Unformatted text preview: resistance to give a combined resistance of 1 + 2 = 3 .
Thus, we replace the circuit in Fig. 2.38(a) with that in Fig. 2.38(b). In
Fig. 2.38(b), we combine the 2 and 3 resistors in parallel to get
2×3
2
3=
= 1.2
2+3
This 1.2 resistor is in series with the 10 resistor, so that
Rab = 10 + 1.2 = 11.2 PRACTICE PROBLEM 2.10
20 Ω Find Rab for the circuit in Fig. 2.39.
Answer: 11 5Ω 8Ω . a
18 Ω Rab 20 Ω
9Ω 1Ω 2Ω
b  v v Figure 2.39 For Practice Prob. 2.10.  eText Main Menu  Textbook Table of Contents  Problem Solving Workbook Contents CHAPTER 2 Basic Laws 47 EXAMPLE 2.11
5S Find the equivalent conductance Geq for the circuit in Fig. 2.40(a).
Solution:
The 8S and 12S resistors are in parallel, so their conductance is Geq 12 S 8S 6S 8 S + 12 S = 20 S
(a) This 20S resistor is now in series with 5 S as shown in Fig. 2.40(b) so
that the combined conductance is
20 × 5
=4S
20 + 5 5S
Geq 6S 20 S This is in parallel with the 6S resistor. Hence
Geq = 6 + 4 = 10 S (b) We should note that the circuit in Fig. 2.40(a) is the same as that in
Fig. 2.40(c). While the resistors in Fig. 2.40(a) are expressed in siemens,
they are expressed in ohms in Fig. 2.40(c). To show that the circuits are
the same, we ﬁnd Req for the circuit in Fig. 2.40(c).
Req = 1
6 = 1
6
1
6 11
+
58
×
+ 1
4
1
4 = 1
12 = 1
6 1
1
+
5 20 = 1
6 1
5 Req 1
6 Ω 1
8 Ω 1
4 Ω 1
12 Ω (c) 1
10 Figure 2.40 Geq = For Example 2.11: (a) original
circuit, (b) its equivalent circuit, (c) same
circuit as in (a) but resistors are expressed in
ohms. 1
= 10 S
Req This is the same as we obtained previously. PRACTICE PROBLEM 2.11
Calculate Geq in the circuit of Fig. 2.41.
Answer: 4 S. 8S 4S Geq
2S Figure 2.41 12 Ω 6S For Practice Prob. 2.11. EXAMPLE 2.12
Find io and vo in the circuit shown in Fig. 2.42(a). Calculate the power
dissipated in the 3 resistor.
Solution:
The 6 and 3 resistors are in parallel, so their combined resistance is  v v 6  3 eText Main Menu = 6×3
=2
6+3  Textbook Table of Contents  Problem Solvi...
View
Full
Document
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.
 Spring '12
 bkav

Click to edit the document details