(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In a series circuit V = V<0 @50hz with an R and C, show that the graph of the loci or the port impedance, Z, and port admittance, Y, as the resistance R is varied from 0 to inf ohms are as shown.

[URL]http://ivila.net/prob.png[/URL]

[URL]http://ivila.net/loci.png[/URL]

2. Relevant equations

3. The attempt at a solution

Z = R + j*X;

Y = Z^{-1};

Map to Y = G + jB (Separate Real and Complex)

G = R/(R^{2}+ X^{2});

B = -X/(R^{2}+ X^{2});

G^{2}+ B^{2}= 1/(R^{2}+X^{2}) = B/-X

Then I get lost,

I know I need to arrange into the format below with the condition that the R term (varying from 0 to inf) remains in the LHS, ie, out of the radius. however I am stuck .

(G-x)^{2}+ (B-y)^{2}= radius^{2}

Any help would be much appreciated.

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# Homework Help: RLC Locus Diagrams

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