Help with Circuit Homework: XL=4pi

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Discussion Overview

The discussion revolves around solving a circuit homework problem involving reactance (XL and XC) and impedance in a resonant circuit. Participants explore the relationships between the components and the steps needed to find the unknown values.

Discussion Character

  • Homework-related
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant states that the first step is to determine the resultant impedance of the two parallel branches, noting the need for an imaginary operator in the impedance terms for the inductor (L) and capacitor (C).
  • Another participant suggests equating the impedance to be purely resistive at resonance, implying that XL should equal XC.
  • A participant mentions that while equating XL and XC can provide a rough approximation for C, it may not always yield accurate results, potentially being off by about 15%.
  • One suggestion involves expressing impedance in the form Z = f(R) + j*f(R, XL, XC) and solving for C with given values of R, XL, and w.
  • Another participant provides a method to calculate the total impedance of the two parallel branches using the formulas for ZL and ZC, and suggests forcing the imaginary part of Z to equal zero to find C.
  • A participant requests clarification on a previous point, indicating some confusion about the explanations provided.
  • One participant expresses difficulty in performing the calculations and requests a visual aid, such as a screenshot of the working out.

Areas of Agreement / Disagreement

Participants express varying approaches to solving the problem, with some agreeing on the need to equate XL and XC, while others highlight the complexity introduced by the presence of resistance (R). The discussion remains unresolved with multiple competing views on the best method to proceed.

Contextual Notes

There are limitations in the clarity of the steps provided, as well as potential dependencies on specific definitions of impedance and resonance. Some mathematical steps remain unresolved, particularly in the context of finding C.

jafferrox
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Homework Statement



q3.png


Homework Equations


XL = wL
XC = 1/wC


The Attempt at a Solution


XL = 4pi


Thanks in advance.
 
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The first step is to determine the resultant impedance of the two parallel branches. There should be an imaginary operator, j, included in your impedance term for the L and C elements.
 
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and then what's the next step?
 
Step 2 is to equate the impedance to be a pure resistance, because at resonance a circuit appears purely resistive to any applied voltage.
 
doesn't this mean XL=XC, i already found XL and XC is the same and then solve for c?
 
jafferrox said:
doesn't this mean XL=XC,
It does, where XL and Xc are the only impedances present. But there is an R here, and that makes things more interesting.

i already found XL and XC is the same and then solve for c?
That gives a rough approximation, and will usually get you near the right answer, but can be wrong by up to about 15%.
 
I think you need to find impedance in the form: Z= f(R) + j*f(R, XL, XC).
Then solve f(R, XL, XC) = 0 for C with R, XL and W given.
 
I don't know what you mean, can you please make it clearer?

Thanks
 
Can you get the impedance of two parallel branches?
Using ZL = jXL and ZC = -jXC
The first branch: Z1= ZC = -jXC
The second branch: Z2 = R + jXL
Then total impedance:
1/Z = 1/Z1 + 1/Z2
You need to solve for Z and then force imaginary part of Z equals zero. You will find C.
 
  • #10
I couldn't do it, can someone please do it and attach a picture or a screenshot of the working out.

Thanks
 

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