Question

The goal of this lab is to write MATLAB scripts to perform basic vector and matrix operations. To submit your answers, open a word processor window and copy all scripts, graphs, and answers to questions into one file. Submit the file using the link on the course moodle page. 1. Linear Systems: We want to find the mesh currents $i_1, \dots, i_5$ in the circuit where $R_1 = R_2 = \dots = R_{10} = 1 \, \Omega$ and $v_s = 89 \, V$. A mesh current analysis of the circuit would apply KVL to each loop: $-v_s + R_1i_1 + R_2(i_1 - i_2) = 0$ $R_2(i_2 - i_1) + R_3i_2 + R_4(i_2 - i_3) = 0$ $R_4(i_3 - i_2) + R_5i_3 + R_6(i_3 - i_4) = 0$ $R_6(i_4 - i_3) + R_7i_4 + R_8(i_4 - i_5) = 0$ $R_8(i_5 - i_4) + R_9i_5 + R_{10}i_5 = 0$, or equivalently $(R_1 + R_2)i_1 - R_2i_2 = v_s$ $-R_2i_1 + (R_2 + R_3 + R_4)i_2 - R_4i_3 = 0$ $-R_4i_2 + (R_4 + R_5 + R_6)i_3 - R_6i_4 = 0$ $-R_6i_3 + (R_6 + R_7 + R_8)i_4 - R_8i_5 = 0$ $-R_8i_4 + (R_8 + R_9 + R_{10})i_5 = 0$ Write a MATLAB script to find $i_1, \dots, i_5$ from these equations using the rref command. If there is a unique solution, find it; if there is no solution, or more than one, explain why.

          The goal of this lab is to write MATLAB scripts to perform basic vector and matrix operations. To submit your answers, open a word processor window and copy all scripts, graphs, and answers to questions into one file. Submit the file using the link on the course moodle page.
1. Linear Systems: We want to find the mesh currents $i_1, \dots, i_5$ in the circuit
where $R_1 = R_2 = \dots = R_{10} = 1 \, \Omega$ and $v_s = 89 \, V$. A mesh current analysis of the circuit would apply KVL to each loop:
$-v_s + R_1i_1 + R_2(i_1 - i_2) = 0$
$R_2(i_2 - i_1) + R_3i_2 + R_4(i_2 - i_3) = 0$
$R_4(i_3 - i_2) + R_5i_3 + R_6(i_3 - i_4) = 0$
$R_6(i_4 - i_3) + R_7i_4 + R_8(i_4 - i_5) = 0$
$R_8(i_5 - i_4) + R_9i_5 + R_{10}i_5 = 0$,
or equivalently
$(R_1 + R_2)i_1 - R_2i_2 = v_s$
$-R_2i_1 + (R_2 + R_3 + R_4)i_2 - R_4i_3 = 0$
$-R_4i_2 + (R_4 + R_5 + R_6)i_3 - R_6i_4 = 0$
$-R_6i_3 + (R_6 + R_7 + R_8)i_4 - R_8i_5 = 0$
$-R_8i_4 + (R_8 + R_9 + R_{10})i_5 = 0$
Write a MATLAB script to find $i_1, \dots, i_5$ from these equations using the rref command. If there is a unique solution, find it; if there is no solution, or more than one, explain why.

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the goal of this lab is to write matlab scripts to perform basic vector and matrix operations to submit your answers open a word processor window and copy all scripts graphs and answers to q 59832

Added by Gary G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sam Stansfield

10/04/2024

Step 1

Step 1: The given equations can be written in matrix form as $Ax = b$, where $A = \begin{bmatrix} (R_1 + R_2) & -R_2 & 0 & 0 & 0 \\ -R_2 & (R_2 + R_3 + R_4) & -R_4 & 0 & 0 \\ 0 & -R_4 & (R_4 + R_5 + R_6) & -R_6 & 0 \\ 0 & 0 & -R_6 & (R_6 + R_7 + R_8) & -R_8 \\ 0 & Show more…

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The goal of this lab is to write MATLAB scripts to perform basic vector and matrix operations. To submit your answers, open a word processor window and copy all scripts, graphs, and answers to questions into one file. Submit the file using the link on the course moodle page. 1. Linear Systems: We want to find the mesh currents $i_1, \dots, i_5$ in the circuit where $R_1 = R_2 = \dots = R_{10} = 1 \, \Omega$ and $v_s = 89 \, V$. A mesh current analysis of the circuit would apply KVL to each loop: $-v_s + R_1i_1 + R_2(i_1 - i_2) = 0$ $R_2(i_2 - i_1) + R_3i_2 + R_4(i_2 - i_3) = 0$ $R_4(i_3 - i_2) + R_5i_3 + R_6(i_3 - i_4) = 0$ $R_6(i_4 - i_3) + R_7i_4 + R_8(i_4 - i_5) = 0$ $R_8(i_5 - i_4) + R_9i_5 + R_{10}i_5 = 0$, or equivalently $(R_1 + R_2)i_1 - R_2i_2 = v_s$ $-R_2i_1 + (R_2 + R_3 + R_4)i_2 - R_4i_3 = 0$ $-R_4i_2 + (R_4 + R_5 + R_6)i_3 - R_6i_4 = 0$ $-R_6i_3 + (R_6 + R_7 + R_8)i_4 - R_8i_5 = 0$ $-R_8i_4 + (R_8 + R_9 + R_{10})i_5 = 0$ Write a MATLAB script to find $i_1, \dots, i_5$ from these equations using the rref command. If there is a unique solution, find it; if there is no solution, or more than one, explain why.

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Transcript

00:01 All right, so we have this circuit.

00:03 I've drawn in the values of all the resistors and batteries.

00:09 And what we want to do is we want to find the three mesh, the four mesh current.

00:14 All right.

00:15 So first of all, we want to write down the equations.

00:20 And we use the loop law for that in each of our four loops.

00:31 Okay, so there's the equation we get from loop one.

00:34 From loop 2, we got...

02:33 So those are our four equations.

02:36 And i'm going to rewrite those by combining the...

02:42 With different terms.

02:45 Okay, so we look like this.

02:46 And now i'm going to rewrite them.

02:51 I don't know if i have enough space to do everything i'm going to do.

02:54 But now i'm going to rewrite them so that all the voltages are on the right.

03:04 I'm also going to put the currents in order in each one.

04:16 Okay, so i'm going to set this up as a matrix equation.

05:30 All right, so i'm going to solve this using kramer's rule, and i don't have enough space to write all the matrices out.

05:42 But the goal is we have to calculate a few determinants.

05:48 So if this is the matrix a, the determinant of that matrix goes into my denominator...

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