Solve 4-Mesh Network for Rx & Lx w/ R, C & Source Freq.

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In summary, the unknowns Rx and Lx can be expressed in terms of R, C and the source frequency (rad/s). Loop 2, 3 and 4 have been set up to solve for Lx. However, no matter what is done, Lx cannot be determined using just the values for R, C and the angular frequency.
  • #1
sandy.bridge
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Homework Statement


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The four-mesh network has the mesh currents
[tex]I_1, I_2, I_3, I_4[/tex]
in the indicated regions 1, 2, 3 and 4 respectively. In this circuit, the resistor R and the identical capacitors (Zc) are adjusted such that
[tex]I_4=0[/tex]
For this condition, the unknowns Rx and Lx can be expressed in terms of R, C and the source frequency (rad/s). Find the expressions for Rx and Lx.

What I did was I set up loop equations for loop 2, 3 and 4. I neglected loop 1.

Loop 2:
[tex]-Z_CI_1+(R+2Z_C)I_2-Z_CI_4=0\rightarrow{-Z_CI_1+(R+2Z_C)I_2=0}\rightarrow{I_1=\frac{(R+2Z_C)I_2}{Z_C}}[/tex]

Since the potential across Zd is zero, we have:
[tex](-j\omega{L_x}I_3)/Z_C=I_2[/tex]
applying substitution we have,
[tex]I_1=\frac{(R+2Z_C)((-j\omega{L_x}I_3)/Z_C)}{Z_C}[/tex]

Next, around loop 3:
[tex]-R_xI_1+(R_x+j\omega{L_x})I_3=0\rightarrow{-R_x(\frac{(R+2Z_C)((-j\omega{L_x}I_3)/Z_C)}{Z_C})+(R_x+j\omega{L_x})I_3=0}[/tex]
The current I3 cancels, and algebraic manipulation results in:
[tex]L_x=\frac{1}{j\omega{^3}CR+2\omega{^2}-\frac{j\omega}{R_xC}}[/tex]
No matter what I do, I cannot seem to get Lx in terms of simply C, R and the angular frequency; that is, the expression always has Rx when solving for Lx, and Lx when solving for Rx.

Any suggestions?
 
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  • #2
Replace Rx and Lx with a single impedance Zx and eliminate loop 4. Solve for Zx in terms of the other components. That result will be a complex impedance; convert it to an admittance Yx by taking the complex reciprocal. Rx will be the inverse of the real part of Yx and the imaginary part can be converted to an inductance Lx by use of the radian frequency.
 
  • #3
the electrician,

can you please show the working out. I've have got the answers but am unsure of my working out.
 
  • #4
Go have a look at this thread:

http://forum.allaboutcircuits.com/showthread.php?t=84745
 
  • #5




It seems like you are on the right track with your approach. However, there may be an error in your algebraic manipulation. I would suggest double-checking your calculations and possibly seeking assistance from a colleague or professor. It is also possible that the expressions for Rx and Lx may not be able to be simplified further and may require the use of the quadratic formula. Overall, it is important to carefully check your work and seek help if needed to ensure accurate and complete solutions.
 

1. What is a 4-Mesh Network?

A 4-Mesh Network is a type of electrical network that contains four interconnected nodes or components. It is commonly used in electronic circuits to solve for the values of Rx and Lx with the known values of R, C, and the source frequency.

2. How do I solve for Rx and Lx in a 4-Mesh Network?

To solve for Rx and Lx in a 4-Mesh Network, you will need to use a combination of Kirchhoff's Laws and Ohm's Law. By setting up and solving a system of equations based on these laws, you can determine the values of Rx and Lx.

3. What role do R, C, and the source frequency play in a 4-Mesh Network?

R, C, and the source frequency are known as the circuit parameters and are essential in determining the values of Rx and Lx in a 4-Mesh Network. R represents the resistance, C represents the capacitance, and the source frequency is the frequency of the electrical signal being input into the circuit.

4. Can I use a 4-Mesh Network for any type of circuit?

Yes, a 4-Mesh Network can be used for a variety of circuits as long as they contain four interconnected nodes or components. However, the values of Rx and Lx will vary depending on the specific circuit parameters.

5. What are the practical applications of solving a 4-Mesh Network for Rx and Lx?

Solving a 4-Mesh Network for Rx and Lx can be useful in various areas of electrical engineering, such as designing and analyzing electronic circuits, troubleshooting circuit problems, and optimizing circuit performance for specific applications.

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