Finding Impedance Values in a Series Circuit at Different Frequencies

[pj83]

Homework Statement

My question is a series circuit is connected to a power supply set to 300Hz. At this frequency R=30 ohms, Xc=20 ohms, XL=40 ohms. I've then to work out values of R,Xc, XL at a range of frequencys from 100-600Hz.

Homework Equations

Xc=2x3.14xFxC, XL=2 x 3.14 x F x L

The Attempt at a Solution

I have worked out the values of XL, Xc which I'm fairly sure are correct, just wondering does R stay at the same value despite the change in frequency ? Any help greatly appreciated !

 

[vk6kro]

Yes, R stays the same.

You would have worked out the actual values for the capacitor and the inductor and then worked out the reactances at other frequencies. Can you see that the coil and capacitor cancel each other out at some frequency?

So, what were your conclusions? Where is this circuit resonant?
Why is the resonance so broad?

 

[pj83]

I worked the capacitor out to be 26.5 microfarads, inductor 21.2mH by re-arranging the reactance equations, then I made a table for the reactance values at frequencies between 100-600Hz. The closest I got to reasonace was 200 Hz with a inductive reactance of 26.6ohms and capacitive reactance of 30 ohms, nearly cancelling out. I don't know why the reasonace is so broad ?
Thanks for your help.

 

[vk6kro]

Yes, those values seem close to what I got (so they must be right! ... :) ...)

I got resonance at about 212 Hz by calculating it directly. So this agrees with what you got when you took 100 Hz steps.

The resonance is very broad because of the large series resistance compared with the quite low values of reactance of the L and C at this frequency.

 

[pj83]

Thanks for your help it was very useful.

Thanks :)