Problema 5-3    Source:   Problem 3.54 - page 61 - NILSSON & RIEDEL - Book: Circuitos Elétricos - 8ª edição - Ed. Pearson - 2010.

Use Delta-Star transformation and calculate the equivalent resistance between the points a - b in the circuit shown in Figure 05-03.1

Solution of the Problem 5-3

In order to solve this problem we have to use the transformations star-triangle. Initially we will calculate the equivalent circuit for parts of the circuit that are highlighted in green and yellow. For the transformations we will use the equations below, already studied in   Theory.

We replaced the triangle circuit highlighted in green in the previous figure, by their corresponding star circuit with their respective numerical values as shown in the Figure 05-03.2.

We see in the Figure 05-03.3 the other transformation relative to the circuit highlighted in yellow.

And finally in the Figure 05-03.4 appears the resulting circuit where we show the transformations made. Between the points c and e, we have a series association of 7.5 and 12.5 ohms, totaling 20 ohms. And from point c through 2 and 4 points until we reach to point e we have three resistors in series resulting in a single resistor of 3 + 47 + 10 = 60 ohms.

Note that the parallel between the 20 and 60 ohms, in the Figure 05-03.5, results in a resistor of value equal to  [60 x 20 / (60 + 20)] = 15 ohms. The 20 ohms resistor at the top of the circuit is the sum of 15 and 5 ohms that connect the a-1-c points. And at the bottom of the circuit, we have the 64 ohms resistor, which is the result of the sum of 50 and 14 ohms which are interconnected to points b-3-e.