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| [[Image:NTC bead.jpg|thumb|Negative temperature coefficient (NTC) thermistor, bead type, insulated wires]]A '''thermistor''' is a type of [[resistor]] whose [[electrical resistance|resistance]] varies significantly with [[temperature]], more so than in standard resistors. The word is a [[portmanteau]] of ''[[Thermal (disambiguation)|thermal]]'' and ''[[resistor]]''. Thermistors are widely used as [[inrush current limiter]]s, temperature [[sensors]], self-resetting overcurrent protectors, and self-regulating [[heating element]]s.
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| Thermistors differ from [[Resistance thermometer|resistance temperature detector]]s (RTD) in that the material used in a thermistor is generally a ceramic or polymer, while RTDs use pure metals. The temperature response is also different; RTDs are useful over larger temperature ranges, while thermistors typically achieve a higher precision within a limited temperature range, typically −90 °C to 130 °C.<ref>[http://www.microchiptechno.com/ntc_thermistors.php "NTC Thermistors"]. Micro-chip Technologies. 2010.</ref>
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| ==Basic operation==
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| [[Image:Thermistor.svg|150px|thumb|Thermistor symbol]]
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| Assuming, as a first-order approximation, that the relationship between resistance and temperature is [[linear]], then:
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| :<math>\Delta R=k\Delta T \,</math>
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| where
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| :<math>\Delta R</math> = change in resistance
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| :<math>\Delta T</math> = change in temperature
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| :<math>k</math> = first-order temperature coefficient of resistance
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| Thermistors can be classified into two types, depending on the sign of ''<math>k</math>''. If ''<math>k</math>'' is [[Positive number|positive]], the resistance increases with increasing temperature, and the device is called a [[Temperature coefficient#Positive temperature coefficient of resistance|positive temperature coefficient]] ('''PTC''') thermistor, or '''posistor'''. If ''<math>k</math>'' is negative, the resistance decreases with increasing temperature, and the device is called a [[Temperature coefficient#Negative temperature coefficient|negative temperature coefficient]] ('''NTC''') thermistor. Resistors that are not thermistors are designed to have a ''<math>k</math>'' as close to zero as possible, so that their resistance remains nearly constant over a wide temperature range.
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| Instead of the temperature coefficient ''k'', sometimes the ''temperature coefficient of resistance'' <math>\alpha_T</math> (alpha sub T) is used. It is defined as<ref>[http://www.ussensor.com/terminology.html Thermistor Terminology]. U.S. Sensor</ref>
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| :<math>\alpha_T = \frac{1}{R(T)} \frac{dR}{dT}.</math>
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| This <math>\alpha_T</math> coefficient should not be confused with the <math>a</math> parameter below.
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| ==Steinhart–Hart equation==
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| In practice, the linear approximation (above) works only over a small temperature range. For accurate temperature measurements, the resistance/temperature curve of the device must be described in more detail. The [[Steinhart–Hart equation]] is a widely used third-order approximation:
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| :<math>{1 \over T}=a+b\,\ln(R)+c\,(\ln(R))^3</math>
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| where ''a'', ''b'' and ''c'' are called the Steinhart–Hart parameters, and must be specified for each device. ''T'' is the temperature in [[kelvin]] and ''R'' is the resistance in [[Ohm (unit)|ohm]]s. To give resistance as a function of temperature, the above can be rearranged into:
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| :<math>R=e^{{\left( x-{y \over 2} \right)}^{1\over 3}-{\left( x+{y \over 2} \right)}^{1\over 3}}</math>
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| where
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| :<math>y={{a-{1\over T}}\over c}</math> and <math>x=\sqrt{{{{\left({b\over{3c}}\right)}^3}+{{y^2}\over 4}}}</math>
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| The error in the Steinhart–Hart equation is generally less than 0.02 °C in the measurement of temperature over a 200 °C range.<ref>[http://cp.literature.agilent.com/litweb/pdf/5965-7822E.pdf "Practical Temperature Measurements"]. Agilent Application Note. Agilent Semiconductor.</ref> As an example, typical values for a thermistor with a resistance of 3000 Ω at room temperature (25 °C = 298.15 K) are:
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| :<math>a = 1.40 \times 10^{-3}</math>
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| :<math>b = 2.37 \times 10^{-4}</math>
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| :<math>c = 9.90 \times 10^{-8}</math>
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| ==''B'' or ''β'' parameter equation==
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| NTC thermistors can also be characterised with the ''B'' (or ''β'') parameter equation, which is essentially the Steinhart Hart equation with <math>a = (1/T_{0}) - (1/B) \ln(R_{0})</math>, <math>b = 1/B</math> and <math>c = 0</math>,
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| :<math>\frac{1}{T}=\frac{1}{T_0} + \frac{1}{B}\ln \left(\frac{R}{R_0}\right)</math>
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| Where the temperatures are in [[kelvin]] and ''R''<sub>0</sub> is the resistance at temperature ''T''<sub>0</sub> (25 °C = 298.15 K). Solving for ''R'' yields:
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| :<math>R=R_0e^{B(\frac{1}{T} - \frac{1}{T_0})}</math>
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| or, alternatively,
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| :<math>R=r_\infty e^{B/T}</math>
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| where <math>r_\infty=R_0 e^{-{B/T_0}}</math>.
