Reactance and impedance

Discussion in 'Homework Help' started by student777, Jul 19, 2006.

  1. student777

    Thread Starter New Member

    Jul 19, 2006
    2
    0
    Someone please help! I am stuck on this problem and I dont understand the equation or how to apply it here. Please help?


    a) The reactance of the inductor L.

    b) The impedance of the resistor and inductor in series.



    You do not need to find the phase of the current in this series circuit.




    R1 = 10 Ω


    L = 20 mH


    E = 10 VAC
    60 Hz
     
  2. student777

    Thread Starter New Member

    Jul 19, 2006
    2
    0
    X(L) = 2 * pi * F(total) * F(L)
    X(L) = 2 * pi * 60Hz * .02H
    X(L) = 7.5398 Ohms

    Is this correct?
     
  3. beenthere

    Retired Moderator

    Apr 20, 2004
    15,815
    282
    Hi,

    If my calculator isn't lying, that's the answer.
     
  4. Papabravo

    Expert

    Feb 24, 2006
    10,157
    1,795
    The equation for inductive reactance is quite straightforward. The inductive reactance is a function of frequency and the inductance. The factor of 2*pi converts frequency in Hertz(cycles per second) to radians per second. A radian is a dimensionless measure of angular displacement. So
    Code ( (Unknown Language)):
    1.  
    2. X-sub-L = 2 * pi * f * L
    3.         = 2 * 3.1415926 * 60 * 20 e -3
    4.         = 7.54 Ohms
    5.  
    Impedance is a complex number with a Real and an Imaginary part. Individual components may have either a real or an imaginary part or both when modeling less than ideal components. So
    Code ( (Unknown Language)):
    1.  
    2. Z-sub-R  = 10 + j0
    3. Z-sub-L  =  0 + j7.54
    4.     and
    5. Z-series = 10 + j7.54
    6.  
    For a resistor and an inductor in series you add the complex impedances. Another way to express the impeadance is as a magnitude and an angle.
    Code ( (Unknown Language)):
    1.  
    2. MAG = sqrt(10^2 + (7.54)^2) = 12.54 Ohms
    3. ARG = arctan(7.54/10) = 37 degrees = .646 radians
    4.  
     
  5. jimgallagher

    New Member

    Dec 22, 2006
    1
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    The reactance of the inductor is 7.54ohms ( Xsub l = 2pi fl, however, the total circuit impedance in series is 7.54ohms + 10 ohms = 17.54 ohms. Impedance is the total opposition to AC, inductive reactance + capacitive reactance + resistance.
     
  6. JoeJester

    AAC Fanatic!

    Apr 26, 2005
    3,373
    1,159
    papabravo is correct.
     
  7. Papabravo

    Expert

    Feb 24, 2006
    10,157
    1,795
    You can't add reactance to resistance. The algebra of complex numbers won't allow that. Resistances are always in the real part of the complex impedance. If the resistance in the wire in the inductor were measurable it would be added to the external series resistance. Reactances are always in the imaginary part. If the external series resistor was a wirewound with some small inductance, that reactance could be added to the reactance of the inductor.

    Resistance and reactance are both real numbers. Impedance is a complex number and the algebra of complex numbers is different than the algebra of real numbers.
     
  8. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
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