Question

1. An e lectric motor with resistance 15.0 ? and inductance 53.0 mH is connected to a 60.0 Hz ac generator. What is the power factor for this circuit?

2. Refer to the previous problem. In order to obtain more power from the circuit, you would like to reduce the impedance by adding a capacitor in series with the inductor and resistor. What capacitance is needed to increase the power factor to 0.80? There are TWO possible answers. Find both answers and enter the smaller value here.

3. Refer to the previous problem. There are two possible answers. Enter the larger value here.

I'm really confused about this kind of quetion and hope someone can help me.

Answer 1

1.

Inductive reactance

XL=2pi*f*L=2pi*60*(53*10^-3)

XL=19.98 ohms

Impedance

Z=sqrt[R^2+XL^2] =sqrt[15^2+19.98^2]

Z=24.98 ohms

Power factor

PF=cos(o)=R/Z =15/24.98

PF= 0.6

2.

Given

PF=cos(o)=R/Z =0.8

=>Z=R/0.8 =15/0.8

Z=18.75 ohms

since

Z=sqrt[R^2+(XL-Xc)^2]

18.75 =sqrt[15^2+(19.98-Xc)^2]

(19.98-Xc)^2=126.56

19.98-Xc=(+ or -) 11.25

when

19.98-Xc=11.25

Xc=8.73

since Xc=1/2pifC

=>C=1/2pif*Xc =1/2pi*60*8.73

C=3.04*10^-4 F or 303.8 uF

when

19.98-Xc=-11.25

Xc=31.23

=>C=1/2pi*60*31.23

C=8.49*10^-5 F or 84.9 uF

so

smallest value

C=8.49*10^-5 F or 84.9 uF

c)

Largest value

C=3.04*10^-4 F or 303.8 uF