Example (4):

Three resistances R, 2R and 3R are connected in delta, Fig. (1(a)). Determine the resistances for an equivalent star connection. In Fig. (2), 160 volts are applied to the terminals AB. Determine (a) the resistance between the terminals A and B and (b) the current.

Solution:

The three resistances are joined in delta in Fig. (1(a)).

We have in Fig. (1(b))

R₁ =      R x 3R /( R + 2R + 3R) = R/2

R₂ =      R x 2R /6 R = R/3

R₃ =      2R x 3R / 6R= R           

Take the network of Fig. (2). The three resistances of 100 Ω, 60 Ω and 40 Ω are delta connected between terminal points C, D and E as shown in Fig. (3(a)). They can be converted into equivalent star connection as shown in Fig. (3(b)).

R₁ = 60 x 100 /(60+100+40)           = 30 Ω

R₂ = 100 x 40 / 200                         = 20 Ω

R₃ = 40 x 60 / 200                           = 12 Ω

Then the network of Fig. (14) is reduced to a simple structure of Fig. (4(a)).

As seen, there are two parallel paths between points S and B, one of resistance (20 + 80)=100 Ω and the other also of (12 + 88) = 100 Ω. Hence, equivalent resistance between points S and B

= 100 x 100 / 200 = 50 Ω

The whole network is reduced to a simple circuit of Fig. (4(b)).

(a)   Then resistance between points A and B = 30 + 50 = 80 Ω.

(b) Current I = 160 / 80 = 2 A