Question

A series ac circuit contains a 210 Ω resistor, a 20.0 mH inductor, a 3.30 μF capacitor, and an ac power source of voltage amplitude 45.0 V operating at an angular frequency of 360 rad/s . 1)What is the power factor of this circuit? 2)Find the average power delivered to the entire circuit. 3)What is the average power delivered to the resistor, to the capacitor, and to the inductor?

Answer 1

answer) 1) the power factor is given by

cos=cos(tan^-1(XL-Xc/R))

XL=*L=360*20*10^-3=7.2 ohm

Xc=1/C=1/360*3.3*10^-6=841.7508 ohm

now putting all the values we have

cos=cos(tan^-1(7.2-841.7508/210))=0.244

so the answer is 0.244

2) the formula for power is

P=IrmsV cos...........1)

Irms=I/2

Irms=E/Z2=45/((Xl-Xc)²-R²))*2)=45/(834.5508²+210²)2)=0.03698A

now using eqn 1)

P=0.03698*45*0.244=0.406 W

so the answer is 0.406 W

3) Power delivered to resistor = same as power delivered to entire circuit

so power delivered to circuit is 0.406 W

Power delivered to capacitor is =0 W

Power delivered to inductor=0W.

because in an ideal capacitor and inductor, the consumption of power is zero.