Engineering Nodal analysis of an AC circuit

AI Thread Summary
The discussion centers on a homework question regarding nodal analysis in an AC circuit, specifically the confusion surrounding part b after successfully solving part a. The user has calculated a current of -9.2 + 17.3i amps but is struggling with the equations presented in a previous thread. They propose a correction to a term in the bottom equation, suggesting it should be divided by Z3 instead of Z2. The explanation provided clarifies that the direction of current flow determines the voltage difference used in the equations. Understanding these directional definitions is crucial for correctly applying Kirchhoff's current law in nodal analysis.
Morgz129
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Homework Statement


Hi I have this question as part of my assignment but cannot get my head around part b, I have worked out part a with an answer of -9.2+17.3i amps which from a previous thread I know is correct, but can't understand why the equations given in the previous thread are different to what I have.

Homework Equations


Kirchhoffs current law

The Attempt at a Solution


V20-v30=v3

((V20-V1)/Z1)+((v20-v30)/z2)+(v20/z4)=0
((v20-v1)/z1)+(v3/z2)+(v20/z4)=0

((v30-v20)/z2)+((v30-v2)/z2)+(v30/z5)=0
 

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For the bottom equation, I think that middle term should be ##\frac {V2 - V30}{Z3}##. And that would be equal to the other two terms.
 
osilmag said:
For the bottom equation, I think that middle term should be ##\frac {V2 - V30}{Z3}##. And that would be equal to the other two terms.

My mistake it should be divided by z3, but if I may ask why would it be ((v2-v30)/z3) instead of ((v30-v2)/z3)?
 
It depends on how you define your directions. If current is flowing into the node from z3 and out of it at z5 and z2 then ##v2-v30 ## is the difference and ## I,z3 = I,z5 + I,z2##
 
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