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Calculating L to Make Net Impedance Resistive at a Certian Freq.

  • Thread starter Azdle
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  • #1
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Homework Statement



An industrial load is modeled as a series combination of a capacitance and a resistance as shown [below]. Calculate the value of an inductance L across the series combination so that the net impedance is resistive at a frequency of 50 kHz.
The circuit is a resistor (200 ohms) and a capacitor (200 nF) in series, and that is in parallel with an inductor.

Homework Equations


[tex]$Z=j \omega L$[\tex]

[Gah, how do I make the latex render?]

The Attempt at a Solution


I'm not really sure where to start with this, I'm not asking anyone to complete this for me. I just need help knowing where to start.

I'm assuming that omega is going to 50 lHz, but what is Z? Do I set it to infinity or something like that?


EDIT: Wait, do I just set the impedance to the impedance of the cap+resistor? Trying that now...
EDIT2: That didn't seem to work. I end up with an inductance of -.002-.004*j H. The answer in the back of the book is 8.05 mH, I just have no idea how to get there.
 
Last edited:

Answers and Replies

  • #2
Zryn
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Impedance is generally a real (resistive) component + an imaginary (reactive) component.

There is a special situation called resonance when an impedance becomes solely a resistance, and is characterized by the inductive reactance being equal to the capacitive reactance, so that their difference equals zero (wC = wL --> wC - wL = 0).
 
  • #3
berkeman
Mentor
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2. Homework Equations
Z=j \omega L

[Gah, how do I make the latex render?]
You used a downslash "\" instead of an upslash "/" to try to end the tex. Fix that and it should render okay. I also got rid of the "$" characters -- not sure what those do.

[tex]Z=j \omega L[/tex]


Welcome to the PF! :smile:
 

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