AC circuit, mystery impedance

  1. 1. The problem statement, all variables and given/known data

    a) Write an expression for V1 and V2 both in time domain and phasor domain (Solved)

    b) Write an expression for the current I both in time domain and phasor domain (Solved)
    c) Calculate the Power factor of the supply and specify whether it is lagging or
    leading (Solved)
    d) Specify the type of the reactance (XC or XL)
    e) Determine the value of X and hence the corresponding value of L or C
    f) Calculate the supply average, reactive and apparent power
    g) Draw the phasor diagram of the circuit

    2. Relevant equations
    f= 250/3

    3. The attempt at a solution
    V1 = 10sqrt(2)<48 = 9.46+10.51
    V2 = 5/sqrt(2)<0 = 3.54
    I = v2/r2 = 0.354<0
    PF = 0.669, lagging

    X is an inductor

    VCh2 + Vxl = Vsource
    Vxl = 9.46+10.51j - 5/sqrt(2) = 5.93 +10.51j = 12.1<60.6

    Zx = Vxl/Is = 12.1<60.6 / 0.354<0 = 16.77+ 29.73j

    This tells me that there's a physical impedance associated with the coil, equal in value to 16.77ohms...Meaning that it's not a pure inductor?

    To find L:

    29.73 = 2*pi*f*L ... 29.73/ (2*pi*250/3) = L = 0.057H

    But these results don't add up to the next few parts:

    -Active Power-
    P(10ohm)=I^2*R=(0.354)^2*10 = 1.25W
    P(16.77ohm)=I^2*R=(0.354)^2*16.77 = 2.10W

    -Reactive Power-
    P(XL)=I^2*R=(0.354)^2*29.73 = 3.72VAR

    -Apparent Power-
    Active+Reactive*j = 3.35+3.72j

    which matches:

    S=EI=10sqrt(2)<48 * 0.354<0 = 3.35 + 3.72j

    Have I done this question correctly? Is it possible that the inductor has a simple resistance component to it?
  2. jcsd
  3. You have apparently chosen the first positive peak of V1 for its phase, but for the phase of V2 you have chosen the first positive going zero crossing. You have to be consistent in these choices.

    Looking at the zero crossings of V1, the angle appears to be closer to 45 degrees than 48 degrees.

    Since the positive going zero crossing of V1 nearest to the zero time of the graph is at -45 degrees, I would say that V1 = 10sqrt(2)<-45, and then it would be consistent to say that V2 = 5/sqrt(2)<0.

    Redo your calculations with this number for V1 and see if you get better results.
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