Nodal analysis exercise,are my equations correct?

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Discussion Overview

The discussion focuses on the application of nodal analysis to a circuit problem, specifically verifying the correctness of equations derived for the analysis. Participants explore the formulation of equations based on circuit components and their relationships.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The initial equations for node v1 and node v are presented, with a request for verification of their correctness.
  • One participant suggests a preference for summing all currents leaving each node and setting the sums to zero, expressing confusion over the current directions in the equations.
  • Another participant questions the handling of the sinusoidal source, noting a discrepancy in the sign used for the phasor representation in the equations.
  • A later reply proposes a revised form of the equations, suggesting a consistent approach to writing them.

Areas of Agreement / Disagreement

Participants express differing preferences for how to set up the equations, with some agreeing on the need for consistency in current direction while others focus on the correctness of the initial equations. No consensus is reached on the best approach.

Contextual Notes

There are unresolved aspects regarding the handling of the sinusoidal source and the direction of currents in the equations, which may affect the correctness of the participants' approaches.

Who May Find This Useful

Students and practitioners interested in circuit analysis, particularly those learning about nodal analysis and the formulation of equations in electrical engineering contexts.

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Homework Statement


We have the circuit in the figure.I have to find v using nodal analysis only.

Homework Equations


Converted 1/6 F to -3j and 2sin2t to -2j.

The Attempt at a Solution


In node v1 we have the equation
6= -12+ [v1/2] + [( v1-v)/1]
In node v we have the equation
2j+ [(v1-v)/1]= 12 + [ v/(-3j)]

Solving these equations to find v is very easy,the crucial part is finding out if the two main equations here are correct.Are they?http://i.imgur.com/nAEsUpo.jpg
 
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Elaia06 said:

Homework Statement


We have the circuit in the figure.I have to find v using nodal analysis only.

Homework Equations


Converted 1/6 F to -3j and 2sin2t to -2j.

The Attempt at a Solution


In node v1 we have the equation
6= -12+ [v1/2] + [( v1-v)/1]
In node v we have the equation
2j+ [(v1-v)/1]= 12 + [ v/(-3j)]

Solving these equations to find v is very easy,the crucial part is finding out if the two main equations here are correct.Are they?http://i.imgur.com/nAEsUpo.jpg

They look basically right, but I usually prefer to just sum all of the currents leaving each node, and set each sum = 0. It's confusing having 2 sides to the equations, with some currents entering and some leaving each node. At least it is confusing for me. :-)
 
I would only question your handling of the sin() source. You've made the correct translation to a phasor value (-2j), then used +2j for it in your v-node equation on the left hand side where apparently you're summing currents flowing into the node.

I agree wholeheartedly with berkeman's suggestion about summing all currents and setting the sum to zero. Choose either in-flow or out-flow for the direction and be consistent. Do it the same way every time and you won't have to think about each current and the side of the equation to put it on and what sign to give it.
 
Many thanks to both of you :)
I guess finally I should write them like this?
6 +12- [v1/2] - [( v1-v)/1]=0
-2j+ [(v1-v)/1]- 12 - [ v/(-3j)]=0
 
Yes, looks good!
 

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