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Calculating Impedance Using Capacitive Reactance

  1. Oct 3, 2012 #1
    1. The problem statement, all variables and given/known data

    A 29kΩ resistor is in series with a 62mH inductor and an ac source. Calculate the impedance of the circuit if the source frequency is 80Hz .

    2. Relevant equations

    XL = ωL
    Z = [(R^2 + (XL - XC)^2)] ^ 1/2


    3. The attempt at a solution

    R = 29,000 Ω

    XL = 0.062 H (2∏ * 80 Hz)
    XL = 31.16 Ω

    I'm having difficulty figuring out how to find XC. XC = 1 / ωC but what is "C?"
     
  2. jcsd
  3. Oct 3, 2012 #2

    vela

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    Your formula for Z applies to RLC circuits. You have an RL circuit. Do you know how that formula for Z was derived? It was probably using a phasor diagram. If you understand the derivation, it's pretty easy to see what you need to do.
     
  4. Oct 3, 2012 #3
    Was the formula for "Z" derived using the Pythagorean theorem? If so, I still do not see the connection to capacitance.
     
  5. Oct 3, 2012 #4

    vela

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    Describe how the formula was derived.
     
  6. Oct 3, 2012 #5
    It looks as if it uses the following relations:

    Vrms = Irms * Z
    Vnaught = InaughtZ

    The book also shows a phasor diagram where Vnaught is the sum vector and acts as the hypotenuse of the triangle.
     
  7. Oct 4, 2012 #6

    vela

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    And where does the triangle come from?
     
  8. Oct 4, 2012 #7
    The triangle comes from a phasor diagram. I'm attaching an image made in paint of the one I see in the textbook. It's a tad messy, but it is readable.
     

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  9. Oct 4, 2012 #8

    vela

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    In your picture, I should actually point in the same direction as VR=IR.

    Do you understand why the one leg is VL-VC and why you add all the voltages?
     
  10. Oct 4, 2012 #9
    Are the voltages being added together to find the peak voltage source, Vnaught?
    Is Vc subtracted from Vl because Vc lags the current by 90°?
     
  11. Oct 4, 2012 #10

    vela

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    Yes, it's Kirchoff's voltage law applied to the elements in series.

    And because VL leads the current by 90°. The two phasors point in opposite directions, so when you add them vector-wise, you subtract their magnitudes.

    So back to your original problem, if you follow the same analysis, what do you get for the impedance?
     
  12. Oct 5, 2012 #11
    Since this is an RL circuit then

    Z = [(R^2 + XL^2)]^1/2
     
  13. Oct 6, 2012 #12

    vela

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    Yup, you have it.
     
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