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Phase shift & circuits

  1. Jun 13, 2014 #1
    1. The problem statement, all variables and given/known data

    An RLC circuit has a resistance of 2.0 kΩ, a capacitance of 8.0 µF, and an inductance of 9.0 H. If the frequency of the alternating current is 4.0/π kHz, what is the phase shift between the current and the voltage?
    A) -1.6 rad
    B) -1.5 rad
    C) 36 rad
    D) 3.1 rad



    2. Relevant equations

    Tan-1 (XL-Xc/R)


    3. The attempt at a solution

    at first i thought that since current phasors lag by 90 degrees that it may be -1.5 rads. but that isn't correct.
    then i used the the inverse tangent equation above in hopes of finding the angle which came out to be 88.4 degrees (which is about 1.5 rads)
    i then took the 88.4 degrees and subtracted it from 90 degrees, because I thought it might turn out a correct answer because the phasors are perpendicular to each other. but that gives you 1.6 which is not correct either.
    I'm not sure what equation to use ...
     
  2. jcsd
  3. Jun 14, 2014 #2

    ehild

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    Gold Member

    Your work is correct, the current lags the voltage by 1.54 rad. The book might have rounded off too early, so it can be A or B.


    ehild
     
  4. Jun 14, 2014 #3
    yeah that's what i thought, but i submitted both of those and neither is correct but i think that may be a mistake! thanks!
     
  5. Jun 15, 2014 #4

    rude man

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    I calculated -1.44 rad:
    w = 8 rad/s
    angle = tan-1{(8*9 - 1/64e-6)/2e3} = tan-1(-7.78) = -82.7 deg = -1.443 rad.
     
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