Problema 83-7    Source:    Problem 4 - page 601 - BOYLESTAD, Robert L. - Book: Introdução à Análise de Circuitos - Ed. Prentice Hall - 10ª edição - 2008.

For the system shown in Figure 83-07.1:

a) Calculate P_T, Q_T and S_T.

b) Determine the power factor FP.

c) Draw the power triangle.

d) Calculate I_S.

Solution of the Problem 83-7

Item a

Adding the average power of each load, we get:

Doing the same for reactive power, we have:

Note that we use - j600 for load 2, because depending on the circuit, load 2 is capacitive (C). Therefore, we can write the total apparent power, or:

In phasor form we have:

Item b

With the phasor form of S_T we can already calculate the power factor, because:

Item c

The Figure 83-07.2 shows the graph of the circuit's power triangle.

Item d

In order to find the current value I_S we remember that:

Note that from the source voltage and apparent power, we can calculate the value of the complex conjugate of the current. So, after this calculation we must change the angle sign to find I_S.

Now the value of I_S will be: