34 6 req 4 for example 29 2 req 6 4 resistor in

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Unformatted text preview: 6×3 =2 6+3 (The symbol is used to indicate a parallel combination.) Also, the 1and 5- resistors are in series; hence their equivalent resistance is 6 3 2Ω Req +2 Figure 2.34 =6 Req = 4 For Example 2.9. 2Ω Req 6Ω =4 resistor in Fig. 2.35(a); (a) 4Ω = + 2.4 +8 Req 2.4 Ω 8Ω = 14.4 (b) Figure 2.35 PRACTICE PROBLEM 2.9 2Ω By combining the resistors in Fig. 2.36, find Req . Answer: 6 . Req v v Figure 2.36 | e-Text Main Menu | Textbook Table of Contents | Equivalent circuits for Example 2.9. 3Ω 6Ω 1Ω | 2Ω 8Ω 4×6 = 2.4 4+6 The circuit in Fig. 2.35(a) is now replaced with that in Fig. 2.35(b). In Fig. 2.35(b), the three resistors are in series. Hence, the equivalent resistance for the circuit is 6 3Ω 4Ω This 4- resistor is now in parallel with the 6their equivalent resistance is 4 6Ω 8Ω Thus the circuit in Fig. 2.34 is reduced to that in Fig. 2.35(a). In Fig. 2.35(a), we notice that the two 2- resistors are in series, so the equivalent resistance is 2 5Ω = +5 1 1Ω 4Ω 4Ω 3Ω For Practice Prob. 2.9. Problem Solving Workbook Contents 5Ω 46 PART 1 DC Circuits EXAMPLE 2.10 Calculate the equivalent resistance Rab in the circuit in Fig. 2.37. 10 Ω c a 1Ω 1Ω d 6Ω Rab 4Ω 3Ω 5Ω 12 Ω b b Figure 2.37 10 Ω a c 1Ω d 2Ω b b 3Ω 6Ω b b (a) 10 Ω c a 3Ω 2Ω b b b (b) Figure 2.38 Equivalent circuits for Example 2.10. b For Example 2.10. Solution: The 3- and 6- resistors are in parallel because they are connected to the same two nodes c and b. Their combined resistance is 3×6 3 6= (2.10.1) =2 3+6 Similarly, the 12- and 4- resistors are in parallel since they are connected to the same two nodes d and b. Hence 12 × 4 12 4= (2.10.2) =3 12 + 4 Also the 1- and 5- resistors are in series; hence, their equivalent resistance is 1 +5 =6 (2.10.3) With these three combinations, we can replace the circuit in Fig. 2.37 with that in Fig. 2.38(a). In Fig. 2.38(a), 3- in parallel with 6- gives 2- , as calculated in Eq. (2.10.1). This 2- equivalent resistance is now in series with the 1-...
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