Node Method Problem: Identifying Errors

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The discussion revolves around a homework problem involving the node method in circuit analysis, specifically focusing on the calculations for voltages a1, a2, and b1. The user expresses confidence in their calculations for a1 and a2 but doubts the accuracy of b1, indicating that the resulting expression is more complex than expected. They seek guidance on identifying errors in their approach, particularly regarding the calculation of b1. The conversation highlights the importance of presenting work clearly, suggesting the use of LaTeX for better readability. Overall, the thread emphasizes the need for clarity in problem-solving and the application of circuit analysis principles.
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Homework Statement


upload_2015-1-19_16-38-8.png

upload_2015-1-19_16-38-34.png


Homework Equations



V=IR

The Attempt at a Solution



upload_2015-1-19_16-39-3.png

upload_2015-1-19_16-39-22.png


I believe my a1 and a2 are correct.

But my b1 is definitely wrong. Even if I carry out the above subtraction for the v1 part (which gives you b1) I will not have somethign as simple as R2 + R3 on the numerator
upload_2015-1-19_16-40-30.png

[/B]

Where would be some starting places to pinpoint the error?
 

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I'll try putting in dark blue.

Is this any easier to read?

I cannot change some of the below because some of it is pasted images

upload_2015-1-19_16-43-19.png
upload_2015-1-19_16-43-38.png
 
You're not supposed to post working as handwritten images. It's hard to read and hard to reference when making comments.
Given the answer for a1, please post your working to obtain b1 in typed text - preferably LaTeX, or using subscripts, but that's not essential.
 
This is a good time to apply the superposition principle.
 
Thread 'Correct statement about size of wire to produce larger extension'
The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...

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