Solved Problems about AC Phasors

Problem 51-3 Source: Problem 6.29 - page 102 - EDMINISTER, Joseph A. - Book: Circuitos Elétricos - Ed. McGraw Hill - 1971.

Find Z and Y corresponding to the phasor diagram as shown in the Figure 51-03.1.

Solution of the Problem 51-3

As the phasors turn counterclockwise, the graph concludes that the electric current is advanced in relation to the voltage. This characterizes a circuit capacitive. On the other hand, knowing the current and voltage, as well as their angles, we can calculate the impedance Z. Initially, writing these variables in polar form, we get:

V = 85 ∠205°

And for the electric current:

I = 41.2 ∠219.05°

Now we can calculate the value of Z, because:

Z = V / I = 85 ∠ 205° / 41.2 ∠ 219.05°

Performing the calculation:

Z = 2.0631 ∠-14.05 = 2 - j0.5 Ω

On the other hand, it is known that the admittance Y is the inverse of the impedance Z. Soon:

Y = 1 / Z = 1 / 2.0631 ∠-14.05°

Performing the calculation, we find:

Y = 0.485 ∠+14.05° = 0.47 + j0.118 S

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