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Impedance & complex currents & voltages

  1. Jun 20, 2017 #1
    1. The problem statement, all variables and given/known data
    upload_2017-6-20_22-50-29.png

    Just problem 19C.

    2. Relevant equations
    P=IV=Ieiwt*Veiwt. T

    3. The attempt at a solution
    P = IVe2iwt=IVcos(2wt). What did I do wrong?
     
  2. jcsd
  3. Jun 21, 2017 #2
    It asks for the time average. Integrate it over a cycle, i.e. t = 0 to 2π/ω.
     
  4. Jun 21, 2017 #3

    ehild

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    The instantaneous power is the product of the real voltage and the real current. The complex form of power and voltage can be used for linear operations only (addition, multiplication with constant). In general, the current and voltage need not be in phase.
    The complex voltage U and complex current I are related through the complex impedance Z=Ze: U=ZI. Writing in the Euler form, I=I0eiωt, U=ZI=I0Z ei(ωt+φ)=U0ei(ωt+φ).
    The instantaneous power is the product or the real part of the complex current (I(t)=I0cos(ωt) with the real part of the complex voltage U(t)=U0cos(ωt+φ)), where U0=I0Z. The problem asks the average power, so you integrate the instantaneous power for a period and divide by the period T.
     
  5. Jun 22, 2017 #4
    So this means that we can't use their complex form because whatever operators we use on them are only linear? Also, is another way to understand this is that since power & voltage are real, that means we must take their real part when doing operations with them?
     
  6. Jun 22, 2017 #5

    ehild

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    You can do linear operations with the complex voltages and currants, but in any other case, the real quantities should be used.
     
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