Finding Impedance Values in a Series Circuit at Different Frequencies

  • Thread starter Thread starter pj83
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around finding impedance values in a series circuit at different frequencies, specifically analyzing the behavior of resistance (R), capacitive reactance (Xc), and inductive reactance (XL) as the frequency varies from 100Hz to 600Hz. The context includes homework-related problem-solving and calculations involving resonant frequency.

Discussion Character

  • Homework-related, Technical explanation, Exploratory

Main Points Raised

  • One participant questions whether resistance (R) remains constant despite changes in frequency, suggesting that R does not change.
  • Another participant indicates that the reactances of the inductor and capacitor can cancel each other out at certain frequencies, prompting further exploration of resonance.
  • A participant shares their calculations for the capacitor and inductor values, noting that they found resonance at approximately 200Hz, with nearly cancelling reactances at that frequency.
  • Another participant confirms their resonance calculation at about 212Hz, agreeing with the previous participant's findings and attributing the broad resonance to the high series resistance compared to the low reactance values.
  • Participants express appreciation for the assistance provided in the discussion.

Areas of Agreement / Disagreement

Participants generally agree on the constancy of resistance and the calculations of resonance frequency, though there is some variation in the exact resonance values reported. The reasons for the broad resonance are discussed but not fully resolved.

Contextual Notes

The discussion includes assumptions about the behavior of reactance and resistance in a series circuit, as well as limitations in the precision of resonance frequency calculations based on the provided data.

pj83
Messages
5
Reaction score
0

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 !
 
Physics news on Phys.org
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?
 
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.
 
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.
 
Thanks for your help it was very useful.

Thanks :)
 

Similar threads

Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 20 ·
Replies
20
Views
5K
Replies
5
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 10 ·
Replies
10
Views
5K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 3 ·
Replies
3
Views
8K
  • · Replies 5 ·
Replies
5
Views
2K