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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