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Need some help with some material


I am a past engineering student (AAS in EE) reviewing the material for the GROL FCC test, elements one and three. I have seen a good majority of the example problems in school (about two years ago), and work, but I am hung up and have a hard time understanding this one.

I need to find Z (impedance) for a circuit, in rectangular form. Frequency is 50KHz, and the two components in the circuit are a 0.01uF capacitor in parallel with a 300Ohm resistor. I calculated Xc to be 318.3 Ohms. I am unsure as to where to go from here, or how to arrive at Z. The solution is 159-j150. Thanks a million, I hope someone can help.

Resistance in Rectangular form is 300.  Capacitive Reactance is 0 - j318.3

Let's check that.  Xc = 1/2 Pi F C  = 318.3  That looks good.

The resulting Inductance is Z = 1 / ( 1 / R  + 1 / -jXc)

If I remember correctly, this expands to

Z = (R * Xc^2) / (R^2 + Xc^2) - j (R^2 * Xc) / (R^2 * Xc^2)

Z = 30394467/191314.89 -j 28647000/191314.89 = 158.9 - j149.7

Edit: Did a search and found a resource that explains it better: http://www.play-hookey.com/ac_theory/ac_rc_parallel.html

Thank you. I worked through the problem this evening, and checked out the link that you had provided. I feel a little bit better about operating around the imaginary numbers now.


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