Question

An effective AC voltage of 175 V at 60 Hz is applied to an RLC circuit with 26.7 mH in- ductor, 0.547 μF capacitor, and 42 Ω resistor in series. What is the effective current? Answer in units of A. What is the power factor of the circuit? What is the power consumed in the circuit? Answer in units of W. Answer within a tolerance of ± 2 percent.

Answer 1

Given

   Vrms = 175 V, f= 60 Hz, W = 2pi*f = 2pi*60 = 120 pi rad/s

   L = 26.7*10^-3 H

   C = 0.547*10^-6 F

   R = 42 ohm

first calculating the impedance in the circuit as

   Z = sqrt(R^2+(X_L-X_C)^2)

here X_L,X_C are reactances of inductor and capacitor

   X_L = W*L = 120pi*26.7*10^-3 = 10.066 ohm

   X_C = 1/(W*C) = 1/(120pi*0.547*10^-6) ohm = 4849.328 ohm

now Z = sqrt(42^2+(10.066 - 4849.328)^2) ohm

   = 4839.44 ohm

the effective current is I = V0/Z = Vrms*sqrt(2) /Z = 175*sqrt(2) /(4839.44) A = 0.0511396718 A= 51.139 mA

power factor is cos phi = R/Z = 42/4839.44 = 0.00867869

Average power consumed is P avg = Vrms*Irms*cos phi = (Vrms^2 /Z)(cos phi)

  

       P = 175^2*0.00867869 / 4839.44 = 0.0549205861112 W