Problem 83-8    Source:   Problem 12.25 - page 486 -    SADIKU, Mathew & ALEXANDER, Charles -    Book: Fundamentos de Circuitos Elétricos - Ed. McGraw Hill - 5ª edição - 2013.

For the circuit shown in Figure 83-08.1 we have to

V_AB = 440 ∠ 10°, V_BC = 440 ∠ -110° and V_CA = 440 ∠ 130°.

We also know that Z_L = 3 + j2 Ω  and  Z = 10 - j8 Ω.

a) Calculate line currents I_a, I_b and I_c.

b) Calculate the voltages V_an, V_bn and V_cn.

Solution of the Problem 83-8

Item a

Through the circuit of Figure 83-08.1, we see that the phase impedance between the points A and n is given by:

On the other hand, we know that it is possible to transform the line voltage, V_AB , in phase voltage, using eq. 83-03, reproduced below for clarity.

With this information, we can calculate the phase voltage, or:

As the circuit is balanced the other two voltages have the same module that V_An but lagged by 120°. Therefore, the line current, I_a , is worth:

Carrying out the calculation, we find:

As the circuit is balanced, the modulus of the line currents are equal, varying only the angle. So:

Item b

To calculate the voltages on the Z loads, we have to:

Carrying out the calculation, we find:

And the voltages V_Bn and V_Cn, in module, are equal to V_An, but lagged by 120°. Soon