A series RLC circuit has a 100 ohm resistor a 4 microF capac

A series RLC circuit has a 100 ohm resistor, a 4 microF capacitor and a 2.0 mH inductor connected across a 120 V rms ac voltage source operating at (1000/pi) Hz. what is the power factor of this circuit?

Solution

L=2mH

f=1000/pi

w=2*pi*f=2*pi*(1000/pi)=2000 rad/sec.

xl=wl=2000*2*10^-3=4 ohm.

xc=1/(wc)=1/(2000*4*10^-6)=125 ohms.

phase angle=inverse tan of[(xl-xc)/R]=inverse tan [(4-125)/100]=-50.42 degrees.

power factor=cos(phase angle)=cos(-50.42)=0.637