Potentiometer

Last updated
Potentiometer
Electronic-Component-Potentiometer.jpg
A typical single-turn potentiometer
Type Passive
Electronic symbol
Potentiometer symbol Europe.svg (IEC Standard)
Potentiometer symbol.svg (ANSI Standard)

A potentiometer is a three-terminal resistor with a sliding or rotating contact that forms an adjustable voltage divider. [1] If only two terminals are used, one end and the wiper, it acts as a variable resistor or rheostat.

Contents

The measuring instrument called a potentiometer is essentially a voltage divider used for measuring electric potential (voltage); the component is an implementation of the same principle, hence its name.

Potentiometers are commonly used to control electrical devices such as volume controls on audio equipment. It is also used in speed control of fans. Potentiometers operated by a mechanism can be used as position transducers, for example, in a joystick. Potentiometers are rarely used to directly control significant power (more than a watt), since the power dissipated in the potentiometer would be comparable to the power in the controlled load.

Nomenclature

Some terms in the electronics industry used to describe certain types of potentiometers are:

Construction

Cutaway drawing of potentiometer showing parts: (A) shaft, (B) stationary carbon composition resistance element, (C) phosphor bronze wiper, (D) shaft attached to wiper, (E, G) terminals connected to ends of resistance element, (F) terminal connected to wiper. A mechanical stop (H) prevents rotation past end points. Potentiometer cutaway drawing.png
Cutaway drawing of potentiometer showing parts: (A) shaft, (B) stationary carbon composition resistance element, (C) phosphor bronze wiper, (D) shaft attached to wiper, (E, G) terminals connected to ends of resistance element, (F) terminal connected to wiper. A mechanical stop (H) prevents rotation past end points.
Single-turn potentiometer with metal casing removed to expose wiper contacts and resistive track Single-turn potentiometer with internals exposed, oblique view.jpg
Single-turn potentiometer with metal casing removed to expose wiper contacts and resistive track

Potentiometers consist of a resistive element, a sliding contact (wiper) that moves along the element, making good electrical contact with one part of it, electrical terminals at each end of the element, a mechanism that moves the wiper from one end to the other, and a housing containing the element and wiper.

Many cheap potentiometers are constructed with a resistive element (B in cutaway drawing) formed into an arc of a circle usually a little less than a full turn and a wiper (C) sliding on this element when rotated, making electrical contact. The resistive element can be flat or angled. Each end of the resistive element is connected to a terminal (E, G) on the case. The wiper is connected to a third terminal (F), usually between the other two. On panel potentiometers, the wiper is usually the center terminal of three. For single-turn potentiometers, this wiper typically travels just under one revolution around the contact. The only point of ingress for contamination is the narrow space between the shaft and the housing it rotates in.

Another type is the linear slider potentiometer, which has a wiper which slides along a linear element instead of rotating. Contamination can potentially enter anywhere along the slot the slider moves in, making effective sealing more difficult and compromising long-term reliability. An advantage of the slider potentiometer is that the slider position gives a visual indication of its setting. While the setting of a rotary potentiometer can be seen by the position of a marking on the knob, an array of sliders can give a visual impression of settings as in a graphic equalizer or faders on a mixing console.

The resistive element of cheap potentiometers is often made of graphite. Other materials used include resistance wire, carbon particles in plastic, and a ceramic/metal mixture called cermet. Conductive track potentiometers use conductive polymer resistor pastes that contain hard-wearing resins and polymers, solvents, and lubricant, in addition to the carbon that provides the conductive properties.

PCB mount trimmer potentiometers, or "trimpots", intended for infrequent adjustment 12 board mounted potentiometers.jpg
PCB mount trimmer potentiometers, or "trimpots", intended for infrequent adjustment
Electronic symbol for pre-set potentiometer Pre-Set Potentiometer.png
Electronic symbol for pre-set potentiometer

Multiturn potentiometers are also operated by rotating a shaft, but by several turns rather than less than a full turn. Some multiturn potentiometers have a linear resistive element with a sliding contact moved by a lead screw; others have a helical resistive element and a wiper that turns through 10, 20, or more complete revolutions, moving along the helix as it rotates. Multiturn potentiometers, both user-accessible and preset, allow finer adjustments; rotation through the same angle changes the setting by typically a tenth as much as for a simple rotary potentiometer.

