Question

Problem 32.51-- A series RLC circuit consists of a 80 Ω resistor, a 0.52 H inductor, and a 50 μF capacitor. It is attached to a 120 V/60 Hz power line.

a) What is the peak current I at this frequency? Express your answer with the appropriate units

b) What is the phase angle ϕ?

c) What is the average power loss? Express your answer with the appropriate units.

Answer 1

given data

80.0 Ω resistor,

a 0.52 H inductor,

and a 50.0 μF capacitor.

120 V/60 Hz power line.

ω =2*pi*f

ω = 2*3.1416*60 = 377 rad/sec
inductive reactance Xl = ω*L = 377*0.52= 196.04 ohm (j196.04)
capacitive reactance Xc = 10^6/(50*377) = 53.05 ohm (-j53.05)
total reactance X = Xl +Xc

= j196.04-j53.05 = -j142.99 ohm
Z = square root R^2+X^2 = square root 80^2+142.99^2 = 163.84 ohm
Irms = 120/163.84= 0.732 A

Ipeak = Irms*√2 = 1.0358 A

Part C What is the average power loss?

P loss = R*Irms^2 = 80*0.732^2 =42.86 watt