The mesh current method - Am I doing it right?

In summary, the problem was that the mesh current direction was wrong and the potential changes across the resistors in the second mesh should drop in the direction of mesh current flow. Additionally, the mesh current in the top right mesh also passes through the 2Ω resistor shared with the bottom right mesh. The top left mesh affects conditions in the top right mesh (in general, all the meshes interact due to shared components).
  • #1
foxofdesert
22
0

Homework Statement


Apply the mesh current method to find I0


Homework Equations


Mesh current method


The Attempt at a Solution



On the left bottom square circuit, I set a mesh current, I1, and on the right bottom square circuit, I set a mesh current, I2.

Then, I0=I1-I2.

Since there is a current source on the mesh I1, I1=-5 (negative sign because of the direction.)
and
(1+2+4)I2+22.5=0, so I2=(-22.5)/7.
Therefore, I0=-5-(-22.5)/7=(-12.5)/7.

Am I doing it right?
 

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  • #2
Please check the attachment to see the problem.
 
  • #3
foxofdesert said:
On the left bottom square circuit, I set a mesh current, I1, and on the right bottom square circuit, I set a mesh current, I2.

Then, I0=I1-I2.
Okay.
Since there is a current source on the mesh I1, I1=-5 (negative sign because of the direction.)
and
(1+2+4)I2+22.5=0, so I2=(-22.5)/7.
Therefore, I0=-5-(-22.5)/7=(-12.5)/7.
Check your mesh current direction; the potential changes across the resistors in the second mesh should drop in the direction of mesh current flow.

Also, you need to take into account the effect of the other currents in the circuit. In particular, the mesh current in the top right mesh also passes through the 2Ω resistor shared with the bottom right mesh. Similarly, the top left mesh affects conditions in the top right mesh (in general, all the meshes interact due to shared components).

You'll have to write equations relating all the meshes in order to capture the interactions. For the bottom left mesh you can take its current as given (-5A) since it's constrained by a current source there. For the top pair, you might want to employ the supermesh method to write the two equations that describe it.
 
  • #4
Thanks for your help.

I set up the super mesh on the top since they share a current source, so I set up total of 3 mesh ( 1 supermesh, 2 mesh for each bottom circuit) and solved the problem.

Thank you so much
 
  • #5


Yes, your approach using the mesh current method to find I0 seems correct. By setting up two mesh currents and using Kirchhoff's voltage law, you were able to solve for I0. Your calculations also seem to be correct. However, it would be helpful to provide a diagram or more context for the circuit in order to fully understand your solution. Additionally, it's always a good idea to double check your calculations and make sure they are consistent with the given circuit. Keep up the good work!
 

1. What is the mesh current method?

The mesh current method is a technique used in circuit analysis to determine the currents flowing through different branches in a circuit. It involves assigning currents, known as mesh currents, to each individual loop in the circuit and using Kirchhoff's Voltage Law to solve for the unknown currents.

2. How do I know if I am using the mesh current method correctly?

To ensure you are using the mesh current method correctly, you should follow these steps:

  • Assign a current to each loop in the circuit, in the same direction as the loop.
  • Apply Kirchhoff's Voltage Law to each loop, setting up equations for each mesh current.
  • Solve the equations simultaneously to find the values of the mesh currents.
  • Check your solution by substituting the values back into the equations to ensure they satisfy Kirchhoff's Voltage Law.

3. Can I use the mesh current method for any type of circuit?

Yes, the mesh current method can be used for any type of circuit, including circuits with multiple voltage sources and resistors connected in parallel. However, it is most commonly used for circuits with multiple loops and no current sources.

4. Are there any limitations to using the mesh current method?

While the mesh current method is a powerful technique, it does have some limitations. It can only be used for planar circuits, meaning all elements are in the same plane, and it cannot be used for circuits with dependent sources. Additionally, it may become more complex and time-consuming to use for circuits with a large number of loops or complex circuit configurations.

5. Can I use the mesh current method to find the voltage across a specific element in the circuit?

Yes, the mesh current method can be used to find the voltage across a specific element in the circuit. After solving for the mesh currents, you can use Ohm's Law to find the voltage drop across any resistor or other element in the circuit.

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