How can I find Vab in a circuit using Mesh Current Analysis?

In summary, The conversation is about finding Vab in a circuit using Mesh Currents. The person is having trouble finding the correct answer and is asking for advice on how to proceed. They provide a matrix equation and ask for help in solving it. Another person suggests checking the equation and provides a possible solution using Ohm's Law to find Vab.
  • #1
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Hi I need to find Vab in the following circuit using Mesh Currents...Ive tried this a million times, I understand the method...but I am definitely doing something wrong. Whould I Simplify the top loop?...if its possible. I've been doing it as 3 loops, but i don't know what to use as a voltage for the top.

the file is attached,

Here is my matrix:[tex] \left( \begin{array}{ccc} 8 & -6 & -2\\-6 & 19 & -5\\-2 & -5 &7\end{array}\right) \left( \begin{array}{c} I_1\\I_2\\I_3\end{array}\right) = \left( \begin{array}{c} 28\\0\\20\end{array}\right)[/tex]

[tex]V_{ab}[/tex] is suppose to equal 10V...

Thanks
 

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  • #2
I assume you have I1 in top loop, I2 in left loop, I3 in right loop, all going clockwise? Please show us your full initial equations so we can check how you got to the final matrix. Like, for the top loop you get:

8(I1) + 5(I1-I3) + 6(I1-I2) = 0

Right? What are the other two loop equations, and then show the steps to get to your matrix equation, and then show how you solved it with the determinant.
 
  • #3
The way we were taught to do it was for the i1ji position in the matrix, you sum all the resistances in that loop. i2j2 is the same for that loop and i3j3 is the same for the 3rd loop. the i1j2 position is the resistances that are common to the 1st and second loop...etc..
 
  • #4
Well, okay, but if it were me and I was getting the wrong answer, I'd do it the long way that I mentioned just to check my answer...
 
  • #5
The last equation coefficient on the right side vector should be -20 based upon the equation you wrote for Loop 3. If you then take the difference between the 2 loop currents coupling the 2 Ohm resistor and use Ohm's Law you should get 10 Volts.
In your case this would be (i1-i3)2=10 Volts. i1 = 4 A; i2 = 1 A; i3 = -1 A
 

1. What is mesh current analysis?

Mesh current analysis is a method used in circuit analysis to determine the currents flowing through individual branches of a circuit. It involves assigning a direction and magnitude to each loop in the circuit and using Kirchhoff's voltage law (KVL) to write equations and solve for the currents.

2. When is mesh current analysis used?

Mesh current analysis is typically used when analyzing circuits with multiple current sources and/or complex components such as resistors and capacitors. It is also useful when trying to determine the voltage drop across a specific component in the circuit.

3. How is mesh current analysis different from nodal analysis?

The main difference between mesh current analysis and nodal analysis is that mesh current analysis uses KVL to analyze loops in the circuit, while nodal analysis uses Kirchhoff's current law (KCL) to analyze the currents at individual nodes in the circuit. Additionally, nodal analysis is typically used for circuits with voltage sources, while mesh current analysis is used for circuits with current sources.

4. What are the advantages of using mesh current analysis?

One advantage of using mesh current analysis is that it can be used to solve complex circuits with multiple current sources and components. It also allows for the determination of individual currents in specific branches of the circuit, making it useful for troubleshooting and optimizing circuit designs.

5. Are there any limitations to using mesh current analysis?

One limitation of mesh current analysis is that it can become time-consuming and tedious for circuits with a large number of loops. It also assumes that the currents in each loop can be easily determined, which may not always be the case in more complex circuits. In these situations, nodal analysis or other methods may be more suitable.

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