Series and parallel circuits: Difference between revisions

Revision as of 16:48, 22 February 2023

Revision as of 16:52, 22 February 2023

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===Capacitors<span class="anchor" id="Cseries"></span>===

{{seeSee also|Capacitor#Networks}}

[[Capacitor]]s follow the same law using the reciprocals. The total [[capacitance]] of capacitors in series is equal to the reciprocal of the sum of the [[Multiplicative inverse|reciprocals]] of their individual capacitances:

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A [[Battery (electricity)|battery]] is a collection of [[electrochemical cell]]s. If the cells are connected in series, the [[voltage]] of the battery will be the sum of the cell voltages. For example, a 12 volt [[car battery]] contains six 2-volt cells connected in series. Some vehicles, such as trucks, have two 12 volt batteries in series to feed the 24-volt system.

==Parallel circuits<span class="anchor" id="Zparallel"></span><span class="anchor" id="Xparallel"></span><span class="anchor" id="Yparallel"></span><span class="anchor" id="Bparallel"></span><span class="anchor" id="Parallel_circuit_anchor"></span>Parallel circuits==

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{{resistors inductors capacitors in series and parallel.svg}}

If two or more components are connected in parallel, they have the same difference of potential ([[voltage]]) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applied to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with [[Kirchhoff's circuit laws#Kirchhoff's current law (KCL)|Kirchhoff's current law]].

===Voltage<span class="anchor" id="Rparallel"></span>===

In a '''parallel circuit''', the voltage is the same for all elements.

<math display="block">V = V_1 = V_2 = \dots = V_n</math>

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===Resistance units===

To find the total [[Electrical resistance|resistance]] of all components, add the [[multiplicativeMultiplicative inverse|reciprocals]] of the resistances <math>R_i</math> of each component and take the reciprocal of the sum. Total resistance will always be less than the value of the smallest resistance:

[[File:Resistors in parallel.svg|A diagram of several resistors, side by side, both leads of each connected to the same wires.]]

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<ref name="Smith_1966">{{cite book |author-last=Smith |author-first=R. J. |date=1966 |title=Circuits, Devices and Systems |publisher=[[Wiley (publisher)|Wiley]] |edition=International |___location=New York |lccn=66-17612 |page=21 }}</ref>

<ref name="BRS">{{cite book |series=Board Review Series |title=Physiology |author-first=Linda S. |author-last=Costanzo |page=74 }}</ref>

<ref name="Ellerman_1995">{{cite book |title=Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics |chapter=Chapter 12: Parallel Addition, Series-Parallel Duality, and Financial Mathematics |series=G - Reference, Information and Interdisciplinary Subjects Series |work=The worldly philosophy: studies in intersection of philosophy and economics |author-first=David Patterson |author-last=Ellerman |author-link=David Patterson Ellerman |edition=illustrated |publisher=[[Rowman & Littlefield Publishers, Inc.]] |date=1995-03-21 |isbn=0-8476-7932-2 |pages=237–268 |url=http://www.ellerman.org/wp-content/uploads/2012/12/IntellectualTrespassingBook.pdf |chapter-url=https://books.google.com/books?id=NgJqXXk7zAAC&pg=PA237 |access-date=2019-08-09 |url-status=live |archive-url=https://web.archive.org/web/20160305012729/http://www.ellerman.org/wp-content/uploads/2012/12/IntellectualTrespassingBook.pdf |archive-date=2016-03-05 |quote=[…] When resistors with resistance a and b are placed in series, their compound resistance is the usual sum (hereafter the ''[[series sum]]'') of the resistances a&nbsp;+ b. If the resistances are placed in parallel, their compound resistance is the ''[[parallel sum]]'' of the resistances, which is denoted by the [[full colon]] […]}} [https://web.archive.org/web/20150917191423/http://www.ellerman.org/Davids-Stuff/Maths/sp_math.doc] (271 pages)</ref>

<ref name="Ellerman_2004">{{cite web |title=Introduction to Series-Parallel Duality |author-first=David Patterson |author-last=Ellerman |author-link=David Patterson Ellerman |publisher=[[University of California at Riverside]] |date=May 2004 |orig-year=1995-03-21 |citeseerx=10.1.1.90.3666 |url=http://www.ellerman.org/wp-content/uploads/2012/12/Series-Parallel-Duality.CV_.pdf |access-date=2019-08-09 |url-status=live |archive-url=https://web.archive.org/web/20190810011716/http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.3666&rep=rep1&type=pdf<!-- https://archive.today/20190810080659/http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.3666&rep=rep1&type=pdf --> |archive-date=2019-08-10 |quote=The [[parallel sum]] of two positive real numbers x:y&nbsp;= [(1/x)&nbsp;+ (1/y)]⁻¹ arises in electrical circuit theory as the resistance resulting from hooking two resistances x and y in parallel. There is a [[duality (mathematics)|duality]] between the usual [[series sum|(series) sum]] and the parallel sum. […]}} [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.3666&rep=rep1&type=pdf] (24 pages)</ref>

}}

==Further reading==

* {{cite book |author-last=Williams |author-first=Tim |title=The Circuit Designer's Companion |publisher=[[Butterworth-Heinemann]] |date=2005 |isbn=0-7506-6370-7 }}

* {{cite magazine |url=http://www.edn.com/design/components-and-packaging/4421194/Resistor-combinations--How-many-values-using-1kohm-resistors-- |title=Resistor combinations: How many values using 1K ohm resistors? |magazine=[[EDN magazine]] }}

* {{cite book |chapter-url=https://www.grund-wissen.de/physik/mechanik/festkoerper-fluessigkeiten-gase/fluessigkeiten.html |title=Mechanik der Flüssigkeiten |chapter=Strömungswiderstand |language=de |date=2018-01-04 |author-first=Bernhard |author-last=Grotz }}<!-- analog parallel and serial circuits. Find English source and add to article -->

[[Category:Electrical circuits]]