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lecture5 - i i G G i R R i G G G G R R R R eq 3 3 eq 3 eq 2...

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1 Outline Series and parallel connections Voltage sources in series Current sources in parallel Resistors in series – Equivalent resistance – Voltage-divider Resistors in parallel – Equivalent resistance – Current-divider • Y- Transformations HW2: 2.4, 2.8, 2.20, 2.12, 2.22, 2.33 Elements in Series and Parallel Two elements are in series if they exclusively share a single node Two elements are in parallel if they are connected to the same two nodes 1 2 3 4 i 1 i 2 i 3 i 4 i 1 = i 2 = i 3 = -i 4 a b 1 3 2 + v 1 - + v 3 - + v 2 - v 1 =v 2 =v 3 Elements in Series and Parallel Which circuit elements are in series? Which circuit elements are in parallel? 2 3 1 6 5 4
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2 Series Voltage Sources v 1 v 2 v 3 v 1 +V 2 -V 3 Parallel Current Sources i 1 i 2 i 3 i 1 -i 2 -i 3 Parallel voltage sources? Series current sources?
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3 Resistors in series and parallel R 1 R 1 R 1 R 1 +R 2 +R 3 G 1 G 2 G 3 G 1 +G 2 +G 3 series resistances parallel conductances Series Resistors and Voltage Division v R R v v R R v v R R v R R R R eq 3 3 eq 2 2 eq 1 1 3 2 1 eq = = = + + = o o a b R 1 R 2 R 3 i + v 1 - + V 2 - + V 3 - o v v o a b R eq Parallel Resistors and Current Division o a b R 1 R 2 R 3 i v v o a b R eq o i 1 i 2 i 3 + V 1 - + V 2 - + V 3 - i o i G G i R R i i G G i R R i i G G i
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Unformatted text preview: i i G G i R R i G G G G R R R R eq 3 3 eq 3 eq 2 2 eq 2 eq 1 1 eq 1 3 2 1 eq 3 2 1 eq 1 1 1 1 = = = = = = + + = + + = 4 What current flows in the 3 Ω resistor? 7 Ω 7 Ω 3 Ω 3 Ω 3 Ω 3 Ω 6 Ω 6 Ω 10V 10V 3 A 3 A i i i i Examples Examples 60 V 1 k Ω 5 k Ω 6x10-3 V + V-2 k Ω 500 Ω i 1 i 2 i 3 Find i 1 , i 2 , and i 3 ∆ (Π29 and Y (T) Interconnections R 1 R 1 R 2 R 2 R 3 R 3 R a R a R b R b R c R c 1 1 1 1 3 3 3 3 2 2 2 2 4 4 4 4 Y T D P 5 ∆-Y Conversions R 1 R 2 R 3 R a R b R c 1 1 3 3 2 2 4 4 Y D c b a b a c b a c a c b a c b R R R R R R R R R R R R R R R R R R + + + + + + = = = 3 2 1 ∆-to-Y conversion Y-to-∆ conversion 3 1 3 3 2 2 1 2 1 3 3 2 2 1 1 1 3 3 2 2 1 R R R R R R R R R R R R R R R R R R R R R R R R c b a + + + + + + = = = Example • Find I 40 V 5 Ω 100 Ω 125 Ω 25 Ω 40 Ω 37.5 Ω I...
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