A string potentiometer is a multi-turn potentiometer operated by an attached reel of wire turning against a spring, allowing it to convert linear position to a variable resistance.

User-accessible rotary potentiometers can be fitted with a switch which operates usually at the anti-clockwise extreme of rotation. Before digital electronics became the norm such a component was used to allow radio and television receivers and other equipment to be switched on at minimum volume with an audible click, then the volume increased, by turning a knob. Multiple resistance elements can be ganged together with their sliding contacts on the same shaft, for example, in stereo audio amplifiers for volume control. In other applications, such as domestic light dimmers, the normal usage pattern is best satisfied if the potentiometer remains set at its current position, so the switch is operated by a push action, alternately on and off, by axial presses of the knob.

Others are enclosed within the equipment and are intended to be adjusted to calibrate equipment during manufacture or repair, and not otherwise touched. They are usually physically much smaller than user-accessible potentiometers, and may need to be operated by a screwdriver rather than having a knob. They are usually called "trimmer", "trim[ming]", or "preset" potentiometers (or pots), or the genericized brand name "trimpot". Some presets are accessible by a small screwdriver poked through a hole in the case to allow servicing without dismantling.

Resistance–position relationship: "taper"

Size scaled 10k and 100k pots that combine traditional mountings and knob shafts with newer and smaller electrical assemblies. The "B" designates a linear (USA/Asian style) taper. Pots 10k 100k.jpg
Size scaled 10k and 100k pots that combine traditional mountings and knob shafts with newer and smaller electrical assemblies. The "B" designates a linear (USA/Asian style) taper.

The relationship between slider position and resistance, known as the "taper" or "law", can be controlled during manufacture by changing the composition or thickness of the resistance coating along the resistance element. Although in principle any taper is possible, two types are widely manufactured: linear and logarithmic (aka "audio taper") potentiometers.

A letter code may be used to identify which taper is used, but the letter code definitions are not standardized. Potentiometers made in Asia and the USA are usually marked with an "A" for logarithmic taper or a "B" for linear taper; "C" for the rarely seen reverse logarithmic taper. Others, particularly those from Europe, may be marked with an "A" for linear taper, a "C" or "B" for logarithmic taper, or an "F" for reverse logarithmic taper. [2] The code used also varies between different manufacturers. When a percentage is referenced with a non-linear taper, it relates to the resistance value at the midpoint of the shaft rotation. A 10% log taper would therefore measure 10% of the total resistance at the midpoint of the rotation; i.e. 10% log taper on a 10 kOhm potentiometer would yield 1 kOhm at the midpoint. The higher the percentage, the steeper the log curve. [3]

Linear taper potentiometer

A linear taper potentiometer (linear describes the electrical characteristic of the device, not the geometry of the resistive element) 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 potentiometers [4] are used when the division ratio of the potentiometer must be proportional to the angle of shaft rotation (or slider position), for example, controls used for adjusting the centering of the display on an analog cathode-ray oscilloscope. Precision potentiometers have an accurate relationship between resistance and slider position.

Beckman Helipot precision potentiometer Beckman Helipot potentiometer SA1400A 2007.075.002.jpg
Beckman Helipot precision potentiometer

Logarithmic potentiometer

A logarithmic taper potentiometer is a potentiometer that has a bias built into the resistive element. Basically this means the center position of the potentiometer is not one half of the total value of the potentiometer. The resistive element is designed to follow a logarithmic taper, aka a mathematical exponent or "squared" profile. A logarithmic taper potentiometer is constructed with 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 function of the slider position.

