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212 identify which elements are in series and which

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Unformatted text preview: ermine the number of branches and nodes in the circuit shown in Fig. 2.12. Identify which elements are in series and which are in parallel. Solution: | v v Since there are four elements in the circuit, the circuit has four branches: 10 V, 5 , 6 , and 2 A. The circuit has three nodes as identified in | e-Text Main Menu | Textbook Table of Contents | Problem Solving Workbook Contents CHAPTER 2 Basic Laws 35 Fig. 2.13. The 5- resistor is in series with the 10-V voltage source because the same current would flow in both. The 6- resistor is in parallel with the 2-A current source because both are connected to the same nodes 2 and 3. 5Ω 10 V 5Ω 1 + − 6Ω 2A 10 V 2 + − 6Ω 2A 3 Figure 2.12 For Example 2.4. Figure 2.13 The three nodes in the circuit of Fig. 2.12. PRACTICE PROBLEM 2.4 How many branches and nodes does the circuit in Fig. 2.14 have? Identify the elements that are in series and in parallel. Answer: Five branches and three nodes are identified in Fig. 2.15. The 1- and 2- resistors are in parallel. The 4- resistor and 10-V source are also in parallel. 5Ω 1Ω Figure 2.14 2Ω 3Ω 1 + 10 V − 4Ω 1Ω 2 + 10 V − 2Ω 4Ω 3 For Practice Prob. 2.4. Figure 2.15 Answer for Practice Prob. 2.4. 2.4 KIRCHHOFF’S LAWS | v v Ohm’s law by itself is not sufficient to analyze circuits. However, when it is coupled with Kirchhoff ’s two laws, we have a sufficient, powerful set of tools for analyzing a large variety of electric circuits. Kirchhoff ’s laws were first introduced in 1847 by the German physicist Gustav Robert Kirchhoff (1824–1887). These laws are formally known as Kirchhoff ’s current law (KCL) and Kirchhoff ’s voltage law (KVL). Kirchhoff ’s first law is based on the law of conservation of charge, which requires that the algebraic sum of charges within a system cannot change. | e-Text Main Menu | Textbook Table of Contents | Problem Solving Workbook Contents 36 PART 1 DC Circuits Kirchhoff’s current law (KCL) states that the algebraic sum o...
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