Solve Mesh Currents: Find i1, i2 & i3

In summary, the conversation discusses the attempt at finding the mesh currents i1, i2, and i3. The equations used are KVL at i1, i2, and i3, but there is a question about the polarity of the voltage sources on the mesh at i1. The suggestion is to first solve equations 1 and 2 and then substitute the value in the third equation.
  • #1
engineer_dave
35
0

Homework Statement



Find the mesh currents i1, i2 and i3

Homework Equations





The Attempt at a Solution



I did it this way

KVL at i1: 12 + 1i2 + 1i1 - 1I2 + 10 = 0

KVL at i2: 10 + 1i2 - 1i1 + 1i2 + 1i2 - 1i3 = 0

KVL at i3: 1i3 - 1i2 + 1i3 + 12 = 0

I was wondering though for KVL at i1, should i add a -10 to go with the 10?? Thanks.
 

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  • #2
I would take a 2nd look at the polarity of your voltage sources on your mesh at i1. Remember you are looking clockwise.
 
  • #3
What's the polarity on each of the voltage sources? You can't really write any equations without knowing them...or at least arbitrarily assigning them. The way you have your equations written, though, I would take Ouabache's advice...
 
  • #4
THIS WILL BE DONE BY ,FIRST,SOLVING EQUATION 1 AND 2,THEN SUBSTITUTING THE VALUE IN THE 3RD EQUATION ...THIS PROCEDURE MAY HELP U,I HAVE DONE THIS TYPE OF QUESTION TODAY,,IT MIGHT WORK,,,DO REPLY ME IF WORKED...THNX

..ATHAR
engineer_dave said:

Homework Statement



Find the mesh currents i1, i2 and i3

Homework Equations





The Attempt at a Solution



I did it this way

KVL at i1: 12 + 1i2 + 1i1 - 1I2 + 10 = 0

KVL at i2: 10 + 1i2 - 1i1 + 1i2 + 1i2 - 1i3 = 0

KVL at i3: 1i3 - 1i2 + 1i3 + 12 = 0

I was wondering though for KVL at i1, should i add a -10 to go with the 10?? Thanks.
 

1. What is the purpose of solving mesh currents in a circuit?

Solving mesh currents allows us to determine the flow of current through each individual loop or mesh in a circuit. This is important for analyzing and understanding the behavior of a circuit, as well as for calculating other important quantities such as voltage and power.

2. How do you find the mesh currents in a circuit?

To find the mesh currents, we use Kirchhoff's Current Law (KCL) to write equations for each node in the circuit. Then, we use Kirchhoff's Voltage Law (KVL) to write equations for each loop or mesh in the circuit. Finally, we solve this system of equations to determine the values of the mesh currents.

3. What are the steps for solving mesh currents?

The steps for solving mesh currents are as follows:

  1. Identify all the loops or meshes in the circuit.
  2. Assign a direction for each mesh current.
  3. Apply KVL to each loop or mesh, writing an equation for the voltage drops and rises around the loop.
  4. Apply KCL to each node in the circuit, writing an equation for the sum of currents entering and leaving the node.
  5. Solve the resulting system of equations to find the values of the mesh currents.

4. What are some common mistakes when solving mesh currents?

Some common mistakes when solving mesh currents include:

  • Not correctly labeling the direction of the mesh currents.
  • Forgetting to include all the loops or meshes in the circuit.
  • Not applying KVL or KCL correctly, such as using the wrong signs for voltage drops or not considering all the currents at a node.
  • Making errors in algebra when solving the system of equations.

5. What are some tips for solving mesh currents efficiently?

To solve mesh currents efficiently, it can be helpful to:

  • Start by labeling the direction of the mesh currents in a logical way.
  • Use a systematic approach when applying KVL and KCL, such as starting at one node and working your way around the circuit.
  • Double check your work and make sure you have included all the loops or meshes in the circuit.
  • Use algebraic shortcuts, such as combining equations or using substitutions, to simplify the system of equations and make it easier to solve.

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