Most (cheaper) "log" potentiometers are not accurately logarithmic, but use two regions of different resistance (but constant resistivity) to approximate a logarithmic law. The two resistive tracks overlap at approximately 50% of the potentiometer rotation; this gives a stepwise logarithmic taper. [5] A logarithmic potentiometer can also be simulated (not very accurately) with a linear one and an external resistor. True logarithmic potentiometers are significantly more expensive.

Logarithmic taper potentiometers are often used for volume or signal level in audio systems, as human perception of audio volume is logarithmic, according to the Weber–Fechner law.

Contactless potentiometer

Unlike mechanical potentiometers, non-contact potentiometers use an optical disk to trigger an infrared sensor, or a magnet to trigger a magnetic sensor (as long as there are other types of sensors, such as capacitive, other types of non-contact potentiometers can probably be built), and then an electronic circuit does the signal processing to provide an output signal that can be analogue or digital.

An example of a non-contact potentiometer can be found with the AS5600 integrated circuit. However, absolute encoders must also use similar principles, although being for industrial use, certainly the cost must be unfeasible for use in domestic appliances.

Rheostat

The most common way to vary the resistance in a circuit continuously is to use a rheostat. [6] Because of the change in resistance, they can also be used to adjust magnitude of current in a circuit. The word rheostat was coined in 1843 by Sir Charles Wheatstone, [7] from the Greek ῥέοςrheos meaning "stream", and -στάτης -states (from ἱστάναιhistanai, "to set, to cause to stand") meaning "setter, regulating device", [8] [9] [10] which is a two-terminal variable resistor. For low-power applications (less than about 1 watt) a three-terminal potentiometer is often used, with one terminal unconnected or connected to the wiper.

Where the rheostat must be rated for higher power (more than about 1 watt), it may be built with a resistance wire wound around a semi-circular insulator, with the wiper 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. Wire-wound rheostats made with ratings up to several thousand watts are used in applications such as DC motor drives, electric welding controls, or in the controls for generators. The rating of the rheostat is given with the full resistance value and the allowable power dissipation is proportional to the fraction of the total device resistance in circuit. Carbon-pile rheostats are used as load banks for testing automobile batteries and power supplies.

Digital potentiometer

A digital potentiometer (often called digipot) is an electronic component that mimics the functions of analog potentiometers. Through digital input signals, the resistance between two terminals can be adjusted, just as in an analog potentiometer. There are two main functional types: volatile, which lose their set position if power is removed, and are usually designed to initialise at the minimum position, and non-volatile, which retain their set position using a storage mechanism similar to flash memory or EEPROM.

Usage of a digipot is far more complex than that of a simple mechanical potentiometer, and there are many limitations to observe; nevertheless they are widely used, often for factory adjustment and calibration of equipment, especially where the limitations of mechanical potentiometers are problematic. A digipot is generally immune to the effects of moderate long-term mechanical vibration or environmental contamination, to the same extent as other semiconductor devices, and can be secured electronically against unauthorised tampering by protecting the access to its programming inputs by various means.

In equipment which has a microprocessor, FPGA or other functional logic which can store settings and reload them to the "potentiometer" every time the equipment is powered up, a multiplying DAC can be used in place of a digipot, and this can offer higher setting resolution, less drift with temperature, and more operational flexibility.

Membrane potentiometers

A membrane potentiometer uses a conductive membrane that is deformed by a sliding element to contact a resistor voltage divider. Linearity can range from 0.50% to 5% depending on the material, design and manufacturing process. The repeat accuracy is typically between 0.1 mm and 1.0 mm with a theoretically infinite resolution. The service life of these types of potentiometers is typically 1 million to 20 million cycles depending on the materials used during manufacturing and the actuation method; contact and contactless (magnetic) methods are available (to sense position). Many different material variations are available such as PET, FR4, and Kapton. Membrane potentiometer manufacturers offer linear, rotary, and application-specific variations. The linear versions can range from 9 mm to 1000 mm in length and the rotary versions range from 20 to 450 mm in diameter, with each having a height of 0.5 mm. Membrane potentiometers can be used for position sensing. [11]

