# Eeng2009lec3 - 4.1 Series Resistance Parallel Resistance Series connection Elements in series are joined at a common node at which no other

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EENG 2009 FS 2006 Part 4: Series & Parallel 118 Part 4. Series & Parallel Resistance and Voltage & Current Division 4.1 Series Resistance & Parallel Resistance 4.2 Voltage Division & Current Division EENG 2009 FS 2006 Part 4: Series & Parallel 119 R 1 R 2 R 3 Elements in series are joined at a common node at which no other elements are attached. The same current flows through the elements. Two resistors in series: R 1 R 2 Resistors not in series: R a R b R c R 1 R 2 R a R b R c R 1 R 2 4.1 Series Resistance & Parallel Resistance Series connection

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EENG 2009 FS 2006 Part 4: Series & Parallel 120 R 1 R 2 + + v 1 + v 2 i Two Resistors in Series R 1 R 2 + + v 1 + v 2 i KVL: v = v 1 + v 2 = R 1 i + R 2 i Same i! = ( R 1 + R 2 ) i = R s i R 1 + R 2 + i v v Memorize me! R s = R 1 + R 2 Very important formula!! i i v EENG 2009 FS 2006 Part 4: Series & Parallel 121 R 1 R 2 + + v 1 + v 2 + v N i N Resistors in Series KVL: v = v 1 + v 2 + … + v N = R 1 i + R 2 i + … + R N i = ( R 1 + R 2 + … + R N ) i = R s i R s = R 1 + R 2 + … + R N Resistors in series “add.” v R N R 1 + R 2 + … + R N + i v
EENG 2009 FS 2006 Part 4: Series & Parallel 122 In the parallel connection, each of the resistors in parallel is connected to the same pair of nodes. The same voltage is across them. R 1 R 2 R b R d R a R c R e R f 2. None of these resistors are in parallel: Examples : 1. R 1 and R 2 are in parallel: node a node b R 1 R 2 Parallel Connection EENG 2009 FS 2006 Part 4: Series & Parallel 123 Two Resistors in Parallel KCL: i = i 1 + i 2 = v /R 1 + v /R 2 Same v! = ( 1/R 1 + 1/ R 2 ) v = 1/R eq v where 1/ R eq = 1/ R 1 + 1/ R 2 = (R 1 + R 2 ) / R 1 R 2 R eq = R 1 R 2 / (R 1 + R 2 ) Another very important formula!Also note that R//R R/2 R eq + v Memorize me! R 1 R 2 i 1 i 2 + v Memorize me! i i v +

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EENG 2009 FS 2006 Part 4: Series & Parallel 124 Resistors in parallel do not add, but their corresponding conductances do: 1/ R 1 = G 1 1/ R 2 = G 2 1/ R eq = G eq R eq = R 1 R 2 / (R 1 + R 2 ) 1/ R eq = 1/ R 1 + 1/ R 2 G eq = G 1 + G 2 Compute the resistance of the parallel connection of R 1 = 6 Ω & R 2 = 9 Ω .
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## This note was uploaded on 06/01/2008 for the course COMPUTER E 203 taught by Professor Uzengil during the Spring '08 term at Jefferson College of Health Sciences.

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Eeng2009lec3 - 4.1 Series Resistance Parallel Resistance Series connection Elements in series are joined at a common node at which no other

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