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 `