Question

A series RLC circuit consists of a 98.0 ? resistor, a 0.190H inductor, and a 45.0 ?F capacitor. It is attached to a 120 V/60 Hz power line.

What is the average power loss?

Answer 1

  I = V/R = 120/98 = 1.22 A

P = VI = 120 x 1.22 = 146.9 J/s (as it is Hz: frequency per second)

Thus 147 W.

Answer 2

w = 2*pi*f = 2*pi*60 = 376.99 rad/s

Xc = 1/w*C = 1/(376.99)*(45*10^-6) = 58.95 ohms

XL = w*L = 376.99*0.190 = 71.63 ohms

Z = sqrt(R^2 + (XL - Xc)^2) = 98.82 ohms

Irms = Vrms/Z = 120/98.82 = 1.214 A

cos = R/Z = 98/98.82 = 0.9917

average power loss = Vrms*Irms*cos = 120*1.214*0.9917 = 144.47 W

Answer 3

power loss is done only through resistors.

inductors and capacitors are energy storing elements.

so the average power loss= $\frac{120^{^{2}}}{98}$ =146.94 watts