Two methods -- neither works, thevenin

[potatowhisperer]

Homework Statement

we are asked to find the tension between the R6 = 20 ohms resistor, using thevenin[/B]

Homework Equations

the given solution for Ethev is 27.78

The Attempt at a Solution

is seen in the pictures below

thank i really appreciate your help as it gets frustrating not to know what is wrong .

i tried a different approach and got this but still wrong
thank you again.

 

[gneill]

Hi potatowhisperer, Welcome to Physics Forums.

One of the nice things about Thevenenin's and Norton's theorems is that you can apply them step-wise. You can "break" a circuit at successive locations, incorporating components into an evolving Thevenin or Norton model as you go. Often this can be easier than performing a mesh or nodal analysis of the entire circuit. Consider the suggested circuit "breaks" here:

At break (A) you have a simple voltage divider to the left. So a Thevenin equivalent is trivial to find. At (B) an "open" resistance R3 is tacked on, modifying the Thevenin resistance. Simple! Then at (C) the then-current Thevenin model is part of a voltage divider with R5, so again a trivial reduction...

Give it a try!

 

[The Electrician]

Bon jour, potatowhisperer,

Your first solution, the nodal analysis, is ok until the very end. You did something wrong when you used your matrix solver.

You must have made some such error.

 

[NascentOxygen]

i tried a different approach and got this but still wrong

Your answer is right, but that's for V_A. You need to go further and determine V₂.

 

[potatowhisperer]

I love y'all
i m glad that the first method was just a calculation mistake , though i am embarrassed to have taken your time just because of a sign, i really appreciate your help again.
about the second method , i can not thank you enough for telling that it was unfinished calculations , as i was confused cause now i can think more logically about what i m doing , i have had many instances when i got so frustrated with my mistakes that i would just stop ... so thank you very much.

 

[potatowhisperer]

GNEILL,I am definitely going to try that method, it does simplify things , A LOT .