KCL to Find Voltage Between a and b

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Homework Help Overview

The discussion revolves around finding the voltage between two points, labeled a and b, in a circuit using Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). Participants are exploring the application of these laws in the context of a circuit with a fixed voltage source.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the necessity of using KCL to derive equations for the circuit and question the reasoning behind labeling certain nodes as "solved." There is an exploration of how the known voltage at a node influences the analysis of the circuit.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the concept of essential nodes and the implications of fixed potentials in circuit analysis. Some guidance has been offered regarding the interpretation of node equations, but multiple interpretations are still being explored.

Contextual Notes

There is a focus on the distinction between essential nodes and fixed voltage nodes, as well as the implications of these definitions on the analysis process. Participants are also considering the effects of known voltages on the overall circuit analysis.

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Homework Statement


Find the voltage between a and b
BrEokIV.jpg

2. Homework Equations
KVL, KCL

The Attempt at a Solution


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I did not understand how they have reach the result we just two equations, and how did they use KCL to get those equations
 
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There are only two essential nodes in the circuit, and they are labeled v and voc. The node at the top of the 20 V supply is not an essential node since its potential with respect to the reference node is fixed by that voltage source. Effectively that node's potential is already "solved".

Since there are only two essential nodes, only two node equations are required in order to completely analyze the circuit.

The KCL equations that were written are node equations. They sum the currents at a given node. Look at them term by term and you should recognize the currents for each branch leading into a given node.
 
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Why is the node on top on the 20V is "solved"? There are different currents coming out of it?
 
Gbox said:
Why is the node on top on the 20V is "solved"? There are different currents coming out of it?
Nodal analysis determines the potentials at the nodes with respect to the reference node. The potential at that node is already known: 20 V.

Given the node potentials the potential difference across every branch in the circuit can be determined, hence the currents can be determined, too, by Ohm/s law.
 

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