Problem 81-1    Source:  Problem elaborated by the author of the site.

Be the voltage V_AN = 127 ∠60°. Find the corresponding line voltage.

Problem 81-2    Source:  Problem elaborated by the author of the site.

Be the voltage V_BC = 440 ∠220°. Find the corresponding phase voltage.

Problem 81-3    Source:  Problem elaborated by the author of the site.

Be the voltage V_AC = 380 ∠250°. Find the phase voltage V_BN.

Problem 81-4    Source:   Problem 11.1 - page 272 -    NILSSON, James W. & RIEDEL, Susan -    Book: Circuitos Elétricos - 5ª edição - Editora LTC - 1999.

Verify that the following voltage assemblies are balanced three-phase assemblies. If the answer is yes, check whether the phase sequence is positive or negative. If the answer is negative, explain why.

a)   v_a = 139 cos 377t,   v_b = 139 cos (377t + 120°)   and   v_c = 139 cos (377t + 120°).

b)   v_a = 381 cos 377t,   v_b = 381 cos (377t + 240°)   and   v_c = 381 cos (377t + 120°).

c)   v_a = 2 771 cos (377t - 30°),   v_b = 2 771 cos 377t   and   v_c = 2 771 cos (377t + 210°).

d)   v_a = 170 cos (ωt + 30°),   v_b = - 170 cos ωt   and   v_c = 170 cos (ωt + 60°).

e)   v_a = 339 cos ωt,   v_b = 339 cos (ωt + 120°)   and   v_c = 393 cos (ωt - 120°).

f)   v_a = 3 983 cos (ωt + 50°),   v_b = 3 983 cos (ωt - 160°)   and   v_c = 3 983 cos (ωt + 70°).

Problem 81-5    Source:   Problem 11.3 - page 272 -    NILSSON, James W. & RIEDEL, Susan -    Book: Circuitos Elétricos - 5ª edição - Editora LTC - 1999.

The expressions in the time domain of the three voltages between line and neutral at the terminals of a type load Y are:

v_AN = 7 620 cos (ω t + 30°), v_BN = 7 620 cos (ω t + 150°) and v_CN = 7 620 cos (ω t - 90°).

What are the expressions in the time domain of the three voltages between lines, v_AB , v_BC and v_CA ?