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Electrodynamics: Amplitude of currents

  1. Dec 10, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all.

    Please take a look at the attached circuit. I've have found the amplitude of the current through the resistance to be:

    \left| {I_0 } \right| = \frac{{\varepsilon _0 }}{{\left| {R - \frac{R}{{\omega ^2 LC}} + \frac{i}{{\omega C}}} \right|}},

    where ε_0 is the amplitude of the EMF, and the EMF is given by ε_0 cos(ωt). This is all good (and correct too! :approve:), but in my book it says that in general, the amplitude of the current is given by:

    \left| {I_0 } \right| = \frac{{\varepsilon _0 }}{{\left| Z \right|}},

    where Z is the impedance. So according to my book, the amplitude of the current through the resistance must be:

    \left| {I_0 } \right| = \frac{{\varepsilon _0 }}{{\left| {R - i\omega L + \frac{i}{{\omega C}}} \right|}}.

    What's wrong here? I mean, I know my result is correct, but it is obviously not the same as the one my book wants. What impedance is it I have in my denominator then?

    Thanks in advance.


    Attached Files:

    Last edited: Dec 10, 2008
  2. jcsd
  3. Dec 10, 2008 #2


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    Something's amiss here. Don't know where your first equation came from, but the third equation (from your book, you say) describes a series tank circuit and not the series/parallel circuit you drew.
    Last edited: Dec 10, 2008
  4. Dec 10, 2008 #3


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    Note that

    [tex] {R - i\omega L + \frac{i}{{\omega C}}} [/tex]

    would be the impedance if all three elements were in series. However that is not the case in the circuit you show.
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