Question

#4) A series RCL circuit contains a 48.0-? resistor, a 1.70-?F capacitor, and a 4.20-mH inductor. When the frequency is 2575 Hz, what is the power factor of the circuit?

Answer 1

XC=1/(2*3.14*2575*1.7*10^-6)=36.38 ohm

XL=2*3.14*2575*(4.2*10^-3)=67.92 ohm

R=48 ohm

Z=(R^2+(XL-XC)^2)^0.5=57.43 ohm

power factor=R/Z=0.8356

Answer 2

XC=1/(2*3.14*2575*1.7*10^-6)=36.375ohm

XL=2*3.14*2575*(4.2*10^-3)=67.918ohm

R=48ohm

Z=(R^2+(XL-XC)^2)^0.5=57.43ohm

power factor=R/Z=0.8358

you got correct

Answer 3

? = 2pi*f = 2pi*2575 = 16171 rad/s

Inductive reactance XL = ?*L = 16171 * 4.20*10^-3 H = 67.91 ?

Capacitive reactance Xc = -1 / ?*C = 1/(16171 * 1.7*10^-6) = -36.37 ?

Net reactance X = 67.91 - 31.2 = 36.71 ?

Impedance angle is arctan(X/R) = tan(36.71 / 48) = 37.40 deg

Power Factor = cos(37.40) = 0.794

Power Factor =0.794