en>Yobot: WP:CHECKWIKI error 61 fix, References after punctuation per WP:REFPUNC and WP:PAIC using AWB (8459)

2012-10-12T18:43:13Z

WP:CHECKWIKI error 61 fix, References after punctuation per WP:REFPUNC and WP:PAIC using AWB (8459)

← Older revision		Revision as of 20:43, 12 October 2012
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	~~Myrtle Benny~~ is ~~how I'm known as and I feel comfortable when people use~~ the ~~full name~~. ~~California~~ is ~~our beginning place~~. ~~To gather coins~~ is ~~one of~~ the ~~things I love most~~. ~~Managing people is his profession~~.<br><br>~~Also visit my site at home std testing (~~[~~http:~~//~~www~~.~~alemcheap~~.fi/~~people~~/~~anhipkiss additional hints~~])		{{Unreferenced\|date=December 2009}}

			In [[electrical engineering]], '''Millman's theorem''' (or the '''parallel generator theorem''') is a method to simplify the solution of a [[electrical network\|circuit]]. Specifically, Millman's theorem is used to compute the [[voltage]] at the ends of a circuit made up of only [[series and parallel circuits\|branches in parallel]].

			It is named after [[Jacob Millman]], who proved the theorem.

			==Explanation==
			[[Image:milman ex01.gif\|frame\|Figure 1]]

			Let e<sub>k</sub> be the voltage [[Electrical generator\|generators]] and a<sub>m</sub> the current generators.

			Let R<sub>i</sub> be the [[electrical resistance\|resistance]]s on the branches with no generator.

			Let R<sub>k</sub> be the resistances on the branches with voltage generators.

			Let R<sub>m</sub> be the resistances on the branches with current generators.

			Then Millman states that the voltage at the ends of the circuit is given by:

			:<math>v=\frac{\sum_{}\frac{\pm e_{k}}{R_{k}}+\sum_{}\pm a_{m}}{\sum_{}\frac{1}{R_{k}}+\sum_{}\frac{1}{R_{i}}}</math>

			It can be proved by considering the circuit as a single [[supernode (circuit)\|supernode]]. Then, according to [[Ohm's law\|Ohm]] and [[Kirchhoff's circuit laws\|Kirchhoff]], "the voltage between the ends of the circuit is equal to the total current entering the supernode divided by the total equivalent conductance of the supernode".

			The total current is the sum of the currents flowing in each branch.

			The total equivalent [[Electrical conductance\|conductance]] of the supernode is the sum of the conductance of each branch, since all the branches are in parallel. When computing the equivalent conductance all the generators have to be switched off, so all voltage generators become [[short circuit]]s and all current generators become [[open circuit]]s. That's why the resistances on the branches with current generators do not appear in the expression of the total equivalent conductance.

			==See also==
			* [[Analysis of resistive circuits]]

			[[Category:Electrical engineering]]
			[[Category:Circuit theorems]]

en>Alan Liefting: cat sort

2010-02-06T00:41:42Z

cat sort

New page

Myrtle Benny is how I'm known as and I feel comfortable when people use the full name. California is our beginning place. To gather coins is one of the things I love most. Managing people is his profession.<br><br>Also visit my site at home std testing ([http://www.alemcheap.fi/people/anhipkiss additional hints])

Resource holding potential - Revision history

en>Yobot: WP:CHECKWIKI error 61 fix, References after punctuation per WP:REFPUNC and WP:PAIC using AWB (8459)

en>Alan Liefting: cat sort