Problem 83-1    Source:   Problem elaborated by the author of the site.

In the balanced circuit of the Figure 83-1.1, assuming a direct sequence, we have:

V_C = 220 ∠30°  , and   Z_A = Z_B = Z_C = 10∠45° . Calculate:

a) The line and phase voltages.

b) The phase and line currents.

c) The total real, total reactive and apparent total power in the load.

Problem 83-2    Source:   Adapted from Example 22.1 - page 668 - BOYLESTAD, Robert L. - Book: Introdução à Análise de Circuitos - 10ª Edição - Editora Prentice Hall - 2004.

In the circuit of the Figure 83-2.1, assuming a direct sequence, we have:

V_AN = 120 ∠0°  , V_BN = 120 ∠θ₂   e   V_CN = 120 ∠θ₃. In addition, we have Z_A = Z_B = Z_C = 3 + j4. Calculate:

a) The angles θ₂ and θ₃

b) The line voltages.

c) The phase and line currents.

d) Since the load is balanced, check that I_N = 0.

Attention - In the book, page 668, the current I_Bb when passed to the rectangular form, there is a typo in its value, because the correct value is -23.83 - j2.87, and not -22.83 - j2.87.

Problem 83-3    Source:   Problem elaborated by the author of the site.

In the circuit of the Figure 83-3.1, assuming a direct sequence, we have:

V_AN = 127 ∠0° and Z_AB = Z_BC = Z_CA = 15∠-60° . Calculate:

a) the line voltages and their respective phases.

b) the phase and line currents.

c) the active power dissipated by the circuit.

Problem 83-4    Source:   Problem 78 - page 226 - FOERSTER, Gerd & TREGNAGO, Rodrigo - Book: Circuitos Elétricos - 1ª edição - Ed.da Universidade - Ufrgs - 1987.

For the three-phase symmetric network in the Figure 83-4.1, sequence ABC, it is known that the line voltage V_AB = 100√3∠0° and that Z = 10√3∠83.13°. Determine:

a) The currents I₁, I₂ and I_A.

b) The voltage V₁₂.

Problem 83-5    Source:   Problem 11.17 - page 273 - Book: Circuitos Elétricos - NILSSON, James W. & RIEDEL, Susan A. - 5ª edição - Editora LTC - 1999.

In the balanced circuit of the Figure 83-5.1, assuming a direct sequence, we have

V_1n = 12 600 ∠0°  , V_2n = 12 600 ∠-120°  and V_3n = 12 600 ∠120°. In addition, knowing that Z = 2 514 - j900 Ω calculate:

a) The value rms and the phase angle of the current I_BC.

b) What percentage of the average power provided by the source is dissipated by the load.