Mesh Current circuit calculations with matricies

In summary, the conversation involved finding the voltage across each resistor in a circuit diagram using matrix algebra and simultaneous equations. The attempt at a solution involved finding four mesh equations and transforming them into matrix form. The poster was guided to ensure all four currents were included in each equation before successfully solving the problem.
  • #1
thehippyseal
2
0

Homework Statement


Using matrix algebra calculate the voltage expected across each resister in the circuit diagram.

Only need the simultaneous equations.

The Attempt at a Solution


-15=6800(I_b-I_a )+2200(I_b-I_c)
15=2200(I_c-I_b )+8200(I_c-I_d)
-25=8200(I_d-I_c )+4700I_d

Thanks for any help.
 

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  • #2
thehippyseal said:

Homework Statement


Using matrix algebra calculate the voltage expected across each resister in the circuit diagram.

Only need the simultaneous equations.

The Attempt at a Solution


-15=6800(I_b-I_a )+2200(I_b-I_c)
15=2200(I_c-I_b )+8200(I_c-I_d)
-25=8200(I_d-I_c )+4700I_d

Thanks for any help.

Hi thehippyseal, Welcome to PF.

It looks like you're doing okay finding the mesh equations. You haven't written one for the first mesh (Ia) yet.

Once you have equations for all four loops, for each equation collect the terms for each current so you've got the form: a*Ia + b*Ib + c*Ic + d*Id = V. It should be straightforward to go to the matrix form from there.
 
  • #3
Thanks for the reply. I seem to have got it right then.

With Ia I have
20=3300I_a+6800(I_a-I_c)
-15=6800(I_b-I_a )+2200(I_b-I_c)
15=2200(I_c-I_b )+8200(I_c-I_d)
-25=8200(I_d-I_c )+4700I_d

Cheers.
 

FAQ: Mesh Current circuit calculations with matricies

1. What is a mesh current circuit?

A mesh current circuit is a type of electrical circuit that contains multiple loops or paths for current to flow through. These loops are known as meshes and are typically represented by dashed lines in a circuit diagram. Mesh current analysis is a method used to calculate the currents flowing through each mesh in a circuit.

2. How do you use matrices for mesh current calculations?

To use matrices for mesh current calculations, you first need to label each mesh in the circuit with a unique variable. Each mesh current is then represented as a row in a matrix, with the coefficients of the other mesh currents in the circuit as the elements in each row. The right-hand side of the matrix equation contains the values of the voltage sources and resistors in the circuit. By solving the matrix equation, you can determine the values of the mesh currents.

3. What are the benefits of using matrices for mesh current calculations?

Using matrices for mesh current calculations allows for a more organized and systematic approach to solving complex circuits. It also ensures that all equations are correctly set up and that no mesh currents are overlooked. Additionally, matrices allow for easy manipulation and solving of the equations using mathematical software or calculators.

4. What are some common mistakes when using matrices for mesh current calculations?

Some common mistakes when using matrices for mesh current calculations include incorrectly labeling the meshes, not including all the necessary elements in the matrix equation, and making errors when setting up the equations. It is important to double-check all equations and variables to ensure accuracy in the calculations.

5. When is it necessary to use mesh current analysis with matrices?

Mesh current analysis with matrices is most commonly used for circuits with multiple loops and voltage sources, where other methods such as nodal analysis may become too complex. It is also useful for circuits with dependent voltage sources and when the values of the mesh currents are needed for further analysis of the circuit.

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