two circuits to get null current flow which could be precisely measured. Measurement potentiometers are divided into four main classes listed below.

#### Constant current potentiometer

This is used for measuring voltages below 1.5 volts. In this circuit, the unknown voltage is connected across a section of resistance wire the ends of which are connected to a standard electrochemical cell that provides a constant current through the wire, The unknown emf, in series with a galvanometer, is then connected across a variable-length section of the resistance wire using a sliding contact(s). The sliding contact is moved until no current flows into or out of the standard cell, as indicated by a galvanometer in series with the unknown emf. The voltage across the selected section of wire is then equal to the unknown voltage. All that remains is to calculate the unknown voltage from the current and the fraction of the length of the resistance wire that was connected to the unknown emf. The galvanometer does not need to be calibrated, as its only function is to read zero. When the galvanometer reads zero, no current is drawn from the unknown electromotive force and so the reading is independent of the source's internal resistance.

Because the resistance wire can be made very uniform in cross-section and resistivity, and the position of the wiper can be measured easily, this method can be analyzed to accurately determine the uncertainties in the measurement. When measuring potentials larger than that produced by a standard cell, an external voltage divider is used to scale the measured voltage down to approximately 1 volt for measurement by the potentiometer; the uncertainties due to the voltage divider construction and the load placed on the source by the voltage divider then become part of the uncertainty of the overall measurement.

#### Constant resistance potentiometer

The constant resistance potentiometer is a variation of the basic idea in which a variable current is fed through a fixed resistor. These are used primarily for measurements in the millivolt and microvolt range.

#### Microvolt potentiometer

This is a form of the constant resistance potentiometer described above but designed to minimize the effects of contact resistance and thermal emf. This equipment is satisfactorily used down to readings of 1000 nV or so.

#### Thermocouple potentiometer

Another development of the standard types was the 'thermocouple potentiometer' especially adapted for temperature measurement with thermocouples. [1] Potentiometers for use with thermocouples also measure the temperature at which the thermocouple wires are connected, so that cold-junction compensation may be applied to correct the apparent measured EMF to the standard cold-junction temperature of 0 degrees C.

## Potentiometer as electronic component

File:Reochord.jpg
Construction of a wire-wound circular potentiometer. The resistive element (1) of the shown device is trapezoidal, giving a non-linear relationship between resistance and turn angle. The wiper (3) rotates with the axis (4), providing the changeable resistance between the wiper contact (6) and the fixed contacts (5) and (9). The vertical position of the axis is fixed in the body (2) with the ring (7) (below) and the bolt (8) (above).

A potentiometer is a three terminal resistor where the position of the sliding connection is continuously adjustable. Potentiometers are rarely used to directly control significant power (more than a watt). Instead they are used to adjust the level of analog signals (e.g. volume controls on audio equipment), and as control inputs for electronic circuits. For example, a light dimmer uses a potentiometer to control the switching of a triac and so indirectly control the brightness of lamps.

Potentiometers are sometimes provided with one or more switches mounted on the same shaft. For instance, when attached to a volume control, the knob can also function as an on/off switch at the lowest volume.

### Construction of potentiometers

File:Potentiometer.jpg
A typical single turn potentiometer

A potentiometer is constructed using a flat semi-circular graphite resistive element, with a sliding contact (wiper). The wiper is connected through another sliding contact to the third terminal. On panel pots, the wiper is usually the centre terminal. For single turn pots, this wiper typically travels just under one revolution around the contact. 'Multiturn' potentiometers also exist, where the resistor element may be helical and the wiper may move 10, 20, or more complete revolutions. Besides graphite, other materials may be used to make the resistive element. These may be resistance wire, or carbon particles in plastic, or a ceramic/metal mixture called cermet.

One form of rotary potentiometer is called a String potentiometer. It is a multi-turn potentiometer operated by an attached reel of wire turning against a spring. It is used as a position transducer.

In a linear slider pot, a sliding control is provided instead of a dial control. The resistive element is a rectangular strip, not semi-circular as in a rotary potentiometer. Because of the large opening for the wiper and knob, this type of pot has a greater potential for getting contaminated.

Potentiometers can be obtained with either linear or logarithmic relations between the slider position and the resistance (potentiometer laws or "tapers").

File:PCB variable resistors.jpg
PCB mount trimmer potentiometers, or "trimpots", intended for infrequent adjustment.
##### Linear taper potentiometer

A linear taper potentiometer has a resistive element of constant cross-section, resulting in a device where the resistance between the contact (wiper) and one end terminal is proportional to the distance between them. Linear taper describes the electrical characteristic of the device, not the geometry of the resistive element. Linear taper potentiometers are used when an approximately proportional relation is desired between shaft rotation and the division ratio of the potentiometer; for example, controls used for adjusting the centering of (an analog) cathode-ray oscilliscope.

##### Logarithmic potentiometer

A logarithmic taper potentiometer has a resistive element that either 'tapers' in from one end to the other, or is made from a material whose resistivity varies from one end to the other. This results in a device where output voltage is a logarithmic (or inverse logarithmic depending on type) function of the mechanical angle of the pot.

Most (cheaper) "log" pots are actually not logarithmic, but use two regions of different, but constant, resistivity to approximate a logarithmic law. A log pot can also be simulated with a linear pot and an external resistor. True log pots are significantly more expensive.

