Unformatted text preview: in Fig. 2.50(b). PRACTICE PROBLEM 2.14
Transform the wye network in Fig. 2.51 to a delta network.
Answer: Ra = 140 , Rb = 70 , Rc = 35 R1 R2 10 Ω 20 Ω a . b 40 Ω R3 c Figure 2.51 For Practice Prob. 2.14. EXAMPLE 2.15
i Obtain the equivalent resistance Rab for the circuit in Fig. 2.52 and use it
to ﬁnd current i .
Solution:
In this circuit, there are two Y networks and one network. Transforming
just one of these will simplify the circuit. If we convert the Y network
comprising the 5 , 10 , and 20 resistors, we may select
R1 = 10 , R2 = 20 , a a 10 Ω 12.5 Ω
5Ω 120 V +
− c n
20 Ω 15 Ω R3 = 5 Thus from Eqs. (2.53) to (2.55) we have b Figure 2.52 R1 R2 + R2 R3 + R3 R1
10 × 20 + 20 × 5 + 5 × 10
=
R1
10
350
=
= 35
10
R1 R2 + R2 R3 + R3 R1
350
Rb =
=
= 17.5
R2
20
R1 R2 + R2 R3 + R3 R1
350
Rc =
= 70
=
R3
5 Ra = b For Example 2.15.  v v With the Y converted to , the equivalent circuit (with the voltage
source removed for now) is shown in Fig. 2.53(a). Combining the three
pairs of resistors in parallel, we obtain  eText Main Menu  Textbook Table of Contents  Problem Solving Workbook Contents 30 Ω 54 PART 1 DC Circuits 70 30 = 17.5 = 12.5 15 70 × 30
= 21
70 + 30 12.5 × 17.5
= 7.2917
12.5 + 17.5 35 = 15 × 35
= 10.5
15 + 35 so that the equivalent circuit is shown in Fig. 2.53(b). Hence, we ﬁnd
Rab = (7.292 + 10.5) 21 = 17.792 × 21
= 9.632
17.792 + 21 Then
i= 120
vs
=
= 12.458 A
Rab
9.632 a
12.5 Ω 17.5 Ω a
70 Ω 30 Ω 7.292 Ω
21 Ω 35 Ω 15 Ω 10.5 Ω b b
(b) (a) Figure 2.53 Equivalent circuits to Fig. 2.52, with the voltage removed. PRACTICE PROBLEM 2.15
i For the bridge network in Fig. 2.54, ﬁnd Rab and i . 13 Ω a Answer: 40
24 Ω
100 V +
− 20 Ω 30 Ω , 2.5 A. 10 Ω 50 Ω b Figure 2.54 For Practice Prob. 2.15. † 2.8 APPLICATIONS  v v Resistors are often used to model devices that convert electrical energy
into heat or other forms of energy. Such devices include conducting
wire, lightbulbs, electric heaters, stoves, ovens, and loudspeakers. In this  eText Main Menu  Textbook Table of Contents  Problem Solving Workbook Contents CHAPTER 2 Basic Laws 55 section, we will consider two reallife problems that...
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 Resistor, Electrical impedance, Series and parallel circuits, DC Circuits, eText Main Menu

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