Answer to Question #201759 in Electrical Engineering for weam

Question

A certain circuit has equivalent impedance Z = 8+j4 Ω, and an applied voltage 42.5 cos( 1000t + 30°)

The power factor is:

 

 Select one:

 a 0.45

 b 0.8

 c 0.89

 d 0.32

 e 0.6

Answer 1

The impedance is

$$Z=R+jX,\\ |Z|=\sqrt{R^2+X^2}.$$

The power factor is

$$\cos\phi=\frac{R}{|Z|},\\\space\\ \cos\phi=\frac{8}{\sqrt{8^2+4^2}}=0.89.$$