Editing Resistor (section)

==Theory of operation==
[[File:ResistanceHydraulicAnalogy2.svg|thumb|upright=1.8|right|The [[hydraulic analogy]] compares electric current flowing through circuits to water flowing through pipes. When a pipe (left) is clogged with hair (right), it takes a larger pressure to achieve the same flow of water. Pushing electric current through a large resistance is like pushing water through a pipe clogged with hair: It requires a larger push ([[voltage]]) to drive the same flow ([[electric current]]).<ref>{{cite web|author=Harder, Douglas Wilhelm |title=Resistors: A Motor with a Constant Force (Force Source)|url=https://ece.uwaterloo.ca/~dwharder/Analogy/Resistors/|publisher=Department of Electrical and Computer Engineering, University of Waterloo|access-date=9 November 2014}}</ref>]]

===Ohm's law===
{{Main article|Ohm's law}}

An ''ideal resistor'' (i.e. a resistance without [[Electrical reactance|reactance]]) obeys [[Ohm's law]]:

<math display="block">V=I \cdot R.</math>

Ohm's law states that the [[voltage]] (<math>V</math>) across a resistor is proportional to the [[Electric current|current]] (<math>I</math>) passing through it, where the constant of proportionality is the resistance (<math>R</math>). For example, if a 300-[[ohm]] resistor is attached across the terminals of a 12-volt battery, then a current of 12 / 300 = 0.04 [[ampere]]s flows through that resistor.

The [[ohm]] (symbol: [[Ω]]) is the [[International System of Units|SI]] unit of [[electrical resistance]], named after [[Georg Simon Ohm]]. An ohm is equivalent to a [[volt]] per [[ampere]]. Since resistors are specified and manufactured over a very large range of values, the derived units of milliohm (1&nbsp;mΩ = 10<sup>−3</sup>&nbsp;Ω), kilohm (1&nbsp;kΩ = 10<sup>3</sup>&nbsp;Ω), and megohm (1&nbsp;MΩ = 10<sup>6</sup>&nbsp;Ω) are also in common usage.<ref>{{cite book | author=[[American Radio Relay League]] (ARRL) | title =ARRL Handbook for Radio Communications | publisher =American Radio Relay League |isbn=978-1-62595-139-7 | date=2021 | edition =98| chapter = Fundamental Theory—Circuits and Components}}</ref><ref name=arrl1968>{{cite book | url=https://archive.org/details/arrl_1968_handbook |editor=Doug DeMaw | title =Radio Amateurs Handbook | publisher =American Radio Relay League |date=1968 | edition=45 |chapter = Electrical Laws and Circuits —Resistance}}</ref>{{rp|p.20}}

===Series and parallel resistors{{anchor|Series_and_parallel_circuits}}===
{{anchor|series|Series}}<!-- do not delete, used by redirects -->
{{Main article|Series and parallel circuits}}

The total resistance of resistors connected in series is the sum of their individual resistance values.{{clear|left}}
[[File:resistors in series.svg|alt=Circuit diagram of several resistors, labelled R1, R2 ... Rn, connected end to end]]
<math display="block">
R_\mathrm{eq} = \sum_{i=1}^n R_i = R_1  + R_2 + \cdots + R_n.
</math>
{{anchor|parallel|Parallel}}<!-- do not delete, used by redirects -->
The total resistance of resistors connected in parallel is the reciprocal of the sum of the reciprocals of the individual resistors.<ref name=arrl1968 />{{rp|p.20ff}}{{clear|left}}
[[File:resistors in parallel.svg|alt=Circuit diagram of several resistors, labelled R1, R2 ... Rn, side by side, both leads of each connected to the same wires]]
<math display="block">
R_\mathrm{eq} = \left(\sum_{i=1}^n\frac{1}{R_i}\right)^{-1} = \left({1\over R_1} + {1\over R_2} + {1\over R_3} + \dots + {1\over R_n}\right)^{-1}
</math>

For example, a 10 ohm resistor connected in parallel with a 5 ohm resistor and a 15 ohm resistor produces {{sfrac|1/10 + 1/5 + 1/15}} ohms of resistance, or {{sfrac|30|11}} = 2.727 ohms.

