# Homework Help: Circuit analysis problem

1. Feb 6, 2016

### suv79

1. The problem statement, all variables and given/known data

how did they get this ?? it is like a potential divider, can anyone explain...

2. Relevant equations

3. The attempt at a solution
this is what i got

2. Feb 6, 2016

### cnh1995

Are you familiar with node voltage method?

3. Feb 6, 2016

### suv79

yes i know about node voltage, i want the node at V_

4. Feb 6, 2016

### cnh1995

You can write the node voltage equations and rearrange them to get V_. There will be 3 principal nodes.Assume ground node at the bottom wire and proceed.

5. Feb 6, 2016

6. Feb 6, 2016

### Staff: Mentor

View attachment 95408
Your second term is correct involving V2, and if you had been consistent you'd have a corresponding correct expression involving V1. The method you are using for this is called Superposition.

7. Feb 7, 2016

### suv79

so this

how can i rearrange this to equal this

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8. Feb 7, 2016

9. Feb 7, 2016

### suv79

10. Feb 7, 2016

### cnh1995

Using cross multiplication, you will be able to cancel out Z2+Z3 in the denominator with that in the numerator. Then take Z3 common from the numerators and you are done.

11. Feb 7, 2016

### suv79

i can do this ?

12. Feb 7, 2016

### suv79

13. Feb 7, 2016

### suv79

14. Feb 7, 2016

### suv79

when adding fractions why does the denominator for the Z1 Z2 become Z1*Z2 ?

15. Feb 7, 2016

### suv79

i dont really understand the last step here

16. Feb 7, 2016

### cnh1995

How will you write this term in the denominator
Z1+Z2Z3/(Z2+Z3) using cross multiplication? It is used to make the denominators same. It is basic algebra.
e.g 3/4+2/3=[( 3×3)+(4×2)]/(3×4)=17/12.
You can not directly cancel the terms like you did there.

17. Feb 7, 2016

### suv79

18. Feb 7, 2016

### cnh1995

Consider only the first term i.e. the term before + sign. Apply the cross product rule in its denominator. What will you get?
Similarly proceed for the next term. It is a matter of only one step.

19. Feb 7, 2016

### suv79

20. Feb 7, 2016

### suv79

21. Feb 7, 2016

### suv79

now i got this but still need to move Z3

#### Attached Files:

• ###### upload_2016-2-7_20-24-53.png
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22. Feb 7, 2016

### suv79

23. Feb 7, 2016

### cnh1995

I think you are making it unnecessarily complicated. Just apply the cross multiplication rule to the denominator of each term separately. It is just one step and you'll be done.

24. Feb 7, 2016

### suv79

this is better but what happens to Z3^2

25. Feb 7, 2016

### cnh1995

Let the two terms be A and B.
So, V_=A+B
(I can't use LaTex on my phone, so this is the best format I can write in..)
Denominator of A is Z1+(Z2Z3)/(Z2+Z3)
=[Z1.(Z2+Z3)+Z2.Z3]/(Z2+Z3)
=[z1z2+z2z3+z1z3]/(z2+z3)
This is the denominator of A. Now write A and see what you can cancel out. It is one of the basic algebraic manipulations.

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