# 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