Master Nodal Analysis with this KCL Question | Nodal Analysis Homework

[Cyb3rGlitch]

Homework Statement

Homework Equations

KCL

The Attempt at a Solution

I recognise that the voltage sources form supernodes. This produces:

$$A - B = 10$$ -> $$A = 10 + B$$

We also know that node C is 12v.

I then form KCL equations:
$$6 + \frac{A - C}{12} = \frac{B}{40} + \frac {A}{24}$$

When I simplify this and sub in C and A, I get a ridiculous results. What am I missing here? Cheers!

 

[Cyb3rGlitch]

No one can help?

 

[Yaz Li]

I think Vb-Va=10 -> Va=Vb-10.
To see this, write a kcl around the loop starting from the reference node to Node A and then Node B:

-Va-10+Vb=0 ->Va=Vb-10.

I have explained this on one of my posts:
http://circuits.solved-problems.com/resistive-circuits/nodal-analysis-supernode/
Scroll down to section three of the solution. Read the paragraph starting with "The voltage of Node III can be written in terms of the voltage of Node I."
It is also explained in my Nodal Analysis ebook, which can be downloaded from my website for free (a free and simple registrating is required though):
http://circuits.solved-problems.com/nodal-analysis/

Hope this will be of help.