lec3-Reduction .pdf - Connecting Circuit Elements a Series...

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8/28/17 1 The current in the two element is the same a b c i A i B A B a) Series Connection: The two elements share a common node (no other elements connected to the same node) i A = i B Connecting Circuit Elements b) Parallel Connection: Two or more elements are connected in parallel if they are connected between the same two nodes a A B b V A V B C V C b b a a V A = V B = V C The voltage across elements in parallel is the same.
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8/28/17 2 A F B E C D G H a b c c d d e f Elements in series: C & A & B Elements in Parallel G & H Simple Resistive Circuits Different techniques of circuit analysis: Define the voltage across and the current through every element in the circuit Circuit Reduction technique. Node voltage method. Mesh current method.
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8/28/17 3 Circuit Reduction technique Concept of equivalent circuits Two circuits considered to be equivalent if the (i-v) rela:on between the terminals for the two circuits are exactly the same. V I Circuit (1) a b Circuit (2) c d R L R L V S R 1 R 2 R 3 R 4 R 5 R 6 R 7 i i 1 i 2 i 3 i 4 i 5 i 6 i 7 V s = i R equ { } Resistors in series KCL: i 1 = i 2 = i 3 = i 4 = i 5 = i 6 = i 7 = i KVL: V s i R 1 ( ) i R 2 ( ) i R 3 ( ) i R 4 ( ) i R 5 ( ) i R 6 ( ) = 0 V s = i R 1 ( ) + R 2 ( ) + R 3 ( ) + R 4 ( ) + R 5 ( ) + R 6 ( ) + R 7 ( ) { }
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8/28/17 4 V S R 1 R 2 R 3 R 4 R 5 R 6 R 7 i a b b V S i a R equ Where: R equ = R 1 ( ) + R 2 ( ) + R 3 ( ) + R 4 ( ) + R 5 ( ) + R 6 ( ) + R 7 ( ) { } Note: R equ must be grater than any other resistor in the original circuit R 1 R 4 R 3 R 2 i 1 i 2 i 4 i 3 V S I a b KVL: v 1 = v 2 = v 3 = v 4 = V s KCL: I = i 1 + i 2 + i 3 + i 4 I = V s R 1 + V s R 2 + V s R 3 + V s R 4 I = V s 1 R 1 + 1 R 2 + 1 R 3 + 1 R 4 I = V s 1 R equ Resistors in parallel
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8/28/17 5 R 1 R 4 R 3 R 2 i 1 i 2 i 4 i 3 V S I a b I = V s 1 R 1 + 1 R 2 + 1 R 3 + 1 R 4 I = V s 1 R equ R equ V S I a b The (i – v ) relation at the terminals (a) & (b) for the original circuit and the reduced circuit is the same.
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