Unformatted text preview: how to identify them when they occur as part of a network and
how to apply wyedelta 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 =  eText 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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 Spring '12
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 Resistor, Electrical impedance, Series and parallel circuits, DC Circuits, eText Main Menu

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