Nodal analysis of an AC circuit

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Discussion Overview

The discussion revolves around the application of nodal analysis in an AC circuit, specifically addressing the formulation of equations related to current and voltage at a node. Participants are examining the correctness of equations derived from Kirchhoff's current law and their implications for solving the circuit analysis problem presented in a homework assignment.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents their equations for nodal analysis but expresses confusion about discrepancies with equations from a previous thread.
  • Another participant suggests a correction to the equations, proposing that a term should be expressed as ##\frac {V2 - V30}{Z3}## instead of the original formulation.
  • A later reply acknowledges the correction but questions the reasoning behind the directionality of the voltage difference in the proposed term.
  • One participant notes that the definition of current directions is crucial, indicating that if current flows into the node from Z3 and out through Z5 and Z2, the voltage difference should be ##v2 - v30##.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct formulation of the equations, and multiple competing views regarding the directionality of current and voltage differences remain unresolved.

Contextual Notes

There are unresolved assumptions regarding the definitions of current directions and the specific terms used in the equations, which may affect the 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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