Resistance and reactanceSometimes you’ll get data that tells you the resistance and reactance components in acircuit. To calculate the power factor from this, you can either find the phase angle andtake its cosine, or find the absolute-value impedance and take the ratio R/Z.Problem 17-6A circuit has a resistance of 50 Ω and a capacitive reactance of −30 Ω. What is the powerfactor? Use the cosine method.The tangent of the phase angle is equal to X/R. Therefore, the phase angle is arctan(X/R)arctan (−30/50)arctan (−0.60)−31 degrees. The power factor is the co-sine of this angle; PFcos (−31) 0.8686 percent.Problem 17-7A circuit has a resistance of 30 Ω and an inductive reactance of 40 Ω. What is the powerfactor? Use the R/Z method.Find the absolute-value impedance: Z2R2X230240290016002500; therefore Z50. The power factor is therefore PFR/Z30/500.6060percent. This problem is represented very nicely by a 3:4:5 right triangle (Fig. 17-8).How much of the power is true?31317-8Illustration for Problem17-7.How much of the power is true?The above simple formulas allow you to figure out, given the resistance, reactance, andVA power, how many watts are true or real power, and how many watts are imaginaryor reactive power. This is important in radio-frequency (RF) equipment, because RFwattmeters will usually display VA power, and this reading is exaggerated when there isreactance in a circuit.