- #1
Nodal analysis: simple confusion
- Thread starter Marchese_alex
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Discussion Overview
The discussion revolves around the application of nodal analysis in circuit analysis, specifically addressing confusion regarding voltage sources, current directions, and the treatment of resistances in equations. Participants explore various aspects of nodal analysis, including the correct formulation of equations and the implications of sign changes in current calculations.
Discussion Character
- Technical explanation
- Conceptual clarification
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant questions the rationale behind the 80+20 part in the denominator of a current equation, indicating confusion over its application.
- Another participant explains that the total resistance in a series path is the sum of the resistances and clarifies that there is no need for additional nodes in this context.
- A participant expresses confusion about the positive sign of the 125V source in their equation, leading to an explanation about potential measurements relative to the reference node.
- Several participants discuss the process of simplifying fractions in equations, with questions about which denominator to use and the context of simplification.
- A participant notes inconsistencies in how current equations are presented in their textbook, specifically regarding the sign of voltage terms in relation to assumed current directions.
- Another participant explains that sign changes in equations often correspond to the assumed direction of current flow, emphasizing the importance of consistency in nodal analysis.
Areas of Agreement / Disagreement
Participants express various uncertainties and questions regarding the application of nodal analysis, with no clear consensus reached on some of the specific issues raised, particularly regarding the treatment of signs and simplifications in equations.
Contextual Notes
Participants highlight potential confusion arising from differing assumptions about current directions and the treatment of voltage sources in equations, indicating that these factors can affect the formulation of nodal analysis equations.
Who May Find This Useful
This discussion may be useful for students and practitioners of electrical engineering or physics who are learning about circuit analysis techniques, particularly nodal analysis, and are seeking clarification on common points of confusion.
- #2
gneill
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There is a single series-connected path from node 1 through the two resistors and the voltage source to the reference node. So the total resistance along that path is the sum of the two resistances. That makes the current through that branch (V1 - 24V)/(80Ω + 20Ω).
There's no need to introduce extra nodes along a series branch; just add up the voltage sources and resistance values.
There's no need to introduce extra nodes along a series branch; just add up the voltage sources and resistance values.
- #3
- #4
gneill
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Marchese_alex said:
It's positive because of the polarity of the 125V source along the path from node 3 to the reference node. The potential at its "-" terminal is effectively 125V below the reference potential. Since the potential of node 3 is measured with respect to the reference node, this makes the total potential across the resistor V3 + 125V.
When in doubt, do a "KVL walk" along the path and add up the various potential changes. Starting at the reference node:
-125V + i3*R = v3
So the current is (v3 + 125V)/R
- #5
Marchese_alex
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When i multiply to reduce the fractions, which one should i aim for? Any of the deno?
- #6
gneill
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Marchese_alex said:
In what situation? Sounds like an exercise in fractions and algebra.
- #7
Marchese_alex
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gneill said:
Can i use any denominator to simplify the eacuation
- #8
gneill
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Surely it depends upon the equation and what the goal of the simplification is. You'll have to be more specific.
- #9
Marchese_alex
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I have a doubt when asked to find the current at each resistor. Sometimes the book uses the same ecuaction established in the nodal analysis. For example, (V1-128)/5 + V1/60 etc. is my ecuation after the analysis. Well, some times they use it like it was established I=(V1-128)/5 but sometimes they change it like so, I=(128-V1)/5... .??
- #10
gneill
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A sign change usually means that it was altered in order to match the assumed direction of the current being found.
When you write the equations for nodal analysis it's usually the case that you just assume, for example, that all currents are flowing out of each node (or into each node). This is done in order to make writing the equations a straightforward procedure where you don't have to think about "actual" current directions beforehand.
However, it is also often the case that the circuit drawing will have an indication of what direction should be assumed for a given current when you report the value. The match up can be done by adjusting the sign of of the appropriate nodal analysis term to correspond to the requested direction assumption.
When you write the equations for nodal analysis it's usually the case that you just assume, for example, that all currents are flowing out of each node (or into each node). This is done in order to make writing the equations a straightforward procedure where you don't have to think about "actual" current directions beforehand.
However, it is also often the case that the circuit drawing will have an indication of what direction should be assumed for a given current when you report the value. The match up can be done by adjusting the sign of of the appropriate nodal analysis term to correspond to the requested direction assumption.
- #11
Marchese_alex
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gneill said:
Awesome! Thanks
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