RC parallel circuit, find the value of R and C

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Discussion Overview

The discussion revolves around solving for the resistance (R) and capacitance (C) in a parallel RC circuit given the impedance (Z) and frequency. Participants explore different approaches to derive the values of R and C from the provided information.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant begins by attempting to find a common denominator for the equation involving R and C, expressing uncertainty about their approach.
  • Another participant suggests starting by calculating 1/Z, noting that a numerical complex value for Z is provided.
  • A participant calculates 1/Z and expresses confusion about how to derive R and C from the resulting expression.
  • One participant points out that the admittances of the components can be extracted directly from the complex value of 1/Z, questioning the necessity of finding RC.
  • Another participant claims to have calculated R and C as 118K ohm and 1.37x10-8 F respectively, verifying their results by substituting back into the equation.
  • A later reply suggests that the method used by the participant to find R and C is simpler than the lecturer's proposed method, indicating a potential difference in approaches.

Areas of Agreement / Disagreement

Participants express differing views on the methods for solving the problem, with some favoring a straightforward approach while others seem to adhere to a more complex method suggested by the lecturer. No consensus is reached on the preferred method.

Contextual Notes

There is uncertainty regarding the necessity of finding a common denominator and how to properly apply the concept of admittance in parallel circuits. The discussion reflects various interpretations of the problem and the methods to solve it.

Agent47
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Homework Statement



The circuit is a Parallel RC

Z= 105KΩ∠-27 and Frequency is 50 Hz.

I was given the following information and hints.

1/z = 1/R + jwc

I need to find the common denominator of 1/R + jwc, Invert it to find z and simplify Z into one real and one imaginary part.


Homework Equations



Need to find the value of R and C

The Attempt at a Solution



I started with finding the common denominator,

= 1/R +(jwc*R)/R

1/z = (1+jwRC)/R

To find z i simplified the equation above,

R = z(1+jwCR)

z = R/(1+jwCR)

Im not sure if i did this right as i can't find R and C. Any help will be much appreciated.
 
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Why not start by calculating 1/Z, since you're given a numerical (complex) value for Z?
 
If i do 1/z i would get 8.485x10-6 +j 4.323x10-4. I am not sure on how i would get and RC from 1/z = (1+jwRC)/R.
 
Agent47 said:
If i do 1/z i would get 8.485x10-6 +j 4.323x10-4. I am not sure on how i would get and RC from 1/z = (1+jwRC)/R.

You don't need RC. You can pick out the admittances of the two components directly from the complex value of 1/z.

1/z is the admittance of the parallel circuit. How do admittances in parallel add?

(The resistor analogy is two conductances in parallel).
 
I worked out R= 118K ohm and C = 1.37x10-8. I checked by putting the values back into the equation and got the correct z. I guess i don't understand what my lecturer is going on about finding the common denominator etc.
 
Agent47 said:
I worked out R= 118K ohm and C = 1.37x10-8. I checked by putting the values back into the equation and got the correct z. I guess i don't understand what my lecturer is going on about finding the common denominator etc.

I suppose your lecturer had envisioned a different path to solution. But this one is pretty straightforward, no?
 
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I agree that the way you have explained is much simpler, ill ask my lecturer on what his method is. Thanks for your help.
 

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