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| This can be solved for the temperature:
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| :<math>T={B\over { {\ln{(R / r_\infty)}}}}</math>
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| The B-parameter equation can also be written as <math>\ln R=B/T + \ln r_\infty</math>. This can be used to convert the function of resistance vs. temperature of a thermistor into a linear function of <math>\ln R</math> vs. <math>1/T</math>. The average slope of this function will then yield an estimate of the value of the ''B'' parameter.
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| ==Conduction model==
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| ===NTC===
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| Many NTC thermistors are made from a pressed disc, rod, plate, bead or [[casting|cast]] chip of a [[semiconductor]] such as a [[sintering|sintered]] metal [[oxide]]. They work because raising the temperature of a semiconductor increases the number of active [[Charge carrier|charge carriers]] - it promotes them into the ''[[conduction band]]''. The more charge carriers that are available, the more [[current (electricity)|current]] a material can conduct. In certain materials like ferric oxide (Fe<sub>2</sub>O<sub>3</sub>) with titanium (Ti) doping a ''n-type'' semiconductor is formed and the charge carriers are [[Electron|electrons]]. In materials such as nickel oxide (NiO) with lithium (Li) doping a ''p-type'' semiconductor is created where [[Electron hole|holes]] are the charge carriers.<ref name=EERB>{{cite book|title=Electronics Engineer's Reference Book|year=1976|publisher=Butterworths|isbn=0408001682|pages=6-29 to 6-41|edition=4|editor=L. W Turner|language=English}}</ref>
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| This is described in the formula:
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| :<math>
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| I = n \cdot A \cdot v \cdot e | |
| </math>
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| <math>I</math> = electric current (amperes)
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| <br><math>n</math> = density of charge carriers (count/m³)
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| <br><math>A</math> = cross-sectional area of the material (m²)
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| <br><math>v</math> = velocity of charge carriers (m/s)
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| <br><math>e</math> = charge of an electron (<math>e=1.602 \times 10^{-19} </math> coulomb)
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| Over large changes in temperature, calibration is necessary. Over small changes in temperature, if the right semiconductor is used, the resistance of the material is linearly proportional to the temperature. There are many different semiconducting thermistors with a range from about 0.01 [[kelvin]] to 2,000 kelvins (−273.14 °C to 1,700 °C){{Citation needed|date=May 2013}}.
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| ===PTC===
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| Most PTC thermistors are of the "switching" type, which means that their resistance rises suddenly at a certain critical temperature. The devices are made of a doped polycrystalline [[ceramic]] containing [[barium titanate]] (BaTiO<sub>3</sub>) and other compounds. The [[dielectric constant]] of this [[ferroelectric]] material varies with temperature. Below the [[Curie point]] temperature, the high [[dielectric constant]] prevents the formation of potential barriers between the crystal grains, leading to a low resistance. In this region the device has a small negative temperature coefficient. At the Curie point temperature, the dielectric constant drops sufficiently to allow the formation of potential barriers at the grain boundaries, and the resistance increases sharply. At even higher temperatures, the material reverts to NTC behaviour.
