AC Circuit Analysis: Solving 4x4 Matrix w/ Imaginary Numbers, Real #s & Phasor

In summary, the person is having trouble with solving a matrix involving loop/mesh analysis on an AC circuit. They are more confused with how to do it than they are confused with the circuit theory. They say that it is easier to add, subtract, multiply and divide in complex format than in phasor. They suggest that someone else help them with the solution, as they are rusty on circuits and their notes and textbook are 400 miles away.
  • #1
verd
146
0
Hey,

This is a problem involving loop/mesh analysis on an AC circuit. I'm less confused about the circuit theory, I'm more confused with how to solve the resulting matrix. I get 4 equations with 4 unknowns... Which is something I'm accustomed to solving, but there are three different types of terms. Imaginary numbers, real numbers, and the phasor format (magnitude<angle - 4<60)

Here's the problem. I solved it the same way this person did, I'm just stuck on the matrix.

http://synthdriven.com/images/deletable/EEN201-17.jpg [Broken]

Any tips on an easy/efficient way to go about this?

Thanks!
 
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  • #2
Doing that by hand along with the complex numbers and phasers are a real pain, but not impossible. Just convert them all into complex or phasor fomat.

If you have a TI-89 or Ti86, then you can just punch those numbers that you have there into a matrix and it will solve it for you. I believe the Ti-83 has some limitations on the phasors and complex numbers in matrices, but I'm not sure. Also MATLAB will work.
 
  • #3
How do you convert from phasor format into imaginary numbers??
 
  • #4
I was hoping you wouldn't ask that, but I guess your instructor isn't going to let you use a calculator on a test.
Your textbook should have an explanation of how to do it. Its about the same the same way as breaking a vector into components. I'm a bit rusty on circuits and my notes and textbook are 400 miles away :mad: . Hopefully someones else will comes along and help.

Simple rough example

(4<30)

4 cos 30 = 3.46
4 sin 30 = 2

z = 3.46 + 2j


It's easier to add, subtract, multiply and divide in complex format than phasor.
 
  • #5
Since [itex]I_2 = 4 \angle 30[/itex], this is a system of 3 (instead of 4) unknowns. It would be nice if you can further reduce that to 2 unknowns since systems of equations with 2 unknowns are very much easier to solve than 3.

As far as the solution goes, you'd perhaps need to convert all the terms into the complex equivalent as suggested by teknodude.

teknodude said:
It's easier to add, subtract, multiply and divide in complex format than phasor.
I think it's easier to add and subtract in complex form, but multiplication and division are easier in phasor.
 
  • #6
doodle said:
I think it's easier to add and subtract in complex form, but multiplication and division are easier in phasor.

Crap.. wtf was I thinking. Yea doodle is right on that.
 
  • #7
teknodude
Please, can you explain how to punch the matrix into a ti 89, it will help save a lot of time and possible mistake. o:)
Thanks
 
  • #8
dh19440113 said:
teknodude
Please, can you explain how to punch the matrix into a ti 89, it will help save a lot of time and possible mistake. o:)
Thanks

Read the instruction manual or go to the ti website and download it. I rarely use my 89 except for integration checking. I like my aging ti86 more.
 

1. What is an AC circuit?

An AC (alternating current) circuit is a type of electrical circuit that uses alternating current to transmit and distribute electricity. Unlike DC (direct current) circuits, which use a constant flow of electricity in one direction, AC circuits use a changing flow of electricity that alternates between positive and negative values.

2. What is a 4x4 matrix in the context of AC circuit analysis?

A 4x4 matrix is a mathematical tool used in AC circuit analysis to represent the relationship between voltage, current, and impedance in a circuit. It is essentially a grid of numbers that can be manipulated to solve for unknown variables in the circuit.

3. How are imaginary numbers used in AC circuit analysis?

Imaginary numbers are used in AC circuit analysis to represent the phase angle of voltage and current in the circuit. They are necessary because AC circuits involve the use of complex numbers, which have both a real and imaginary component. Imaginary numbers also help in calculating the impedance of a circuit.

4. What are real numbers in the context of AC circuit analysis?

Real numbers are used in AC circuit analysis to represent the magnitude or amplitude of voltage and current in the circuit. They are also used to represent the resistance and reactance of components in the circuit. Real numbers are necessary for calculating the total impedance of a circuit.

5. What is a phasor and how is it used in AC circuit analysis?

A phasor is a vector representation of a sinusoidal wave in AC circuit analysis. It is used to simplify the calculation of voltage and current in a circuit by converting them to a single complex number. Phasors are useful for analyzing the behavior of AC circuits and can help in solving complex circuit problems.

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