A resistor network that is a combination of parallel and series connections can be broken up into smaller parts that are either one or the other. Some complex networks of resistors cannot be resolved in this manner, requiring more sophisticated circuit analysis. Generally, the [[Y-Δ transform]], or [[Equivalent impedance transforms#2-terminal, n-element, 3-element-kind networks|matrix methods]] can be used to solve such problems.<ref>Farago, P.S. (1961) ''An Introduction to Linear Network Analysis'', pp. 18–21, The English Universities Press Ltd.</ref><ref>{{cite journal|doi=10.1088/0305-4470/37/26/004|title=Theory of resistor networks: The two-point resistance|year=2004|author=Wu, F. Y.|journal=Journal of Physics A: Mathematical and General|volume=37|issue=26|pages=6653–6673|arxiv=math-ph/0402038|bibcode=2004JPhA...37.6653W|s2cid=119611570}}</ref><ref>{{cite book|author1=Wu, Fa Yueh|author2=Yang, Chen Ning |title=Exactly Solved Models: A Journey in Statistical Mechanics : Selected Papers with Commentaries (1963–2008)|url=https://books.google.com/books?id=H-k8dhB7lmwC&pg=PA489|date=2009|publisher=World Scientific|isbn=978-981-281-388-6|pages=489–}}</ref>

===Power dissipation===
[[File:Resistor warming thermal video.webm|thumb|Resistor warming caused by electrical current captured by thermal camera]]
At any instant, the power ''P'' (watts) consumed by a resistor of resistance ''R'' (ohms) is calculated as:
<math display="block">
P = I V = I^2 R =  \frac{V^2}{R}
</math>
where ''V'' (volts) is the voltage across the resistor and ''I'' (amps) is the [[Ampere|current]] flowing through it. Using [[Ohm's law]], the two other forms can be derived. This power is converted into heat which must be dissipated by the resistor's package before its temperature rises excessively.<ref name=arrl1968 />{{rp|p.22}}

Resistors are rated according to their maximum power dissipation.  Discrete resistors in solid-state electronic systems are typically rated as {{frac|10}}, {{frac|8}}, or {{frac|4}} watt. They usually absorb much less than a watt of electrical power and require little attention to their power rating.

[[File:Danotherm HS50 power resistor.jpg|thumb|An aluminium-encased power resistor rated for dissipation of 50 W when mounted on a heat-sink]]
Power resistors are required to dissipate substantial amounts of power and are typically used in power supplies, power conversion circuits, and power amplifiers; this designation is loosely applied to resistors with power ratings of 1 watt or greater. Power resistors are physically larger and may not use the preferred values, color codes, and external packages described below.

If the average power dissipated by a resistor is more than its power rating, damage to the resistor may occur, permanently altering its resistance; this is distinct from the reversible change in resistance due to its [[temperature coefficient]] when it warms. Excessive power dissipation may raise the temperature of the resistor to a point where it can burn the circuit board or adjacent components, or even cause a fire. There are flameproof resistors that will not produce flames with any overload of any duration.

Resistors may be specified with higher rated dissipation than is experienced in service to account for poor air circulation, high altitude, or high [[operating temperature]].

All resistors have a maximum voltage rating; this may limit the power dissipation for higher resistance values.<ref>{{cite web |url=https://seielect.com/news/20170821_-_Resistor_Data_Sheet_Information.pdf |title=Specifications and How to Interpret Them|publisher= Stackpole Electronics|access-date=July 6, 2021}}</ref> For instance, among {{frac|4}} watt resistors (a very common sort of [[through-hole technology|leaded]] resistor) one is listed with a resistance of 100&nbsp;MΩ<ref>{{Cite web |title=Through Hole Resistor, 0.1 Gohm, RGP Series, 250 mW, ± 5%, Axial Leaded, 750 V |url=https://nl.farnell.com/te-connectivity/rgp0207chj100m/res-100m-5-250mw-axial-thick-film/dp/2805251 |url-status=dead |archive-url=https://web.archive.org/web/20210709190647/https://nl.farnell.com/te-connectivity/rgp0207chj100m/res-100m-5-250mw-axial-thick-film/dp/2805251 |archive-date=2021-07-09 |access-date=2023-10-07 |website=nl.farnell.com}}</ref> and a maximum rated voltage of 750&nbsp;V. However even placing 750&nbsp;V across a 100&nbsp;MΩ resistor continuously would only result in a power dissipation of less than 6&nbsp;mW, making the nominal {{frac|4}} watt rating meaningless.

[[File:USSR power resistor VZR 12W.JPG|thumb|VZR power resistor 1.5&nbsp;kΩ 12&nbsp;W, manufactured in 1963 in the Soviet Union]]