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| Another type of thermistor is a '''silistor''', a thermally sensitive silicon resistor. Silistors employ silicon as the semiconductive component material. In contrary to the "switching" type thermistor, silistors have an almost linear resistance-temperature characteristic.<ref>[http://www.resistorguide.com/ptc-thermistor/ "PTC Thermistors and Silistors"] The Resistor Guide</ref>
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| An other device similar in function to PTC thermistor is the [[polymer]] PTC, which is sold under brand names such as "[[Polyswitch]]" "Semifuse", and "Multifuse". This consists of a slice of plastic with [[carbon]] grains embedded in it. When the [[plastic]] is cool, the carbon grains are all in contact with each other, forming a [[electrical conductor|conductive]] path through the device. When the plastic heats up, it expands, forcing the carbon grains apart, and causing the resistance of the device to rise rapidly. Like the BaTiO<sub>3</sub> thermistor, this device has a highly nonlinear resistance/temperature response and is used for switching, not for proportional temperature measurement.
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| ==Self-heating effects==
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| When a current flows through a thermistor, it will generate heat which will raise the temperature of the thermistor above that of its environment. If the thermistor is being used to measure the temperature of the environment, this electrical heating may introduce a significant error if a correction is not made. Alternatively, this effect itself can be exploited. It can, for example, make a sensitive air-flow device employed in a [[sailplane]] rate-of-climb instrument, the electronic [[variometer]], or serve as a [[timer]] for a [[relay]] as was formerly done in [[telephone exchange]]s.
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| The electrical power input to the thermistor is just:
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| :<math>P_E=IV\,</math>
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| where ''I'' is current and ''V'' is the voltage drop across the thermistor. This power is converted to heat, and this heat energy is transferred to the surrounding environment. The rate of transfer is well described by [[Newton's law of cooling]]:
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| :<math>P_T=K(T(R)-T_0)\,</math> | |
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| where ''T(R)'' is the temperature of the thermistor as a function of its resistance ''R'', <math>T_0</math> is the temperature of the surroundings, and ''K'' is the '''dissipation constant''', usually expressed in units of milliwatts per degree Celsius. At equilibrium, the two rates must be equal.
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| :<math>P_E=P_T\,</math>
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| The current and voltage across the thermistor will depend on the particular circuit configuration. As a simple example, if the voltage across the thermistor is held fixed, then by [[Ohm's Law]] we have <math>I=V/R</math> and the equilibrium equation can be solved for the ambient temperature as a function of the measured resistance of the thermistor:
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| :<math>T_0=T(R) -\frac{V^2}{KR}\,</math>
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| The dissipation constant is a measure of the thermal connection of the thermistor to its surroundings. It is generally given for the thermistor in still air, and in well-stirred oil. Typical values for a small glass bead thermistor are 1.5 mW/°C in still air and 6.0 mW/°C in stirred oil. If the temperature of the environment is known beforehand, then a thermistor may be used to measure the value of the dissipation constant. For example, the thermistor may be used as a flow rate sensor, since the dissipation constant increases with the rate of flow of a fluid past the thermistor.
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| The power dissipated in a thermistor is typically maintained at a very low level to ensure insignificant temperature measurement error due to self heating. However, some thermistor applications depend upon significant "self heating" to raise the body temperature of the thermistor well above the ambient temperature so the sensor then detects even subtle changes in the thermal conductivity of the environment. Some of these applications include liquid level detection, liquid flow measurement and air flow measurement.<ref>[http://www.ussensor.com/terminology.html Thermistor Terminology]. U.S. Sensor</ref>
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| ==Applications==
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| {{refimprove section|date=June 2013}}
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| * PTC thermistors can be used as current-limiting devices for circuit protection, as replacements for fuses. Current through the device causes a small amount of resistive heating. If the current is large enough to generate more heat than the device can lose to its surroundings, the device heats up, causing its resistance to increase. This creates a self-reinforcing effect that drives the resistance upwards, therefore limiting the current.
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| * PTC thermistors were used as timers in the [[degauss|degaussing coil]] circuit of most CRT displays. When the display unit is initially switched on, current flows through the thermistor and degaussing coil. The coil and thermistor are intentionally sized so that the current flow will heat the thermistor to the point that the degaussing coil shuts off in under a second. For effective degaussing, it is necessary that the magnitude of the alternating magnetic field produced by the degaussing coil decreases smoothly and continuously, rather than sharply switching off or decreasing in steps; the PTC thermistor accomplishes this naturally as it heats up. A degaussing circuit using a PTC thermistor is simple, reliable (for its simplicity), and inexpensive.
