Did i solve my matrix correctly? (source sub. on 3 window circuit)

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Discussion Overview

The discussion revolves around the setup and solution of a matrix for a circuit problem involving two equations to solve for voltages Va and Vb. Participants explore the formulation of the equations, matrix representation, and the implications of current flow in the circuit.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents two equations to solve for Va and Vb, providing initial answers of Va= 5.655v and Vb= -5.724.
  • Another participant questions the correctness of the equations but agrees with the answers, suggesting that the signs and order of Va and Vb may be reversed in the current calculation.
  • A third participant seeks clarification on the correct matrix setup for the equations, indicating confusion about the representation.
  • A fourth participant critiques the dimensional consistency of the equations, asserting that the first equation is dimensionally incorrect and that Vb is not included in the first equation.
  • The same participant proposes a corrected version of the equations, emphasizing the need for proper representation of the relationships between the voltages and currents.
  • A fifth participant shares their matrix setup, indicating an understanding of the structure but acknowledges typing limitations in representing it accurately.
  • Another participant offers a resource for learning LaTeX, suggesting it could help with formatting equations in future discussions.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the initial equations and their dimensional consistency. While some agree on the final answers, there is no consensus on the initial setup or the interpretation of the equations.

Contextual Notes

There are unresolved issues regarding the dimensional analysis of the equations and the proper representation of the circuit elements. The discussion reflects varying interpretations of the equations and their implications for current flow.

marstery
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I've got two equations that i want to put into a matrix and solve for Va and Vb:

1.7ma = (1/5k + 1/20k) -1/20k Va
-2ma = -1/20k (1/4k + 1/20k) Vb

The answers I got were Va= 5.655v and Vb= -5.724

then, using I= (Vb-Va)/R ----> (-11.379/20k) = 0.65ma

..-----Va----20k----Vb-----
|...|.....|...|
^...5k....4k...V
1.7ma.|.....|...2ma
.| ___|___________|_____|

(ignore the periods, i needed them for spacing)
 
Last edited:
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marstery said:
I've got two equations that i want to put into a matrix and solve for Va and Vb:

1.7ma = (1/5k + 1/20k) -1/20k Va
-2ma = -1/20k (1/4k + 1/20k) Vb

The answers I got were Va= 5.655v and Vb= -5.724

Your equations look wrong, but I agree with your answers.

then, using I= (Vb-Va)/R ----> (-11.379/20k) = 0.65ma

Look again. You've got a negative divided by a positive. That should be negative. However, you've got Vb and Va reversed. Resistors are passive, so to compute the current you subtract the lower potential from the higher one, not the other way around.
 
**I set up my equations based on another example from class, what is the correct matrix set up for an example like this?

..-------Va----R2--I>---Vb------
|...|.....|...|
^...R1......R3...V
Is1...|.....|...Is2
.| _____|_____________|______|



**so after switching Va and Vb and correcting the neg/pos mistake, the current should be the same, right?
 
Regarding your equations: Let me show you how I interpreted them, using LaTeX.

marstery said:
1.7ma = (1/5k + 1/20k) -1/20k Va

I read this as:

[tex]1.7mA=\left(\frac{1}{5k\Omega}+\frac{1}{20k\Omega}\right)-\frac{1}{20k\Omega}V_a[/tex]

The equation, as I read it, is dimensionally wrong. The LHS has units of current. The first term on the RHS has units of reciprocal resistance. Also, Vb doesn't appear at all! Here is how the equation should read.

[tex]1.7mA=\frac{1}{5k\Omega}V_a+\frac{1}{20k\Omega}\left(V_a-V_b\right)[/tex]

On to the second equation.

-2ma = -1/20k (1/4k + 1/20k) Vb

This equation should read as follows.

[tex]-2mA=\frac{1}{4k\Omega}V_b-\frac{1}{20k\Omega}\left(V_a-V_b\right)[/tex]

But I checked your answers using KCL at nodes a and b, and they worked.
 
oh i see. i had set up a matrix as below where brackets above one another are actually one, but i just can't type them that way here.

[1.7ma] = [ (1/5k + 1/20k), -1/20k ] [ Va ]
[-2ma ] = [ -1/20k, (1/4k + 1/20k) ] [ Vb ]

thanks you for your help!
 
Last edited:
No problemo. And if you're interested in learning how to use LaTeX here, you should consult the following thread:

https://www.physicsforums.com/showthread.php?t=8997

You can also see the LaTeX code for any equation that you see by clicking on it (you will need to allow pop-ups for this).
 

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