Question

An AC voltage with an amplitude of 124 V is applied to a series combination of a 235 uF capacitor, a 108 mH inductor, and a 16.4 12 resistor. Calculate the power dissipated by the circuit at a frequency of 50.0 Hz. Submit Answer Incorrect. Tries 1/12 Previous Tries Calculate the power factor at this frequency. Submit Answer Incorrect. Tries 2/12 Previous Tries Calculate the power dissipation at a frequency of 60.0 Hz. Submit Answer Tries 0/12 Calculate the power factor at this frequency. Submit Answer Submit Answer Tries 0/12

Answer 1

a)

Inductive reactance is given by

X_L =2pifL =2pi*50*(108*10^-3) = 33.93 ohms

Capacitive reactance is given by

X_C =1/2pifC =1/2pi*50*(235*10^-6) =13.545 ohms

impedance is given by

Z=sqrt[R²+(X_L-X_C)²]

Z=sqrt[16.4²+(33.93-13.545)²]

Z=26.162 ohms

Total Current is given by

I=V/Z =124/26.162 =4.74 A

Rms current is

I_rms=4.74/sqrt(2) =3.35 A

Power dissipated in resistor is given by

P=I²R=3.35²*16.4 =184.2 Watts

b)

Power Factor is given by

PF =Coso= R/Z =16.4/26.162 = 0.62685

c)

Inductive reactance is given by

X_L =2pifL =2pi*60*(108*10^-3) = 40.715 ohms

Capacitive reactance is given by

X_C =1/2pifC =1/2pi*60*(235*10^-6) =11.288 ohms

impedance is given by

Z=sqrt[R²+(X_L-X_C)²]

Z=sqrt[16.4²+(40.715-11.288)²]

Z=33.69 ohms

Total Current is given by

I=V/Z =124/33.69=3.68 A

Rms current is

I_rms=3.68/sqrt(2) =2.603 A

Power dissipated in resistor is given by

P=I²R=2.603²*16.4 =111.1 Watts

d)

Power Factor is given by

PF =Coso= R/Z =16.4/33.69= 0.4868