Problem 52-2
Source: Problem 33 - page 440 -
BOYLESTAD, Robert - Book: Introdução à Análise de Circuitos -
10ª edição - Ed. Pearson Education do Brasil - 2004.
The power factor of a circuit is 0.5 delayed and the power dissipated is 500 W.
If the input voltage is given by v = 50 sin(ωt + 10°), determine the
input current.
Solution of the Problem 52-2
As we know the power factor we can calculate the angle of lag between the voltage and the current in the circuit. Soon:
The problem statement says that the power factor is delayed. Therefore, the current must be
60° delayed in relation to the voltage. Since v has an angle of 10°, it is clear that the angle of the current must be 10° - 60° = - 50°.
We must determine the value of this current. See below the equation that should be used in this case.
Note that v is expressed in trigonometric form. This means that the 50 value is the
maximum value. Therefore, using this equation we find the maximum value of the electric current, or
Imax. Working algebraically this equation, we have:
Substituting the numerical values, we find:
Now we have all the data needed to write i in the trigonometric form, or:
