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

[Azdle]

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

$$Z=j \omega L[\tex]<br /> <br /> [Gah, how do I make the latex render?]<br /> <br /> <h2>The Attempt at a Solution</h2><br /> I'm not really sure where to start with this, I'm not asking anyone to complete this for me. I just need help knowing where to start.<br /> <br /> I'm assuming that omega is going to 50 lHz, but what is Z? Do I set it to infinity or something like that?EDIT: Wait, do I just set the impedance to the impedance of the cap+resistor? Trying that now...<br /> EDIT2: That didn't seem to work. I end up with an inductance of -.002-.004*j H. The answer in the back of the book is 8.05 mH, I just have no idea how to get there.$$

 

[Zryn]

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).

 

[berkeman]

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.

$$Z=j \omega L$$


Welcome to the PF!