Rules An application of Kirchhoff's Rules to the circuit shown results in the following system o

step 1 All right, we're going to follow the following matrix. So the first step we want to do is you wa

Rules An application of Kirchhoff's Rules to the circuit...

Key Concepts

Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law states that the total current entering a junction in a circuit equals the total current leaving that junction. This principle is fundamental in circuit analysis for setting up relationships between branch currents at a node, ensuring charge conservation in the circuit.

Kirchhoff's Voltage Law (KVL)

Kirchhoff's Voltage Law asserts that the sum of all electromotive forces and voltage drops around any closed loop in a circuit must equal zero. This law is used to relate the voltages across components in a loop, which is key when setting up equations for unknown currents and resistances.

System of Linear Equations

The application of Kirchhoff's laws results in a set of simultaneous linear equations that describe the relationships between currents and voltages within the circuit. The ability to solve these equations using methods such as substitution, elimination, or matrix techniques is crucial in circuit analysis.

Circuit Analysis

Circuit analysis involves systematically applying electrical laws, including KCL and KVL, in combination with Ohm's law, to determine unknown quantities like currents, voltages, and resistances in electrical circuits. It encompasses breaking down complex circuits into simpler parts to facilitate analysis and solution.

Transcript

00:01 All right, we're going to follow the following matrix.

00:02 So the first step we want to do is you want to make sure all of our variables are on one side and all of our constants are on the other.

00:10 So it looks like right now most of my variables are on the left side except for the top equation.

00:15 So i'm going to move that one over.

00:19 So i need to move over the i3 and the i2.

00:23 To do that, i'm just going to subtract that i3 and subtract that i2 to both sides.

00:32 So the first equation i'm going to deal with is going to look like this.

00:36 He said i -1 minus i -2 minus i -3, equal to zero.

00:46 So that one, we have all of our variables on one side, coefficient on the other.

00:49 So now we need to look at our second equation.

00:52 I already have variables on one side, but i want to move my constant.

00:56 I'm going to subtract that 24 over to the other side.

01:01 So that equation will look like negative 6i1 minus 3.

01:07 I3 is equal to negative 24.

01:11 Now that one's done.

01:14 Last one here, i can put these two numbers together and deal with it as 36 instead.

01:19 And then i'm just going to subtract 36 to both sides.

01:23 So i'd have a negative 6i1 minus 86i2 and that equals to negative 30.

01:34 Now that i have this, i can set up my matrix to solve.

01:38 Just remember here in my blanks, i would technically have.

01:40 A 0 i2 and here i would have a 0 which is important when we go to set up the matrix because we do have to put values in each of them and we want to keep each column to the specific variable it's doing with and each for the specific equations i'd have 1 negative 1 negative 1 0 negative 6 0 negative 3 4 and negative 6 negative 6 negative 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0000 and maybe 36.

02:19 That's what i have right now.

02:20 Now just because when i go to solve these i was like to have the one in the top left.

02:25 I have that, but i like to try to keep my rows with my diagonal ones.

02:29 So all i'm going to do here is i'm going to exchange row two and row three because i notice they have zeros.

02:37 In the spot, i don't want them to have.

02:42 So what i'm going to solve is one, negative one, negative one, zero, negative six, negative six zero.

02:51 And negative 6 .0 and negative 3.

03:01 So what i can do now is you can go about any way you want to solve it.

03:05 What i will do, i'm going to work sideways instead of straight down.

03:11 So what i will do is i'm going to take row 2 and i'm going to add the row 1 to that equation to cancel out that negative 6.

03:28 So 1 times 6 is 6 plus negative 6 is 0, so well 3 class is right this in here.

03:35 First there's not changing.

03:38 There's rows not changing.

03:48 So negative 6 plus 6 is 0.

03:52 Negative 6 plus negative 6 is negative 12.

03:57 And negative 6 plus 0 is negative 6.

04:05 And 0 plus negative 36 is negative 36.

04:12 I can see here that my second row is all multiple to six, so i am going to take a negative one -six of that second one.

04:23 Negative one, zero, zero, two, one, six now.

04:31 I'm going to leave my second row alone for right now.

04:41 So i'm going to go to my third row.

04:44 I'm going to take my third row, and i'm going to add six of my first row to back.

04:49 So negative 6 plus 1 is 0...

Please give Ace some feedback