For touch-screen devices using resistive technology, a two-dimensional membrane potentiometer provides x and y coordinates. The top layer is thin glass spaced close to a neighboring inner layer. The underside of the top layer has a transparent conductive coating; the surface of the layer beneath it has a transparent resistive coating. A finger or stylus deforms the glass to contact the underlying layer. Edges of the resistive layer have conductive contacts. Locating the contact point is done by applying a voltage to opposite edges, leaving the other two edges temporarily unconnected. The voltage of the top layer provides one coordinate. Disconnecting those two edges, and applying voltage to the other two, formerly unconnected, provides the other coordinate. Alternating rapidly between pairs of edges provides frequent position updates. An analog-to-digital converter provides output data.

Advantages of such sensors are that only five connections to the sensor are needed, and the associated electronics is comparatively simple. Another is that any material that depresses the top layer over a small area works well. A disadvantage is that sufficient force must be applied to make contact. Another is that the sensor requires occasional calibration to match touch location to the underlying display. (Capacitive sensors require no calibration or contact force, only proximity of a finger or other conductive object. However, they are significantly more complex.)

Applications

Potentiometers are rarely used to directly control significant amounts of power (more than a watt or so). Instead they are used to adjust the level of analog signals (for example volume controls 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 to control the brightness of lamps.

Preset potentiometers are widely used throughout electronics wherever adjustments must be made during manufacturing or servicing.

User-actuated 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 declined in the 1990s, with rotary incremental encoders, up/down push-buttons, and other digital controls now more common. However they remain in many applications, such as volume controls and as position sensors.

Audio control

Slide potentiometers (faders) Faders.jpg
Slide potentiometers (faders)

Low-power potentiometers, both slide and rotary, are used to control audio equipment, changing loudness, frequency attenuation, and other characteristics of audio signals.

The 'log pot', that is, a potentiometer has a resistance, taper, or, "curve" (or law) of a logarithmic (log) form, is used as the volume control in audio power amplifiers, where it is also called an "audio taper pot", because the amplitude response of the human ear is approximately logarithmic. It ensures that on a volume control marked 0 to 10, for example, a setting of 5 sounds subjectively 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 logarithmic potentiometer. It is almost always used in a ganged configuration with a logarithmic potentiometer, for instance, in an audio balance control.

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

In audio systems, the word linear, is sometimes applied in a confusing way to describe slide potentiometers because of the straight line nature of the physical sliding motion. The word linear when applied to a potentiometer regardless of being a slide or rotary type, describes a linear relationship of the pot's position versus the measured value of the pot's tap (wiper or electrical output) pin.

Television

Potentiometers were formerly used to control picture brightness, contrast, and 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, along with other things such as audio-video carrier offset, tuning frequency (for push-button sets) and so on. It also helps in frequency modulation of waves.

Motion control

Potentiometers can be used as position feedback devices in order to create closed-loop control, such as in a servomechanism. This method of motion control is the simplest method of measuring the angle or displacement.

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.

Computation

In analog computers, high precision potentiometers are used to scale intermediate results by desired constant factors, or to set initial conditions for a calculation. A motor-driven potentiometer may be used as a function generator, using a non-linear resistance card to supply approximations to trigonometric functions. For example, the shaft rotation might represent an angle, and the voltage division ratio can be made proportional to the cosine of the angle.

Theory of operation

A potentiometer with a resistive load, showing equivalent fixed resistors for clarity. Potentiometer with load.svg
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 RL can be calculated by:

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:

(dividing throughout by RL and cancelling terms with RL as denominator)

As an example, assume , , , and

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

Because of 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.

See also

Related Research Articles

<span class="mw-page-title-main">Resistor</span> Passive electrical component providing electrical resistance

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements, or as sensing devices for heat, light, humidity, force, or chemical activity.

