Question 13.1: Two resistors and two inductors are connected in series (Fig......
Two resistors and two inductors are connected in series (Fig. 13-29). The circuit is connected to a 130-V, 60-Hz line. The first resistor has a power dissipation of 56 W, and the second resistor has a power dissipation of 44 W. One inductor has a reactive power of 152 VARs and the second a reactive power of 88 VARs. Find the unknown values in this circuit.
The first step is to find the total amount of true power and the total amount of reactive power. The total amount of true power can be computed by adding the values of the resistors together. A vector diagram of these two values would reveal that they both have a direction of 0° (Fig. 13-30).
\mathrm{P_{T}}=\mathrm{P_{1}}+\mathrm{P}_{4}
\mathrm{P_{T}}=56+44
\mathrm{P_{T}}=100\mathrm{\ W}
The total reactive power in the circuit can be found in the same manner. Like watts, the VARs are both inductive and are, therefore, in the same direction (Fig. 13-31). The total reactive power will be the sum of the two reactive power ratings.
\mathrm{VARs_{T}}=\mathrm{VARs_{L2}}+\mathrm{VARs_{L3}}
\mathrm{VARs_{T}}=152+88
\mathrm{VARs_{T}}=240
