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Resonance in LC(R) parallel circuit

  1. Nov 20, 2012 #1
    1. The problem statement, all variables and given/known data

    I did an experiment as followed

    Given following circuit
    IMG096.png
    I measured voltage across capacitor and reciprocal frequency of the generator. espilon, L, C, R, and R_E were given.

    In one configuration, R was shorted.

    I have to calculate relative frequencies (gamma) (easy - resonance frequency divided by frequency) and relative impedances (zeta); q factors and (absolute and relative) bandwidths. I also have to find a relation between U_C and gamma.

    I have no idea whether I did this experiment right - is voltage across capacitor even relevant in this case? What information is possible to extract from this data? What should graphs I vs gamma; U vs gamma; zeta vs gamma look like?

    2. Relevant equations

    In my lecture notes, there's this formula

    [itex]M(\gamma)=\frac{Z}{Z*}=\frac{1}{\sqrt{1+Q^2(\gamma-\frac{1}{\gamma})^2}}[/itex]

    where gamma is relative frequency, Z is impedance, Z* is probably impedance at resonance frequency and Q is ... Q factor.

    [itex]I_C=\omega\epsilon{C}[/itex]

    where I_C is current in capacitor.

    And there's also this thing

    [itex]Z=\frac{L}{C}\frac{1}{\sqrt{R^2+(\omega{L}-\frac{1}{\omega{C}})^2}}[/itex]

    3. The attempt at a solution

    I think the last equation is not complete, so I added R_E and experimented with this value. It gave me silly numbers for Q (it clearly didn't match with plot).

    I also plotted {U_C, I_C, Z, zeta} vs {frequency, gamma} (all combinations imaginable) and they all looked like typical resonance curves. Not sure about that whether it's a good sign or not..

    I fiddled around with my data and found this relation

    [itex]U_C=\frac{U_{C,RESONANCE}}{\sqrt{1+Q^2(\omega-\frac{1}{\omega})^2}}[/itex]

    If more information is needed (e.g. graphs, example data), I'll provide it.
     
  2. jcsd
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