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RCR (series-parallel) Circuit Analysis

  1. Sep 9, 2009 #1
    1. The problem statement, all variables and given/known data
    If the input AC voltage amplitude is Vo and the angular frequency w, find the impedance of the circuit below and the amplitude of the current that the generator provides. What is the behavior of the circuit at very low and at very high frequencies?

    This is a circuit with AC source connected to a resistor R that is in series with a resistor R' and capacitor C that are in parallel. No values are given.

    2. Relevant equations
    Z(w) = f(w) + j*g(w)

    |Z(w)| = sqrt(f^2(w) + g^2(w))

    Vo = Io(w) * Z(w)

    f(w) = ?, g(w) = ?

    3. The attempt at a solution
    Z(w) = R + (1/R' + jwC)^-1

    Z(w) = R + ( (1 + R'jwC) / R' )^-1

    Z(w) = R + R' / (1 + R'*jwC)

    I'm stuck after this point; I can't think of any algebra that lets me isolate a function that ends up as f(w) + j*g(w). Help?
     
  2. jcsd
  3. Sep 11, 2009 #2

    CEL

    User Avatar

    Multiply the numerator and the denominator of your fraction by the complex conjugate of the denominator. In this way you have a real denominator. Then you can separate the real from the imaginary part of the equation.
     
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