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Alternate current problem

  1. Nov 12, 2009 #1

    fluidistic

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    1. The problem statement, all variables and given/known data
    I'm trying to solve the problem 8.12 in Purcell's book on Electricity and Magnetism.

    The circuit is like that :

    |--------------|------------|
    |...................|..................R
    |...................C................|
    emf................|................C
    |....................R...............|
    |--------------|-------------
    (The points represent nothing, I had to write them because otherwise the circuit wouldn't appear as I'd like).
    1)Find the current passing through the emf.
    2)Demonstrate that if [tex]V_{AB}=V_B-V_A[/tex] then [tex]|V_{AB}|^2=V_0^2[/tex] for all [tex]\omega[/tex].
    3)Find the phase difference between the current that passes through the emf and a capacitor.
    2. Relevant equations
    None given.

    3. The attempt at a solution
    I'm currently trying to do part 1).
    I forgot to mention that [tex]\omega[/tex] is the angular frequency and [tex]V_0[/tex] is the amplitude of [tex]V(t)[/tex].
    What I did so far : I notice that the current through both loops is the same and is worth [tex]I=\frac{V(t)}{Z}[/tex] where [tex]Z=R-\frac{i}{\omega C} \Rightarrow I(t)=\frac{2V_0 \cos (\omega t + \phi)\cdot \omega C}{\omega C R-i}[/tex].
    How is that possible that the current is has an imaginary part? I guess I made an error, could you confirm?
     
  2. jcsd
  3. Nov 12, 2009 #2

    Pythagorean

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    currents and voltages both can have an "imaginary part" (I hate the name "imaginary", so misleading).

    It's usually written in phasor notation, so you'd convert the cartesian form:

    [tex]x + iy[/tex]
    to the polar form
    [tex]r^{i\theta}[/tex]

    and then write it in phasor notation:
    [tex] r \angle \theta [/tex]
     
  4. Nov 12, 2009 #3

    fluidistic

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    Ok thank you, I understand.
    Is my answer correct though?
     
  5. Nov 12, 2009 #4

    Pythagorean

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    that I can't say for sure, but I can tell you that it's what I would have done.
     
  6. Nov 12, 2009 #5

    fluidistic

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    Thank you once again. :smile:
     
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