0195136047.pdf

84 CIRCUIT ANALYSIS TECHNIQUES

(a) (b)

B

B

C

C

A

A

RAB

RA

RB RC

RCA

RBC

Figure 2.4.1Wye–delta transfor-

mation.(a)Wye configuration.(b)

Delta configuration.

EXAMPLE 2.4.1

Use delta–wye transformation for network reduction and determine the current through the 12-

resistor in the circuit of Figure E2.4.1(a).

+

−

144 V

(a)

3 Ω

4 Ω

4 Ω

A

O

B

C

8 Ω

2 Ω 12 Ω

I =?

Figure E2.4.1

+

−

(b)

3 Ω

A C

B

2 Ω

12 Ω

R I^ =?

3 =^2 Ω

R 1 = 1 Ω R 2 = 2 Ω

IA

144 V

Solution

The delta-connected portion between terminalsA–B–Cis replaced by an equivalent wye connec-

tion [see Equation (2.4.1)] with

R 1 =

4 × 4

4 + 8 + 4

= 1 

R 2 =

4 × 8

4 + 8 + 4

= 2