Editing Resistor (section)

===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>