Mesh Analysis

Case 1: When the current source is exist only in one mesh.

Consider this is a circuit:

Find i2?

To solve for the given circuit:

• Analyze the problem.
• Assign i1 for first loop and i2 for the second loop.
• Equation for i1:
• 12 -j2(I1) - 3(I1 - I2) = 0

•  Equation for i2:
• -3(I2 - I1) - j4(I2) = 0

• Then simplify the equation you get from the loop.
• Use Matrix or Substitution to get the I2.

• Case 2: When a current source exist between two meshes it is SUPERMESH.

Consider this is a circuit:

Find i?

To solve for the given circuit:

• Analyze the problem.
• You can see to the given circuit that the current source is between the two meshes. Therefore, it is a SUPERMESH.
• Then, Assign Mesh 1 for iA and Mesh 2 for iB and Mesh 3 for iC. See circuit below!
• But still, you can reconstruct the circuit to be more easy. 

•  To get the equation on that SUPERMESH, cut the current source and use KVL. See circuit below!

• Equation for SUPERMESH.
• Using KVL :     - j1(iA) - 3(iB - iC) = 0 
• -j1(iA) - 3iB + 3iC = 0    =====> equation 1

•  To get the second equation, choose node in the current source where to get the second equation. See circuit below!

•  I chose the top node because it more comfortable than the bottom. :)
• Equation for that node.
• Using KCL:    iA + 2 = iB
• iA - iB = - 2  
• Then, get equation 3. Using KVL.
• Using Matrix or Substitution you can now get the value of iA, iB, iC.
•  i = iB - iC.