Mesh Analysis

The Kirchorff's Voltage Law (KVL) is the main basis of the Mesh Analysis. It is either the current only exist in one mesh or when the current source is in between of two meshes. And these are the two cases in solving the mesh analysis.  


To understand such cases, let's have an example.
Considering this circuit:

Here are the steps in solving:
1. Analyze circuit.
2. Look at the figure. I have assigned I1 for the first current loop and I2 for the second current loop.
3. Since that the second loop has the current source of 2 amperes,therefore,I conclude that:

                              I2 = -2 Amps

4. Solve Mesh 1 to get I1:
---------------------------------------------------------------------------------
12/_0 + 3I1 - j2(I1-I2) = 0
12/_0 + 3I1 - j2I1 - j2I2 = 0
12/_0 + I1(3-j2) - j2I2 = 0
I1(3-j2)-j2I2 = -12/_0
I1(3-j2)-j2(-2/_0) = -12/_0
I1(3-j2)+j4 = -12/_0
I1 (3-j2) = -12/_0 - j4

I1 = 3.508/_-127.87 Amps


Itotal = 4.99/_-146.30 Amps
---------------------------------------------------------------------------------

V = IR
V = (4.99/_-146.30)(j2)
V = 9.98/_-56.307 Volts




Considering this circuit:

Here are the steps in solving:
1. Analyze the circuit.
2. In this case, the current source is in between of two meshes. Then it will be changed by an open circuit. See the figure below.

 3. Solve for Supermesh by using KVL:

-j2I1 - 3I2 = 0 ----------> Equation 1

• Get I2 by KCL: 

I2 = 2/_0 + I1  ----------> Equation 2

• Substitute Eq. 2 in 1:

-j2I1 - 3(2/_0 + I1) = 0

-j2I1 - 6 - 3I1 = 0

I1(-3-j2) = 6

I1 = 1.664/_146.309 A

• for I2:

I2 = 2/_0 + 1.664/_146.309

I2 = 1.109/_56.309 Amps

• Solve for V:

V = IR

V = 1.109/_56.309(3)

V = 3.328/_56.309 Volts