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Unformatted text preview: circuit below. 5Ω 5Ω 5i 4Ω + − 10 V i | v v 5Ω | e-Text Main Menu 6Ω | Textbook Table of Contents | Problem Solving Workbook Contents Problem 2.4 Identify all the nodes, branches, and independent loops in Figure 2.1. + − + − + − + − Figure 2.1 There are 8 nodes, as indicated by the dark circles and dark lines in the circuit below. There are 14 branches, 4 independent voltage sources and 10 resistors. There are 7 independent loops. + − + − + − + − | v v Check. Does this satisfy the fundamental theorem of network topology? b = l + n – 1 = 7 + 8 – 1 = 14 YES! | e-Text Main Menu | Textbook Table of Contents | Problem Solving Workbook Contents Problem 2.5 In Figure 2.0, is there a loop? How many nodes are there? A loop is any closed path; therefore it is easy to say there is no loop. However, there really is a loop since there is an infinite resistance connecting the end terminals together. Thus, there is one loop. There are three nodes, one where the voltage source and resistor join and Figure 2.0 the two at the output terminals. In addition, there are three branches. The voltage source, the resistor, and the infinite resistance. Thus, the fundamental theorem of network topology is satisfied. + − R=∞ Problem 2.6 (a) In a circuit containing 26 branches and 12 nodes, how many independent loops will satisfy the fundamental theorem of network topology? (b) In a circuit with 22 branches, is it possible to have 28 nodes? b=l+n–1 {the fundamental theorem of network topology} (a) 26 = l + 12 – 1 l = 26 – 12 + 1 l = 15 A circuit with 26 branches and 12 nodes will have 15 independent loops. (b) 22 = l + 28 – 1 l = 22 – 28 + 1 l=–5 No. It is not possible to have a circuit with 22 branches and 28 nodes because a circuit cannot have –5 loops. KIRCHOFF'S LAWS Kirchoff's current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero. Equivalently, the sum of the currents entering a node = the sum of the currents leaving the node Kirchoff's voltage law (KVL) states that the algebraic sum of all...
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This note was uploaded on 07/16/2012 for the course KA KA 2000 taught by Professor Bkav during the Spring '12 term at Cambridge.

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