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Calculating Impedance, verify.

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data
    Calculate the circuit's impedance Z between input and ground for an applied sinusoidal voltage with frequency f = 1000Hz, and express Z in the form [itex]re^{i\theta}[/itex]

    There is a picture that goes with it, it's just a function generator (makes a sinusoidal AC voltage) connected in series with a 0.1μF capacitor, and a 1kΩ resistor.

    I think I solved it, but I would just like it if someone could verify that I did it correctly as it is going into a lab report.


    2. Relevant equations
    i.[tex]Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}}[/tex]
    where X_L is for a transistor (none exists in the circuit so it's zero) and X_C is for the capacitor

    ii. [tex]X_{C} = \frac{1}{\omega C}[/tex]

    iii.[tex]tan(\phi) = \frac{\omega L - 1/\omega C}{R}[/tex]

    All equations extracted from "University Physics by Young & Freedman 11th edition



    3. The attempt at a solution
    From Eq i, I just plugged in 1kΩ for the resistor, and X_L is zero, and I found X_C from Eq ii (where C is the 0.1μF capacitor and ω is 2π*1000Hz).
    This gave me a value for Z of 1879.6Ω.

    Then, to find it in the form [itex]re^{i\theta}[/itex], more specifically it should be:
    [tex]re^{i(\omega t + \phi)}[/tex]
    I know everything but φ, so I used Eq iii.
    Again, L was zero so the first term in the numerator canceled out, and I found φ to be:
    - 1.010 (radians).

    So my final answer is:

    [tex]1879.6 e^{i(2000\pi t - 1.01)} \Omega[/tex]

    Is that all correct?
    thanks.
     
  2. jcsd
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