Optimizing KCL using Matrix Inversion

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Discussion Overview

The discussion revolves around optimizing a circuit using Kirchhoff's Current Law (KCL) and matrix inversion. Participants are exploring the relationship between resistor values and current output in a circuit with varying voltage inputs, specifically focusing on the conditions under which the current remains within a specified range.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant sets R1 and R2 to 500 ohms and seeks to find an appropriate value for R3 that limits the current to between 0.5 to 2 mA, noting discrepancies in their calculations.
  • The same participant expresses confusion about the accuracy of their results and questions why their calculated values do not meet the desired current range.
  • Another participant requests clarification on the problem statement, specifically regarding the variability of V1 and V2.
  • A participant explains their MATLAB notation for incrementing voltage values, indicating that they are using this for plotting functions.
  • One participant asks for MATLAB plots to visualize the function being discussed.
  • The original poster mentions they have not yet plotted the function but suggests that examining extreme voltage values can provide insight into the function's range.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the problem statement or the accuracy of the calculations. There is some confusion regarding the notation and the plotting of functions, indicating that multiple views and uncertainties remain in the discussion.

Contextual Notes

The discussion includes unresolved aspects such as the specific conditions under which the current is calculated and the assumptions made regarding the resistor values and voltage inputs.

Who May Find This Useful

Individuals interested in circuit optimization, KCL applications, or those working with MATLAB for electrical engineering problems may find this discussion relevant.

chart2006
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Set R1 = R2 = 500 ohms, then choose any R3 and plot I versus V1 and V2 for V1 and V2 are between 1 and 2 volts until you find a value of R3 that limits the magnitude of the current to .5 to 2mA.

DP45-1-1.jpg
;
DP45-2.jpg



KCL
i1, i2 = inv(A)*x
i = i1 - i2


I made some large changes and found a few errors with my previous attempt so I deleted that photo and added the new photo of my current work. The equation was derived from using the formula above in reference to matrices. My question is whether or not this is accurate and if so why are my values off? The closest value i can determine is when R3 = 1000 however it doesn't give me i from .5 to 2mA (0.0005 to 0.002). Checking from the extreme values of the source voltage when R3 = 1000:
Low: v1 = v2 = 1, i = .0008A
High: v1 = v2 = 2, i = .0016A
 
Last edited:
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Sorry, I'm not understanding your problem statement. V1 and V2 both can vary between 1-2V? What does your notation "V1 = 1:0.01:2" mean?
 
sorry it's a MATLAB notation I'm using. It means V1 = 1 to 2 in increments of 0.01. The incrementation is for me when I'm plotting the function.
 
Can you post your MATLAB plots?
 
I only have MATLAB on my laptop and haven't had a chance to plot the function yet but if you take the extreme values as I have with v1=v2=1 and v1=v2=2 that will tell you the range of the function.
 
Last edited:

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