Logarithmic taper potentiometers are often used in connection with audio amplifiers.

File:Pot1.jpg
A high power toroidal wirewound rheostat.

#### Rheostats

A rheostat is a two-terminal variable resistor. Often these are designed to handle much higher voltage and current. Typically these are constructed as a resistive wire wrapped to form a toroid coil with the wiper moving over the upper surface of the toroid, sliding from one turn of the wire to the next. Sometimes a rheostat is made from resistance wire wound on a heat resisting cylinder with the slider made from a number of metal fingers that grip lightly onto a small portion of the turns of resistance wire. The 'fingers' can be moved along the coil of resistance wire by a sliding knob thus changing the 'tapping' point. They are usually used as variable resistors rather than variable potential dividers.

Any three-terminal potentiometer can be used as a two-terminal variable resistor, by not connecting to the 3rd terminal. It is common practice to connect the wiper terminal to the unused end of the resistance track to reduce the amount of resistance variation caused by dirt on the track.

#### Digital control

Digitally Controlled Potentiometers (DCP's) or digipots can be used in analogue signal processing circuits to replace potentiometers. They allow small adjustments to be made to the circuit by software, instead of a mechanical adjustment. Because this type of control is updated only infrequently, it often has a slow serial interface, like I²C. Some types have non-volatile memory to enable them to remember their last settings when the power is switched off.

The same idea can be used to create Digital Volume Controls, attenuators, or other controls under digital control. Usually such devices feature quite a high degree of accuracy, and find applications in instrumentation, mixing consoles and other precision systems.

The DCP should not be confused with the digital to analogue converter (DAC) which actually creates an analogue signal from a digital one. A DCP only controls an existing analogue signal digitally. However, some DACs using resistive R-2R architecture have been functionally used as DCPs where the (varying) analogue signal is input to the reference voltage pin of the DAC and the digitally-controlled attenuated output is taken from the output of the DAC.

### Applications of potentiometers

Potentiometers are widely used as user controls, and may control a very wide variety of equipment functions. The widespread use of potentiometers in consumer electronics has declined in the 1990s, with digital controls now more common. However they remain in many application, such as volume controls and as position sensors.

#### Audio control

One of the most common uses for modern low-power potentiometers is as audio control devices. Both sliding pots (also known as faders) and rotary potentiometers (commonly called knobs) are regularly used to adjust loudness, frequency attenuation and other characteristics of audio signals.

The 'log pot' is used as the volume control in audio amplifiers, where it is also called an "audio taper pot", because the amplitude response of the human ear is also logarithmic. It ensures that, on a volume control marked 0 to 10, for example, a setting of 5 sounds half as loud as a setting of 10. There is also an anti-log pot or reverse audio taper which is simply the reverse of a log pot. It is almost always used in a ganged configuration with a log pot, for instance, in an audio balance control.

Potentiometers used in combination with filter networks act as tone controls or equalizers.

#### Television

Potentiometers were formerly used to control picture brightness, contrast, and (in NTSC receivers) color response. A potentiometer was often used to adjust "vertical hold", which affected the synchronization between the receiver's internal sweep circuit (sometimes a multivibrator) and the received picture signal.

#### Transducers

Potentiometers are also very widely used as a part of displacement transducers because of the simplicity of construction and because they can give a large output signal.

## Theory of operation

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 pot. This is the most common use of pots.

The voltage across ${\displaystyle R_{\mathrm {L} }}$ is determined by the formula:

${\displaystyle V_{\mathrm {L} }={R_{2}\|R_{\mathrm {L} } \over R_{1}+R_{2}\|R_{\mathrm {L} }}\cdot V_{s}}$

The parallel lines indicate components in parallel. Expanded fully, the equation becomes:

${\displaystyle V_{\mathrm {L} }={R_{2}R_{\mathrm {L} } \over R_{1}R_{\mathrm {L} }+R_{2}R_{\mathrm {L} }+R_{1}R_{2}}\cdot V_{s}}$

Although it is not always the case, if ${\displaystyle R_{\mathrm {L} }}$ is large compared to the other resistances (like the input to an operational amplifier), the output voltage can be approximated by the simpler equation:

${\displaystyle V_{\mathrm {L} }={R_{2} \over R_{1}+R_{2}}\cdot V_{s}}$

As an example, assume

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

Since the load resistance is large compared to the other resistances, the output voltage ${\displaystyle V_{\mathrm {L} }}$ will be approximately:

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

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 (${\displaystyle V_{S}}$) to ground (zero volts) as the wiper moves from one end of the pot 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.

## Physics demonstration

The determination of the emf of a cell using a potentiometer is a classic experiment which is sometimes done at A-level in physics. This experiment has the advantage that the emf of a cell can be measured without drawing any current from the cell, in short the measurement can be done as if by a voltmeter of infinite resistance.

If a potentiometer is formed from a length (AB) of uniform resistance wire attached to a DC source such as a Lead-acid battery, then a standard cell whose emf is known (eg 1.0183 volts for a weston standard cell)[2][3] can be used to calibrate the potentiometer.

The standard cell is wired in series with a galvanometer between A and a movable probe on the resistance wire, the galvanometer will give a zero reading at point X. Then distance AX is measured. The experiment should be repeated to find point X' where a zero current reading is obtained for the unknown cell at distance AX'.

Then the emf of the unknown cell can be calculated using:

E = Estandard cell (AX'/AX)