- #1
Niles
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Homework Statement
Hi all.
Please take a look at the attached circuit. I've have found the amplitude of the current through the resistance to be:
[tex]
\left| {I_0 } \right| = \frac{{\varepsilon _0 }}{{\left| {R - \frac{R}{{\omega ^2 LC}} + \frac{i}{{\omega C}}} \right|}},
[/tex]
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! ), but in my book it says that in general, the amplitude of the current is given by:
[tex]
\left| {I_0 } \right| = \frac{{\varepsilon _0 }}{{\left| Z \right|}},
[/tex]
where Z is the impedance. So according to my book, the amplitude of the current through the resistance must be:
[tex]
\left| {I_0 } \right| = \frac{{\varepsilon _0 }}{{\left| {R - i\omega L + \frac{i}{{\omega C}}} \right|}}.
[/tex]
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.Niles.
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