Mesh Circuit Analysis: Solving KCL Equations for i1, i2, and i3 | Homework Help

In summary, the conversation discusses a circuit analysis problem using the KCL equation. The approach to solving the problem is shown, and the process of labeling loops and current directions is recommended. A reference for learning more about mesh analysis is suggested, and a mistake in the second equation is pointed out and corrected.
  • #1
dwn
165
2

Homework Statement



I have attached an image of the problem:

Homework Equations



KCL Equation

The Attempt at a Solution



0 = 2i11 + 3(i1-i2)
212 = 3(i2-i1) + 5(i2-i3)
-122 = 3i3 + 5(i3-i2)

5i1 - 3i2 = 0
-3i1 +8i2 + 5i3 = 212
-5i2 + 8i3 = -122

Is this the correct approach?

Also, does anybody have a good reference to learn this stuff? I'm taking this course online and I'm drowning. Thanks!
 

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  • #2
dwn said:

Homework Statement



I have attached an image of the problem:

Homework Equations



KCL Equation


The Attempt at a Solution



0 = 2i11 + 3(i1-i2)
212 = 3(i2-i1) + 5(i2-i3)
-122 = 3i3 + 5(i3-i2)

5i1 - 3i2 = 0
-3i1 +8i2 + 5i3 = 212
-5i2 + 8i3 = -122

Is this the correct approach?
The approach looks okay. Check the sign on the i3 term for your second equation. Otherwise looks okay to me.

You should label the loops and current directions on the circuit diagram and associate your equations with the labels so it's clear which loop each equation belongs to. Granted it's pretty clear in this relatively simple case with only three loops, but it's good to get in the habit of making your work easy to interpret for those who are just seeing it for the first time.

Also, does anybody have a good reference to learn this stuff? I'm taking this course online and I'm drowning. Thanks!
You can probably find many worked examples on the net by searching for "mesh analysis examples". For that matter there are plenty here on the Physics Forums. Take a look at the "Related Discussions" section at the bottom of your thread. Also investigate the forum search facilities.
 
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  • #3
Thank you for your help and I will make sure to clearly present everything in the future.

I'm not sure I quite understand why the second equation is incorrect..? If the less simplified equation above is correct, which as I understand it, you subtract the current adjacent to the resistor of interest (5 ohm) from the current loop you are analyzing, shouldn't it be a negative 5i3 ::: 212 = 3(i2-i1) + 5(i2-i3)
 
  • #4
dwn said:
Thank you for your help and I will make sure to clearly present everything in the future.

I'm not sure I quite understand why the second equation is incorrect..? If the less simplified equation above is correct, which as I understand it, you subtract the current adjacent to the resistor of interest (5 ohm) from the current loop you are analyzing, shouldn't it be a negative 5i3 ::: 212 = 3(i2-i1) + 5(i2-i3)

Yes, it should be -5i3. That's the point I was making. Look at the relevant section from your first post...
5i1 - 3i2 = 0
-3i1 +8i2 + 5i3 = 212 <---------
-5i2 + 8i3 = -122

The 5i3 in the indicated line should be negative, right?
 
  • #5
Ooops...I thought you had changed it and that's why you used the red...my bad! I think I'm going cross eyed!
Thanks again for the help gneill.
 

Related to Mesh Circuit Analysis: Solving KCL Equations for i1, i2, and i3 | Homework Help

1. What is mesh circuit analysis?

Mesh circuit analysis is a method used to analyze and solve circuits that have multiple loops or meshes. It involves applying Kirchhoff's Voltage Law (KVL) to each mesh in the circuit to find the unknown currents.

2. How do you solve KCL equations for i1, i2, and i3?

To solve for the unknown currents in a mesh circuit, you need to set up and solve a system of equations using Kirchhoff's Current Law (KCL). This involves writing KCL equations for each node in the circuit, and then using the equations to solve for the unknown currents.

3. What is the purpose of using KCL equations in mesh circuit analysis?

KCL equations are used in mesh circuit analysis to ensure that the current entering a node is equal to the current leaving the node. This allows us to solve for the unknown currents in the circuit and determine the flow of current through each component.

4. What are some tips for solving KCL equations in mesh circuit analysis?

Some tips for solving KCL equations in mesh circuit analysis include: labeling the mesh currents consistently, choosing a direction for each mesh current and being consistent with the direction when writing KCL equations, and using a systematic approach to solve the equations (e.g. substitution, elimination, etc.).

5. Can mesh circuit analysis be used for all types of circuits?

No, mesh circuit analysis is most useful for circuits that have multiple loops or meshes. It is not as effective for circuits that have only one loop or for more complex circuits with non-linear components. In these cases, other methods such as nodal analysis may be more appropriate.

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