<span class="mw-page-title-main">Analog-to-digital converter</span> System that converts an analog signal into a digital signal

In electronics, an analog-to-digital converter is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an analog input voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities.

In electronics, a linear regulator is a voltage regulator used to maintain a steady voltage. The resistance of the regulator varies in accordance with both the input voltage and the load, resulting in a constant voltage output. The regulating circuit varies its resistance, continuously adjusting a voltage divider network to maintain a constant output voltage and continually dissipating the difference between the input and regulated voltages as waste heat. By contrast, a switching regulator uses an active device that switches on and off to maintain an average value of output. Because the regulated voltage of a linear regulator must always be lower than input voltage, efficiency is limited and the input voltage must be high enough to always allow the active device to reduce the voltage by some amount.

A transducer is a device that converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another. Transducers are often employed at the boundaries of automation, measurement, and control systems, where electrical signals are converted to and from other physical quantities. The process of converting one form of energy to another is known as transduction.

In electronics, a voltage divider (also known as a potential divider) is a passive linear circuit that produces an output voltage (Vout) that is a fraction of its input voltage (Vin). Voltage division is the result of distributing the input voltage among the components of the divider. A simple example of a voltage divider is two resistors connected in series, with the input voltage applied across the resistor pair and the output voltage emerging from the connection between them.

<span class="mw-page-title-main">Electronic component</span> Discrete device in an electronic system

An electronic component is any basic discrete electronic device or physical entity part of an electronic system used to affect electrons or their associated fields. Electronic components are mostly industrial products, available in a singular form and are not to be confused with electrical elements, which are conceptual abstractions representing idealized electronic components and elements. A datasheet for an electronic component is a technical document that provides detailed information about the component's specifications, characteristics, and performance.

<span class="mw-page-title-main">Mass flow sensor</span> Internal combustion engine sensor

A mass (air) flow sensor (MAF) is a sensor used to determine the mass flow rate of air entering a fuel-injected internal combustion engine.

<span class="mw-page-title-main">Electronic symbol</span> Pictogram used to represent various electrical and electronic devices or functions

An electronic symbol is a pictogram used to represent various electrical and electronic devices or functions, such as wires, batteries, resistors, and transistors, in a schematic diagram of an electrical or electronic circuit. These symbols are largely standardized internationally today, but may vary from country to country, or engineering discipline, based on traditional conventions.

In automotive and aerospace engineering, a fuel gauge is an instrument used to indicate the amount of fuel in a fuel tank. In electrical engineering, the term is used for ICs determining the current State of Charge of accumulators.

<span class="mw-page-title-main">LM317</span> Adjustable linear voltage regulator

The LM317 is an adjustable positive linear voltage regulator. It was designed by Bob Dobkin in 1976 while he worked at National Semiconductor.

<span class="mw-page-title-main">Trimmer (electronics)</span> Miniature adjustable component

A trimmer, or preset, is a miniature adjustable electrical component. It is meant to be set correctly when installed in some device, and never seen or adjusted by the device's user. Trimmers can be variable resistors (potentiometers), variable capacitors, or trimmable inductors. They are common in precision circuitry like A/V components, and may need to be adjusted when the equipment is serviced. Trimpots are often used to initially calibrate equipment after manufacturing. Unlike many other variable controls, trimmers are mounted directly on circuit boards, turned with a small screwdriver and rated for many fewer adjustments over their lifetime. Trimmers like trimmable inductors and trimmable capacitors are usually found in superhet radio and television receivers, in the intermediate frequency (IF), oscillator and radio frequency (RF) circuits. They are adjusted into the right position during the alignment procedure of the receiver.

A string potentiometer is a transducer used to detect and measure linear position and velocity using a flexible cable and spring-loaded spool. Other common names include string pot, cable-extension transducer, draw wire sensor, and yo-yo sensor.