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| * PTC thermistors were used as heater in automotive industry to provide additional heat inside cabin with diesel engine or to heat diesel in cold climatic conditions before engine injection.
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| * NTC thermistors are used as [[resistance thermometer]]s in low-temperature measurements of the order of 10 K.
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| * NTC thermistors can be used as inrush-current limiting devices in power supply circuits. They present a higher resistance initially which prevents large currents from flowing at turn-on, and then heat up and become much lower resistance to allow higher current flow during normal operation. These thermistors are usually much larger than measuring type thermistors, and are purposely designed for this application.<ref>[http://www.ussensor.com/inrush-current-limiting-power-thermistors Inrush Current Limiting Power Thermistors]. U.S. Sensor</ref>
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| * NTC thermistors are regularly used in automotive applications. For example, they monitor things like coolant temperature and/or oil temperature inside the engine and provide data to the ECU and, indirectly, to the dashboard.
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| * NTC thermistors can be also used to monitor the temperature of an incubator.
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| * Thermistors are also commonly used in modern [[Thermostat#Digital|digital thermostats]] and to monitor the temperature of battery packs while charging.
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| *Thermistors are often used in the hot ends of [[3D printing|3D printers]]; they monitor the heat produced and allow the printer's control circuitry to keep a constant temperature for melting the plastic filament.
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| * NTC thermistors are used in the Food Handling and Processing industry, especially for food storage systems and food preparation. Maintaining the correct temperature is critical to prevent food borne illness.
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| * NTC thermistors are used throughout the Consumer Appliance industry for measuring temperature. Toasters, coffee makers, refrigerators, freezers, hair dryers, etc. all rely on thermistors for proper temperature control.
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| ==History==
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| The first NTC thermistor was discovered in 1833 by [[Michael Faraday]], who reported on the semiconducting behavior of [[silver sulfide]]. Faraday noticed that the resistance of silver sulfide decreased dramatically as temperature increased. Because early thermistors were difficult to produce and applications for the technology were limited, commercial production of thermistors did not begin until the 1930s.<ref>{{cite book |first=Thomas |last=McGee |year=1988 |title=Principles and Methods of Temperature Measurement |chapter=Chapter 9 |page=203 |publisher=John Wiley & Sons |url=http://books.google.com/books?id=qfmS7g4JzjwC&lpg=PP1&pg=PA203#v=onepage&q=thermistor&f=false}}</ref>
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| A commercially viable thermistor was invented by [[Samuel Ruben]] in 1930.<ref>{{cite book |title=Biomedical Sensors |editor=Jones, Deric P. |year=2009 |publisher=Momentum Press |page=12| url=http://books.google.com/books?id=7cI83YOIUTkC&pg=PA12&dq=Samuel+Ruben+and+Thermistor&hl=en&ei=gHVyTpyUG5Cltwfkp-SFCg&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDEQ6AEwAQ#v=onepage&q&f=false}}</ref>
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| ==See also==
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| *[[Iron-hydrogen resistor]]
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| *[[Thermocouple]]
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| == References ==
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| {{reflist|2}}
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| ==External links==
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| {{Commons category|Thermistors}}
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| <!--PLEASE DO NOT USE THIS SECTION AS A LINK FARM FOR YOUR WEBSITE OR ARBITRARY FACTS-->
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| *[http://www.facstaff.bucknell.edu/mastascu/eLessonsHTML/Sensors/TempR.html The thermistor at bucknell.edu]
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| *[http://thermistor.sourceforge.net/ Software for thermistor calculation at Sourceforge]
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| *[http://img.en25.com/Web/Vaisala/JVT%20KBull%20Article_final%20pdf.pdf "Thermistors & Thermocouples:Matching the Tool to the Task in Thermal Validation"] - Journal of Validation Technology
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| {{Electronic component}}
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| [[Category:Heating, ventilating, and air conditioning]]
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| [[Category:Resistive components]]
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| [[Category:Sensors]]
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| [[Category:Thermometers]]
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