Solved Problems about AC Powers

Problem 52-5 Source: Problem 19 - page 449 - HAYT, William Jr, KEMMERLY, Jack E. , DURBIN, Steven M. - Book: Análise de Circuitos em Engenharia - 7ª edição - Ed. McGraw Hill - 2008.

Determine the average power supplied by the dependent source in the circuit shown in the Figure 52-05.

Solution of the Problem 52-5

Note that in the figure above the currents of interest were related to I_x. Thus, by applying Kirchhoff in the loop indicated by the arrow blue, we get:

- 4.8 I_x + j9.6 - j1.92 I_x + 4.8 I_x = 0

Therefore, by performing the calculation the value of I_x:

I_x = 5 A

With the value of I_x, we can calculate the value of the dependent current source:

1.6 I_x = 1.6 x 5 = 8 A

To meet the problem request, we need the value of V_b, or:

V_b = 8 x 0.6 x I_x = 24 volts

With this data it is possible to calculate the power supplied by the dependent source. As the source provides power then its value must be negative, or:

P_S = - 8 V_b = - 8 x 24 = - 192 W

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