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# 47 rc 3 1 rb ra 2 4 a r12 y r1 r3 r12 rb ra

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Unformatted text preview: how to identify them when they occur as part of a network and how to apply wye-delta transformation in the analysis of that network. 3 1 R1 R1 R2 R2 3 1 R3 R3 2 2 4 (b) (a) Figure 2.47 Rc 3 1 Rb Ra 2 4 (a) R12 (Y) = R1 + R3 R12 ( ) = Rb (Ra + Rc ) 3 Rb Two forms of the same network: (a) Y, (b) T. Delta to Wye Conversion Suppose it is more convenient to work with a wye network in a place where the circuit contains a delta conﬁguration. We superimpose a wye network on the existing delta network and ﬁnd the equivalent resistances in the wye network. To obtain the equivalent resistances in the wye network, we compare the two networks and make sure that the resistance between each pair of nodes in the (or ) network is the same as the resistance between the same pair of nodes in the Y (or T) network. For terminals 1 and 2 in Figs. 2.47 and 2.48, for example, Rc 1 4 (2.46) Setting R12 (Y)= R12 ( ) gives Ra R12 = R1 + R3 = (b) Figure 2.48 Two forms of the same network: (a) , (b) . (2.47a) R13 = R1 + R2 = 4 Rb (Ra + Rc ) Ra + R b + R c Rc (Ra + Rb ) Ra + R b + R c (2.47b) R34 = R2 + R3 = 2 Ra (Rb + Rc ) Ra + R b + R c (2.47c) Similarly, Subtracting Eq. (2.47c) from Eq. (2.47a), we get | v v R 1 − R2 = | e-Text Main Menu | Textbook Table of Contents | Rc (Rb − Ra ) Ra + R b + R c (2.48) Problem Solving Workbook Contents CHAPTER 2 Basic Laws 51 Adding Eqs. (2.47b) and (2.48) gives R1 = Rb Rc Ra + R b + R c (2.49) and subtracting Eq. (2.48) from Eq. (2.47b) yields R2 = R c Ra Ra + R b + R c (2.50) Subtracting Eq. (2.49) from Eq. (2.47a), we obtain R3 = R a Rb Ra + R b + R c (2.51) We do not need to memorize Eqs. (2.49) to (2.51). To transform a network to Y, we create an extra node n as shown in Fig. 2.49 and follow this conversion rule: Rc a b R2 R1 n Each resistor in the Y network is the product of the resistors in the two adjacent branches, divided by the sum of the three resistors. Rb Ra R3 Wye to Delta Conversion To obtain the conversion formulas for transforming a wye network to an equivalent delta network, we note from Eqs...
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