# Electrical Circuits - Linear Algebra

• tg22542
In summary, the student is seeking help with setting up equations for a circuit problem using the Gauss Jordan elimination method. They are attempting to use Kirchoff's current and voltage laws, but their equations do not seem to correspond to the circuit in the image provided. They need to carefully explain how they are taking their loops before their equations can be checked.
tg22542

## Homework Statement

Here is a picture of the diagram.

http://gyazo.com/f1b7051fda5b9e1d3a185c53abde1211

I must use the Gauss Jordan elimination method and solve for X1, X2 and X3

I am having problems setting up my equations

## The Attempt at a Solution

The way my professor showed an example of a question similar to this was by setting up 2 equations for each junction, and 2 for each loop.

My attempt:

∑ Flows Entering = 0

Junction A (Top of the line inbetween loops) : X1 - X2 - X3 =0 ??
Junction B (Bottom of line inbetween loops) : X1 + X2 - X3 =0 ??

Loop1 (Left side) : 10X1 - 5X2 + X3 = 0
Loop2 (Right Side): X1 + 5X2 - X3 = -52

Can someone correct my equations?

You have 3 unknowns, therefore need a minimum of 3 different equations. However, I think there is a deeper, underlying issue with you misunderstanding Kirchoff's rules, or circuit theory in general based on how you are setting up your equations. For example, your "Loop1" equation implies that there are currents, but they are flowing without a power source (the 52V).

tg22542 said:

## Homework Statement

Here is a picture of the diagram.

http://gyazo.com/f1b7051fda5b9e1d3a185c53abde1211

I must use the Gauss Jordan elimination method and solve for X1, X2 and X3

I am having problems setting up my equations

## The Attempt at a Solution

The way my professor showed an example of a question similar to this was by setting up 2 equations for each junction, and 2 for each loop.

My attempt:

∑ Flows Entering = 0

Junction A (Top of the line inbetween loops) : X1 - X2 - X3 =0 ??
Junction B (Bottom of line inbetween loops) : X1 + X2 - X3 =0 ??

This part is based on Kirchoff's current law. The current flowing into a junction must be equal to the current flowing out of a junction. Which currents are flowing in and which out?

Loop1 (Left side) : 10X1 - 5X2 + X3 = 0
Loop2 (Right Side): X1 + 5X2 - X3 = -52

Can someone correct my equations?

This is based on Kirchoff's voltage law. But the equations don't seem to correspond to the circuit in the image. Loop 1 (as indicated) spans the cell, and the 1Ω and 5Ω resistances. Loop 1 doesn't include the 10Ω resistance. But your first equation has a coefficient of 10, and I don't know where that's coming from. Same issue with the second equation. The 52V (cell voltage) term also seems out of place.

I think you need to very carefully spell out how you're taking your loops before we can help you check your equations. For example, "loop 1 starts with the negative terminal of the cell, goes across the cell to the positive terminal, across the 1Ω resistor in the direction of current x1, down the 5Ω resistor in the direction of current x2 and ends back at the negative terminal".

## 1. What is linear algebra?

Linear algebra is a branch of mathematics that deals with the study of linear equations, vectors, matrices, and their properties. It involves the use of algebraic techniques to solve systems of linear equations and understand the behavior of linear transformations.

## 2. How is linear algebra used in electrical circuits?

Linear algebra is used to analyze and model electrical circuits, especially those with multiple components and varying inputs. It allows us to represent complex networks of resistors, capacitors, and inductors using matrices and solve for voltage and current values at different points in the circuit.

## 3. What are the basic components of an electrical circuit?

The basic components of an electrical circuit are a power source, such as a battery or generator, conductors, such as wires, and electrical devices, such as resistors, capacitors, and inductors. These components work together to allow the flow of electric current through the circuit.

## 4. How do you calculate the total resistance in a series or parallel circuit?

In a series circuit, the total resistance is equal to the sum of all individual resistances. In a parallel circuit, the total resistance is calculated using the formula 1/Rt = 1/R1 + 1/R2 + 1/R3 + ... , where Rt is the total resistance and R1, R2, R3, etc. are the individual resistances.

## 5. Can linear algebra be used to solve non-linear circuits?

No, linear algebra can only be used to solve linear circuits where the components have a linear relationship between voltage and current. Non-linear circuits, such as those with diodes or transistors, require more complex mathematical techniques to analyze and solve.

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