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The average power consumed -- where is my mistake

  1. Jan 27, 2015 #1
    1. The problem statement, all variables and given/known data
    We have the circuit in the figure.I have to find the average power consumed by all the elements and the source.
    PmGUCOu.png
    2. Relevant equations
    P=0.5*(I^2)*R
    P=-VmImcosθ/2
    3. The attempt at a solution
    The inductor consumes zero inductive power.
    I apply nodal analysis at node Vo

    We have (6-Vo)/3=Vo/6
    Vo=4
    Here I find that I1=(6-4)/3=2/3
    So the average power dissipated by 3 ohm
    P=0.5*(4/9)*3=2/3 W
    Current through 6 ohm is Vo/6=4/6
    P=0.5*(16/36)*6=4/3..problem is ,in my book power dissipated by 6 ohm is 10/3....
    Now,the power consumed by the source is
    P=P=-(2/3)(6)cos0/2=-2 W...but the result in my book is -4W
    Where is my mistake?
     
  2. jcsd
  3. Jan 27, 2015 #2

    BvU

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    How do you calculate ##\theta = 0## if there is an L in the circuit ?
     
  4. Jan 27, 2015 #3

    gneill

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    Your book's result of -4 W for the average power "consumed" by the source looks very mysterious to me. I think the source should be delivering more than 4 W to the load.

    Assuming that the source voltage function 6cos(t) implies a 6V peak value, then the RMS value would be 6/√2, and the frequency of the source would be ω = 1 rad/sec. Taking the equivalent impedance Z of the load and using the RMS value of the source voltage I find a real power in the load of closer to 6 W. (I say "closer to" because I'm not going to give away actual results here).
     
  5. Jan 27, 2015 #4

    BvU

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    Here is a cheat sheet. Look here for your load impedance (its complex). I needed it to dust off what I used to know. Didn't end up with the book answer either
     
  6. Jan 28, 2015 #5

    BvU

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    Elaia still there ?

    Imperial college slides are nice too ! You learn about no less than four different Powers (one complex, the other three Re, Im and modulus) and a power factor to boot.
     
    Last edited: Jan 28, 2015
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