Problem 5-4    Source:   Problem 2 - page 26 - Handbook Electric Circuits I - Prof. Douglas Schirmer Scharamm - DPEE - UFSM.

It is known that when we apply a voltage V_ab = 90 V to the circuit shown in Figure 05-04.1, the circuit consumes a power equal to 270 W. Find the value of R₂.

Solution of the Problem 5-4

Note that the voltage applied between points a - b and the power consumed by the circuit were provided. This way, with this data it is possible to find the equivalent resistance value between points a - b. For this we will use eq. 07-03  repeated below for clarity.

Therefore, doing algebraic work on this equation, we obtain:

Knowing the value of R_eq we can calculate the value of R₂. Note from the circuit that for this we must transform the circuit delta between points c-b-e in a star circuit. For the transformations we will use the equations below, already studied in Equivalence between Delta-Star Circuit.

Thus, doing the calculations with the values ​​of the resistors that are between the points c-b-e, we find the equivalent circuit Star as shown in Figure 05-04.2 with their respective numerical values.

Now, replacing the Delta circuit shown in Figure 05-04.1 with the calculated Star circuit we will obtain the circuit shown in Figure 05-04.3 .

The figure above shows that R₁ is in series with R_a. Therefore, adding their values ​​we find 35 Ω. And R₂ is also in series with R_c, that is, we have R₂ + 6. On the other hand, we know that the equivalent resistance between points a-b has been calculated and its value is 30 Ω. Therefore, as we want to find the value of R₂ we can write:

Working algebraically the above equation we obtain:

So, carrying out the relevant operations in the equation above, we find that the value of R₂ is: