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Phase difference question

  1. Jan 20, 2010 #1
    http://i49.tinypic.com/ejyka9.jpg

    i know that there is a phase difference between the current and its voltage for each
    component
    but here its between the voltage of the source and the impidance of each components

    how did they get the angle in each equation?

    in each equation we have Vm divided by some number
    and the resolt is Vm and angle

    how they get the coefficient of Vm
    ?
     
    Last edited: Jan 20, 2010
  2. jcsd
  3. Jan 20, 2010 #2

    cepheid

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    Staff Emeritus
    Science Advisor
    Gold Member

    For the inductor, you know that the impedance is (jωL), and in this case, ωL = (5 ⨉ 103 rad/s )(0.2 ⨉ 10-3 H) = 1 Ω.

    We're assuming a magnitude Vm for the (phasor) voltage, and taking its phase to be zero. Therefore, since the (phasor) current is given by the (phasor) voltage divided by the impedance:


    IL = (Vm∠0) /(jωL) = (Vm) / (j) ​

    Now, dividing by j is the same as multiplying by -j. Multplying by -j is the same as introducing a phase shift of -90°. To see this explicitly, you can write j in complex exponential form (if you are familiar with it):

    -j = e-j(π/2)

    The phase angles of the other currents are determined in a similar way, by noting that current = voltage / impedance, and taking careful account of the phases of these two quantities.
     
  4. Jan 21, 2010 #3
    thanks :)
     
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