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

In summary, the conversation discusses solving two equations for the variables Va and Vb using a matrix set up. The equations are used to calculate the currents and the correct setup is shown using LaTeX. The conversation also mentions using KCL to check the answers and provides a link for learning how to use LaTeX.
  • #1
marstery
11
0
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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  • #2
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.
 
  • #3
**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?
 
  • #4
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.
 
  • #5
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:
  • #6
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).
 

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

Did I follow the correct steps to solve my matrix?

To ensure that you have solved your matrix correctly, make sure you have correctly applied the operations of row reduction and elementary row operations. Check for any errors in your calculations and make sure to double check your final solution.

Are there any specific rules or guidelines to follow when solving a matrix?

Yes, there are specific rules and guidelines to follow when solving a matrix. These include making sure the number of rows and columns are equal, using the correct operations of row reduction and elementary row operations, and checking for any errors in your calculations.

How do I know if my matrix solution is correct?

You can check the correctness of your matrix solution by multiplying your solution with the original matrix and verifying if the resulting matrix is the identity matrix. If the resulting matrix is the identity matrix, then your solution is correct.

Can I use a calculator to solve my matrix?

Yes, you can use a calculator to solve a matrix. However, it is important to make sure that you are familiar with the calculator's functions and know how to correctly input and interpret the results.

What should I do if my matrix solution does not match the answer key?

If your matrix solution does not match the answer key, first double check your calculations and make sure you followed the correct steps. If you are still unsure, you can ask for assistance from a teacher or a peer to review your work and help identify any errors.

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