# Find i and r answer 2 cos t ma 5 k 23 nodes branches

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Unformatted text preview: f 20 cos2 t mW when connected to a voltage source v = 10 cos t V. Find i and R . Answer: 2 cos t mA, 5 k . † 2.3 NODES, BRANCHES, AND LOOPS Since the elements of an electric circuit can be interconnected in several ways, we need to understand some basic concepts of network topology. To differentiate between a circuit and a network, we may regard a network as an interconnection of elements or devices, whereas a circuit is a network providing one or more closed paths. The convention, when addressing network topology, is to use the word network rather than circuit. We do this even though the words network and circuit mean the same thing when used in this context. In network topology, we study the properties relating to the placement of elements in the network and the geometric conﬁguration of the network. Such elements include branches, nodes, and loops. 5Ω a 10 V + − b 2Ω 3Ω 2A A branch represents a single element such as a voltage source or a resistor. c In other words, a branch represents any two-terminal element. The circuit in Fig. 2.10 has ﬁve branches, namely, the 10-V voltage source, the 2-A current source, and the three resistors. Figure 2.10 Nodes, branches, and loops. b A node is the point of connection between two or more branches. 5Ω | v v A node is usually indicated by a dot in a circuit. If a short circuit (a connecting wire) connects two nodes, the two nodes constitute a single node. The circuit in Fig. 2.10 has three nodes a, b, and c. Notice that the three points that form node b are connected by perfectly conducting wires and therefore constitute a single point. The same is true of the four points forming node c. We demonstrate that the circuit in Fig. 2.10 has only three nodes by redrawing the circuit in Fig. 2.11. The two circuits in | e-Text Main Menu | Textbook Table of Contents | 2Ω a 3Ω 2A + − 10 V Figure 2.11 c The three-node circuit of Fig. 2.10 is redrawn. Problem Solving Workbook Contents 34 PART 1 DC Circuits Figs. 2.10 and 2.11 are identical. However, for the sake of clarity,...
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