A series ac circuit contains a 190 ? resistor, a 14.0 mH inductor, a 3.10 ? F ca

Question

A series ac circuit contains a 190 ? resistor, a 14.0 mH inductor, a 3.10 ?F capacitor, and an ac power source of voltage amplitude 45.0 Voperating 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.

MasteringPhysics: Week 7- Google Chrome https://session.masteringphysics.com/myct/.temView?assignmentProblemID=58051172 Physics 202 Ford Spring 2016 WeekZ Problem 22.18 Help | Close Resources previous | 8 of 15 | next » Problem 22.18 What is the power factor of this circuit? A series ac circuit contains a 190 resistor, a 14.0 mH inductor, a 3.10 F capacitor, and an ac power source of voltage amplitude 45.0 V operating at an angular frequency of 360 rad/s COS Submit My Answers Give Up Part B Find the average power delivered to the entire circuit Submit My Answers Give Up Part C What is the average power delivered to the resistor, to the capacitor, and to the inductor?

Explanation / Answer

w = 360 rad/s
R = 190
L = 14.0 mH
C = 3.10 F

(a)
Power factor of the circut is = cos()
Where,
= tan^-1((Xl - Xc)/R)
XL =w*L = 360*14*10^-3 = 5.04
Xc = 1/w*c = 1/(360*3.1*10^-6) = 896.1


= tan^-1((896.1-5.04)/190)
= 77.96o
Power Factor, = cos(77.96)
Power Factor, = 0.208

(b)
Irms = E/sqrt((Xl- Xc)^2 + R^2) * sqrt(2)
Irms = 45.0 / sqrt((896.1- 5.04)^2 + 190^2) * sqrt(2)
Irms = 0.0349

P = Irms * Vrms * cos()
P = 0.0349 * 45/sqrt(2) * 0.208
P = 0.231 W

(c)
Power delivered to Resistor, Pr = 0.231 W
Power delivered to Inductor, Pl = 0
Power delivered to Capacitor, Pc = 0

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