dc1 - ELEC 101 DC Circuits 1 DC Circuits 1 Basic...

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ELEC 101 DC Circuits 1 2009/10 Spring is a graphical representation of a circuit (closed connection of elements). DC Circuits Basic Definitions R 2 R 1 i 4 R 3 R 6 + v 1 Node a (wire, or contains no element) Branch voltage Branch current Circuit diagram branch Physical crossing (no connection, not a node ) 7 nodes, 9 branches (elements) A Node b Node c Example 1
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ELEC 101 DC Circuits 2 2009/10 Spring is the electrical joint connecting the terminals of two or more elements. Node Loop Mesh is any closed path through the circuit. No node is crossed more than once, and the beginning node is also the end node . is a loop that does not contain other loop . It is the simplest loop. C D E Not a node (no electrical contact) a node Two (or more) nodes can be reduced to one node. R 2 R 1 i 4 R 3 R 6 + v 1 Node a (wire, or contains no element) Branch voltage Branch current branch Physical crossing (no connection, not a node ) Node b Node c Branch One branch is one two-terminals element . B 7 nodes, 9 branches (elements) E.g.
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ELEC 101 DC Circuits 3 2009/10 Spring How many nodes ? How many loops ? 3 loops 2 nodes: node A and node B How many meshes ? 2 meshes How many branches ? 5 branches (5 elements) A B B B B A Example Example 5 elements are in parallel A B A circuit containing only resistances R, voltage sources V, and current sources I . Resistive Circuit Two-Terminals (or One-Port) Network i i + v + v F G 2A 4 Ω 4V 4 Ω Example Example Example 3 nodes, 4 elements
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ELEC 101 DC Circuits 4 2009/10 Spring Circuit Theorems Equivalence Two resistive one-port networks are equivalent if they have the same current- voltage (I-V) curve across the two terminals for ALL loads (or sources). V1 Network A load R I1 V2 Network B load R I2 Hence a complex network (Network A) can be replaced by a simple equivalent (Network B) and network analysis can be simplified. If I1 = I2 and V1 = V2 for ALL load R , then network A and network B are equivalent . ( A B ) A 2 Example NO. I1 I2 and V1 V2 for other R. For example, when R = 6 Ω , I1 = 0.5A, V1 = 3V ; I2 = 2/3A, V2 = 4V Is network A equivalent to network B ?? 2 Ω 6 Ω 8V R = 2 Ω 4V R = 2 Ω I1 = 1A I2 = 1A V1 = 2V V2 =2V network A network B Example
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ELEC 101 DC Circuits 5 2009/10 Spring Network A equivalent to network B ? ( YES. For ALL R , I1 = I2, V1= V2 ) network A network B 2 Ω 4V 4 Ω 8V 4 Ω R R I2 V2 V1 I1 Example network A network B 2 Ω 4V 4 Ω 8V 4 Ω R R I2 V2 V1 I1 When R = 0 Ω (short) A V I V V 2 2 4 1 0 1 = Ω = = Q A V I V V 2 4 8 2 0 2 = Ω = = Q network A network B 2 Ω 4V 4 Ω 8V 4 Ω R R I2 V2 V1 I1 When R = ∞Ω (open) V V A I 4 1 0 1 = = Q 2 0 8 2 4 4 8 I A V V V = = × Ω = Ω Q a b I1 I2 V1 For example, when R = 2 Ω , I1 = 1A, V1 = 2V ; I2 = 2/3A, V2 = 4V I2 = ?, not easy to calculate.
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ELEC 101 DC Circuits 6 2009/10 Spring For network A The I1-V1 curve for all R is the line joining R = 0 and R = . The curve is a straight line as the I-V curve for a resistive circuit is linear (can be proved later).
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