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Determine the value of the inductance ?

  1. Dec 21, 2009 #1
    Determine the value of the inductance ...??

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


    Consider a series RLC circuit. The applied voltage has a maximum value of 210 V and oscillates at a frequency of 76 Hz. The circuit contains an inductor whose inductance can be varied, a 900 ohm resistor, and a 1 μF capacitor.Determine the value of the inductance such that the voltage across the capacitor is out of phase with the applied voltage by 54◦, with Vmax leading VC. Answer in units of H.

    2. Relevant equations

    Cos [tex]\phi[/tex] = XL / Z
    Tan [tex]\phi[/tex] = XL - XC / R
    w = 2*pi*f
    Z2 = R2 + (XL - XC)2



    3. The attempt at a solution

    First I used the 2nd Eq. Tan [tex]\phi[/tex] = XL - XC / R

    (R* Tan [tex]\phi[/tex])2 = (XL - XC)2

    Then I used the 1st Eq. Cos [tex]\phi[/tex] = XL / Z

    Z2 = R2 + (XL - XC)2

    I replaced (XL - XC)2 with (R* Tan [tex]\phi[/tex])2

    then ,

    Cos2 [tex]\phi[/tex] = XL2 / (R2 + (XL - XC)2)

    XL2 = Cos2 [tex]\phi[/tex] * (R2 + (XL - XC)2) = w2L2

    Then , L = 1.8827 H which is wrong .

    Am i in the right direction , if not please point me towards it . Thanks.
     
    Last edited: Dec 21, 2009
  2. jcsd
  3. Dec 21, 2009 #2

    rl.bhat

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    Homework Helper

    Re: Determine the value of the inductance ...??

    Since the voltage across the capacitor is out of phase with the applied voltage, angle between Vc and hence VC - VL and Vmax is 54 degrees.
    So tan(54) = R/(XC - XL)
    Solve for XL and find L.
     
  4. Dec 24, 2009 #3
    Re: Determine the value of the inductance ...??

    wow ..thx a ton rl.bhat.

    whould u tell what expression must i use if the question says the voltage across the inductor ??

    and how did you get Vc-Vl why it not Vl-Vc ??

    thanks again ..
     
  5. Dec 24, 2009 #4

    rl.bhat

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    Re: Determine the value of the inductance ...??

    Since applied voltage leads with Vc, Vc must be greater than VL. So net voltage across reactance should be VC - VL.
    If VL leads with the applied voltage then you have to take VL - VC.
     
  6. Dec 24, 2009 #5
    Re: Determine the value of the inductance ...??

    Thanks again for the clarification.

    Hmmmm... why tan(theta) why not cos(theta) ...??

    You have answered same question before and i want to understand it 2 ..

    https://www.physicsforums.com/showthread.php?t=328964


    check the link .

    If i was answering the question i would say the answer must be in this form ...

    tan(theta)= R / XL-XC

    Because it says that Vl is leading so it is greater that Vc like what you 've said ...

    But you answered cos(theta)=Xc/Z ,,,,,??
     
  7. Dec 25, 2009 #6

    rl.bhat

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    Homework Helper

    Re: Determine the value of the inductance ...??

    In both the treads VC is out of phase with the applied voltage.
    So you can write either tanθ = R/(XC - XL) or cosθ = (XC - XL)/Z. In the second thread it was typo.
    In LCR circuit always Vmax leads VC and VL leads Vmax. So it does not change expression for tanθ. In your relevant equation the angle φ is the phase difference between the current and Vmax.
     
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