Engineering What is the voltage in the circuit?

[ee_ess_ee-kid]

Homework Statement

http://i.imgur.com/YRK5L.png

Homework Equations

Loop analysis, so KVL

The Attempt at a Solution

I did the problem, and I got V₀ = 12.5292V. If this is incorrect, I'll be more than happy to upload my work. Can someone verify the answer for me? Just tell me if it's right or wrong.

 

[rude man]

I got Vo+ - Vo- = +14.359 V.

I use nodal equations rather than loop equations. I've always thought loop equations were stupid. I just pick every independent node and sum currents = 0. For example, my first (of three) equation is

(10 - Vx)/2K + (Vo+ - Vx)/3K + 8mA = 0.
Vx is the voltage in the middle. I made the bottom node zero V. (I really should have made Vo- = 0 but it doesn't matter).

I don't want to look at your loop equations, for which I apologize. I just don't like it when one component can carry 2 or 3 or even more "currents"!

BTW I used math app software to do the equation solving so my answer is correct assuming I wrote the equations right. I checked carefully but they could still be wrong, of course.

 

[ee_ess_ee-kid]

It seems like your example nodal equation is for the middle node, in which case, I think it looks incorrect?

If it is the middle node, you forgot to consider the 2k resistor to the right of the node.

 

[rude man]

You are absolutely right!

I will recompute. Thanks for bringiong that to my attention.

 

[rude man]

Now I get +13.12V.

Here are my three equations, maybe you can spot another mistake. Don't be confused by the fact that I use conductances instead of resistances: G = 1/R. It makes the math easier for me. Conductances are in mS, currents in mA (1mS = 1/1K ohm):

0.5(10-x) + .33333(Vop-x) + 8 + 0.5(Von-x) = 0
4 = 0.33333(Vop-x) + 0.125(Vop-Von)
0.125(Vop-Von) + 0.5(x-Von) = 0.125Von

 

[ee_ess_ee-kid]

Now I get +13.12V.

Here are my three equations, maybe you can spot another mistake. Don't be confused by the fact that I use conductances instead of resistances: G = 1/R. It makes the math easier for me. Conductances are in mS, currents in mA (1mS = 1/1K ohm):

0.5(10-x) + .33333(Vop-x) + 8 + 0.5(Von-x) = 0
4 = 0.33333(Vop-x) + 0.125(Vop-Von)
0.125(Vop-Von) + 0.5(x-Von) = 0.125Von

Awesome, I tried doing the problem again and it seemed like I missed something in my loop equations as well. I got 13.12 V too.

 

[rude man]

Yay team!

 

[ee_ess_ee-kid]

Could you possibly look at my other question please?

https://www.physicsforums.com/showthread.php?t=539166"

It uses loop analysis, which I know you said earlier that you dislike, but primarily I'd like to know if my answer is correct. Thanks.

In the best case scenario, you could maybe point out my error in my work. I put all of my equations in the post. Thanks again for your help on this problem!