Engineering RCR (series-parallel) Circuit Analysis

[itsthewoo]

Homework Statement

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.

Homework 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) = ?

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 let's me isolate a function that ends up as f(w) + j*g(w). Help?

 

[CEL]

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.