Kirchoff's Laws Giving Singular System

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Discussion Overview

The discussion revolves around the application of Kirchhoff's laws to analyze a circuit with multiple resistors and currents. The original poster seeks to establish a system of equations to determine the currents through each resistor but encounters issues with redundancy leading to a singular matrix.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • The original poster is attempting to use Kirchhoff's voltage law to create a set of equations for five unknown currents but finds the resulting system to be singular.
  • Some participants suggest that there may be fewer unknowns than the original poster believes, proposing that only two or three unknowns are present.
  • One participant recommends node voltage analysis as a method to identify unknown voltages at nodes and apply Kirchhoff's current law (KCL) to find the currents.
  • Another participant reiterates the importance of identifying the unknown voltages at specific nodes and suggests using KCL to derive the necessary equations.
  • The original poster expresses confusion regarding the identification of unknowns and the application of node voltage and current analysis, despite being familiar with Kirchhoff's laws.
  • There is mention of mesh current analysis as an alternative technique, though one participant expresses a preference for node voltage analysis over mesh current analysis.

Areas of Agreement / Disagreement

Participants exhibit differing views on the number of unknowns in the circuit and the most effective analysis technique to use. The discussion does not reach a consensus on the best approach or the exact nature of the unknowns.

Contextual Notes

There are unresolved assumptions regarding the circuit configuration and the definitions of the unknowns. The discussion reflects a variety of perspectives on analysis techniques without settling on a definitive method.

Hertz
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Hi, I'm trying to use Kirchoff's voltage law to find a system of equations which I can use to find I1, I2, I3, I4, and I5; which are the respective currents going through each resistor in the image.

circuit1-2014.png


I have 5 unknowns so I need to find 5 non redundant equations. The problem is, every system of equations I come up with is singular. In other words... I am trying to set up a matrix equation ##A x = b## but my matrix A keeps having determinant zero!

Is there any general rule to follow in order to find a non redundant set of equations? This is really time consuming!

If you are curious, here is an example system which I came up with, but in some way it's redundant.
Code: 
V = R1 I1 + R4 I4
V = R2 I2 + R5 I5
V = R1 I1 + R3 I3 + R5 I5
V = R2 I2 - R3 I3 + R4 I4
0 = R1 I1 - R2 I2 + R4 I4 - R5 I5
V is the voltage of the battery.
 
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I only see two unknowns. Maybe three.

Have you been introduced to node voltage or mesh current analysis?
 
My favorite analysis technique is node voltage analysis. Basically, you look at the circuit and you identify any unknown voltages, each unknown voltage is a node. In this circuit, there are only two. Then, at each node you use KCL to write that the total current leaving the node is 0. Then you solve those two equations in two unknowns to get the unknown voltages. All of the currents are then uniquely determined.
 
I'm confused, what are the unknowns you are seeing? I'm trying to find the current going through each resistor, and I0, the current going through the wires near the EMF. I need to know the answer of each of these six values.

I'm also not exactly sure what you mean by node voltage and current analysis. I'm familiar with both of Kirchoff's laws though.

e-
1. The total potential difference around any closed loop is zero.
2. At any node there is as much current leaving as is entering.
 
Last edited:
The only unknown voltages are the voltages at the two nodes touching R3. All other voltages are known. Call those two voltages Va and Vb. Then at Va and Vb write KCL.

Once you have Va and Vb then all of the currents are obtained through Ohms law.
 
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DaleSpam said:
The only unknown voltages are the voltages at the two nodes touching R3. All other voltages are known. Call those two voltages Va and Vb. Then at Va and Vb write KCL.

Once you have Va and Vb then all of the currents are obtained through Ohms law.

Oh I see! Thank you!

It's like magic...
 
Glad I could help!

There is another similar technique, called mesh current analysis. It is based on KVL, but I don't like it as much.
 
Thank you, I will surely look into it in due time :)
 

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