<span class="mw-page-title-main">Digital potentiometer</span>

A digital potentiometer is a digitally-controlled electronic component that mimics the analog functions of a potentiometer. It is often used for trimming and scaling analog signals by microcontrollers.

A potentiometer is an instrument for measuring voltage or 'potential difference' by comparison of an unknown voltage with a known reference voltage. If a sensitive indicating instrument is used, very little current is drawn from the source of the unknown voltage. Since the reference voltage can be produced from an accurately calibrated voltage divider, a potentiometer can provide high precision in measurement. The method was described by Johann Christian Poggendorff around 1841 and became a standard laboratory measuring technique.

<span class="mw-page-title-main">Texas Instruments SN76477</span> Sound generating integrated circuit

SN76477 "complex sound generator" is a sound chip produced by Texas Instruments (TI). The chip came to market in 1978, and TI ceased production of the part. A compatible version is identified as ICS76477. The chip is typically used as a sound effects generator in arcade games and toys and for hobby projects. The use of the SN76477 in a musical context is limited by the fact that it was difficult to electronically control the pitch of the produced sound.

<span class="mw-page-title-main">Plate detector (radio)</span>

In electronics, a plate detector is a vacuum tube circuit in which an amplifying tube having a control grid is operated in a non-linear region of its grid voltage versus plate current transfer characteristic, usually near plate current cutoff, to demodulate amplitude modulated carrier signal. This differs from the grid leak detector, which utilizes the non-linearity of the grid voltage versus grid current characteristic for demodulation. It also differs from the diode detector, which is a two-terminal device.

<span class="mw-page-title-main">Guitar wiring</span>

Guitar wiring refers to the electrical components, and interconnections thereof, inside an electric guitar. It most commonly consists of pickups, potentiometers to adjust volume and tone, a switch to select between different pickups, and the output socket. There may be additional controls for specific functions; the most common of these are described below.

A logarithmic resistor ladder is an electronic circuit, composed of a series of resistors and switches, designed to create an attenuation from an input to an output signal, where the logarithm of the attenuation ratio is proportional to a binary number that represents the state of the switches.

Teledeltos paper is an electrically conductive paper. It is formed by a coating of carbon on one side of a sheet of paper, giving one black and one white side. Western Union developed Teledeltos paper in the late 1940s for use in spark printer based fax machines and chart recorders.

References

  1. The Authoritative Dictionary of IEEE Standards Terms (IEEE 100) (seventh ed.). Piscataway, New Jersey: IEEE Press. 2000. ISBN   0-7381-2601-2.
  2. "Resistor Guide" . Retrieved 3 January 2018.
  3. Elliot, Rod. "Beginners' Guide to Potentiometers". Elliott Sound Products. Retrieved 7 June 2012.
  4. Peterson, Phillip. "Linear Type Precision Potentiometer Diagram" (PDF). Precision Sensors. Betatronix. Retrieved 29 April 2015.
  5. "Potentiometer taper". the Resistor Guide. Retrieved 19 November 2012.
  6. Jhakki, Akki (2020). Concise Physics Class IX (ICSE). New Delhi: Selina Publishers Pvt. Ltd. p. 189. ISBN   9789388594387.
  7. Wheatstone, Charles (1843). "An account of several new Instruments and processes for determining the constants of a voltaic circuit". Philosophical Transactions of the Royal Society of London. 133: 303–327. From p. 309: "As the principal use of this instrument is to adjust or regulate the circuit so that any constant degree of force may be obtained, I have called it a Rheostat."
  8. Brian Bowers (ed.), Sir Charles Wheatstone FRS: 1802-1875, IET, 2001 ISBN   0-85296-103-0 pp.104-105
  9. "stat" . Oxford English Dictionary (Online ed.). Oxford University Press.(Subscription or participating institution membership required.)
  10. ῥέος, ἱστάναι . Liddell, Henry George ; Scott, Robert ; A Greek–English Lexicon at the Perseus Project.
  11. Membrane Potentiometer White Paper

Further reading