Resolved Problems about Three Phase Phasors

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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 ?

Solution of the Problem 81-5

To find the line voltage we must multiply the magnitude of the phase voltage by root of three (eq. 81-01) and add 30° to its angle. Recall that there is a correspondence between the voltages, when the first index is the same, in both line voltage and phase voltage. Then:

V_AB = √3 7,620 cos (ω t + 30°+ 30°)

Performing the calculation:

V_AB = 13,198 cos (ω t + 60°) V

Following the same rationale for the other voltages:

V_BC = 13,198 cos (ω t + 180°) V

V_CA = 13,198 cos (ω t - 60°) V

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