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Homework Help: Impedance - Current phasor

  1. Jun 8, 2010 #1
    Impedance -- Current phasor

    In a series circuit of two elements, the voltage and current, for w = 2000 rad/s, are V = 150|-45° and I = 4,74|-116,6°.That variation in the frequency of the source would result in a phasor current of 6 amps? Assuming an unlimited variation in the frequency, what is the maximum possible value for the current?


    The answer is 23.6% reduction in f
    And the maximum 15 amps


    I not find the answer
    My attempt:

    Z = V/I = 31,6|71,6° = 9,97 + 30i
    Xl = 30
    wL = 30
    L = 0,015 and f = 318Hz

    For I = 6 amps I assumed I' = 6|-116,6
    Z' = V/I' = 25|71,6° = 7,89 + 23,72i
    Xl = 23,72
    2pif'L = 23,72
    f' = 252 Hz

    I find f' reduction 20,76% is correct ? How I find the maximum value for the current ?
     
  2. jcsd
  3. Jun 8, 2010 #2

    vela

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    Re: Impedance -- Current phasor

    Your mistake is in assuming the phase of the 6-amp current is the same as the previous phase. As the frequency changes, the phase of the impedance changes, so the phase relationship of the voltage and current will change.

    You have an RL circuit, so the impedance is given by Z=R+iωL. At the new frequency ω', you should have Z'=R+iω'L. Note that the real part of the impedance doesn't change between the two cases; only the imaginary part does.
     
  4. Jun 8, 2010 #3
    Re: Impedance -- Current phasor

    To find w' I need z'. How calculate z' ?
     
  5. Jun 8, 2010 #4

    vela

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    Re: Impedance -- Current phasor

    Try solving for the magnitude of Z'. Since you know the real part, you can find the imaginary part and solve for ω.
     
  6. Jun 8, 2010 #5
    Re: Impedance -- Current phasor

    Xl = sqrt(25^2 - 9,97^2)
    Xl = 22,93
    w' = 1528,67 and f' = 243,3 (23,6% reduction)
    Thanks

    How I find maximum possible value for the current ?
     
  7. Jun 9, 2010 #6
    Re: Impedance -- Current phasor

    Think about how the magnitude of impedance changes in time. Does it stay constant? Does it have a minimum or a maximum? What should it be to yield the maximum value for the current?
     
  8. Jun 9, 2010 #7
    Re: Impedance -- Current phasor

    The maximum value is when the imaginary part is 0.
    Z = V / I = 150 / 9,97(real part) = 15A
     
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