Problem 84-2    Source:   Problem elaborated by the author of the site.

Using the data from the previous problem and suppose the unbalanced impedances with the following values:

Z_AB = 10 ∠30°  ,   Z_BC = 12 ∠-30°   and   Z_CA = 18 ∠60°. In the circuit configuration shown in the Figure 84-2.1, calculate:

a) the phase currents.

b) the line currents.

Solution of the Problem 84-2

From the previous problem (84-1) we calculate the line voltages. So we have the following data to solve this problem:

V_AB = 180.3 ∠86.3°,   V_BC = 234.3 ∠-33.7°,     V_CA = 212.6 ∠-166.4°   and

Z_AB = 10 ∠30°  ,   Z_BC = 12 ∠-30°,     Z_CA = 18 ∠60°

Item a   

Using the data provided by the problem it is possible to calculate the phase currents, or:

Item b   

And the line currents are:

We leave it to the student to check that   I_A + I_B + I_C = 0