Editing Temperature coefficient (section)

==Electrical resistance== <!-- NOTE: The article "Servomechanism" links directly to the section. If you change the name of this section, please also change the link in that article (or any others that link here) -->
{{see also|Electrical resistivity and conductivity#Resistivity and conductivity of various materials|l1=Table of materials' resistivities}}

The temperature dependence of [[electrical resistance]] and thus of electronic devices ([[wire]]s, resistors) has to be taken into account when constructing devices and [[electrical network|circuits]].  The temperature dependence of [[Electrical conductor|conductors]] is to a great degree linear and can be described by the approximation below.
:<math>\operatorname{\rho}(T) = \rho_{0}\left[1 + \alpha_{0}\left(T - T_{0}\right)\right]</math>

where
:<math>\alpha_{0} = \frac{1}{\rho_{0}}\left[ \frac{\delta \rho}{\delta T} \right]_{T=T_{0}}</math>
<math>\rho_{0}</math> just corresponds to the specific resistance temperature coefficient at a specified reference value (normally ''T'' = 0&nbsp;°C)<ref>{{cite book |first=S. O. |last=Kasap |title=Principles of Electronic Materials and Devices |url=https://archive.org/details/principlesofelec0000kasa |url-access=limited |edition=Third |publisher=Mc-Graw Hill |year=2006 |page=[https://archive.org/details/principlesofelec0000kasa/page/126/mode/2up 126]}}</ref>

That of a [[semiconductor]] is however exponential:
:<math>\operatorname{\rho}(T) = S \alpha^{\frac{B}{T}}</math>

where <math>S</math> is defined as the cross sectional area and <math>\alpha</math> and <math>B</math> are coefficients determining the shape of the function and the value of resistivity at a given temperature.

{{anchor|TCR}}For both, <math>\alpha</math> is referred to as the ''temperature coefficient of resistance'' (TCR).<ref>{{cite book|last=Alenitsyn|first=Alexander G.|author2=Butikov, Eugene I. |author3=Kondraryez, Alexander S. |title=Concise Handbook of Mathematics and Physics|publisher=CRC Press|date=1997|pages=331–332|isbn=0-8493-7745-5}}</ref>

This property is used in devices such as thermistors.

===Positive temperature coefficient of resistance===
A '''positive temperature coefficient''' (PTC) refers to materials that experience an increase in electrical resistance when their temperature is raised. Materials which have useful engineering applications usually show a relatively rapid increase with temperature, i.e. a higher coefficient. The higher the coefficient, the greater an increase in electrical resistance for a given temperature increase. A PTC material can be designed to reach a maximum temperature for a given input voltage, since at some point any further increase in temperature would be met with greater electrical resistance. Unlike linear resistance heating or NTC materials, PTC materials are inherently self-limiting. On the other hand, NTC material may also be inherently self-limiting if constant current power source is used.

Some materials even have exponentially increasing temperature coefficient. Example of such a material is [[PTC rubber]].

===Negative temperature coefficient of resistance===
A '''negative temperature coefficient''' (NTC) refers to materials that experience a decrease in electrical resistance when their temperature is raised. Materials which have useful engineering applications usually show a relatively rapid decrease with temperature, i.e. a lower coefficient. The lower the coefficient, the greater a decrease in electrical resistance for a given temperature increase. NTC materials are used to create inrush current limiters (because they present higher initial resistance until the current limiter reaches quiescent temperature), [[temperature sensor]]s and [[thermistor]]s.

===Negative temperature coefficient of resistance of a semiconductor===
An increase in the temperature of a semiconducting material results in an increase in charge-carrier concentration. This results in a higher number of charge carriers available for recombination, increasing the conductivity of the semiconductor. The increasing conductivity causes the resistivity of the semiconductor material to decrease with the rise in temperature, resulting in a negative temperature coefficient of resistance.