Mesh Analysis 2

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METHODS OF ANALYSIS
• Nodal analysis
• Mesh Analysis
Mesh Analysis 2
Supermesh
6
10
Solve the mesh
currents
2
20V
+

i1
6A
i2
4
Step 1
Assign mesh currents to the meshes
Step 2
For every mesh, apply KVL – Using Ohm’s law, write down the
equations in terms of mesh currents
We cannot write equation for the meshes since we cannot write the voltage drop
across the 6A source in terms of mesh currents!
Mesh Analysis 2
Supermesh
6
10
Solve the mesh
currents
2
20V
+

i1
6A
i2
4
We form a supermesh by EXCLUDING the branch containing the
current source and elements connected in series with it
We cannot write equation for the meshes since we cannot write the voltage drop
across the 6A source in terms of mesh currents!
Mesh Analysis 2
Supermesh
6
10
SUPERMESH
Solve the mesh
currents
2
20V
+

i1
i2
6A
4
We cannot write equation for the meshes since we cannot write the voltage drop
across the 6A source in terms of mesh currents!
We form a supermesh by EXCLUDING the branch containing the
current source and elements connected in series with it
KVL for the supermesh :
-20 + 6i1 + 10i2 + 4i2 = 0
Mesh Analysis 2
Supermesh
6
10
Solve the mesh
currents
2
20V
+

i1
6A
i2
4
Since we have combined meshes 1 and 2, we lost one equation. We
need one more equation to solve the mesh current
We obtain the extra equation by using KCL on the branch current that we have removed.
-20 + 6i1i2+- 10i
i1 =2 6+ 4i2 = 0
Mesh Analysis 2
Supermesh
6
10
Solve the mesh
currents
2
20V
i1
+

6A
i2
4
Step 3
Solve mesh currents in equations obtained in step 2, simultaneously
-20 + 6i1 + 10i2 + 4i2 = 0
i2 - i1 = 6
Mesh Analysis 2
Supermesh
6
10
Solve the mesh
currents
2
20V
i1
+

6A
i2
4
Step 3
Solve mesh currents in equations obtained in step 2, simultaneously
-20 + 6i1 + 10i2 + 4i2 = 0 i = - 3.2 A,
1
i2 = 2.8 A
i2 - i1 = 6
Mesh Analysis 2
Supermesh
To summarize ….
We form a supermesh when there is a current source in a
branch sharing 2 mesh currents
Supermesh has no current of its own.
To solve the mesh currents, we need extra equation which can
be obtained by applying KCL in the branch containing the
current source.
Mesh Analysis 2
Supermesh
Example 2
2
6V
+
-
i1
4
1
3A
Step 1
Assign mesh currents to the meshes
2
i3
i2
8
Mesh Analysis 2
Supermesh
Example 2
2
6V
+
-
2
i3
i1
4
1
3A
i2
8
Step 2
For every mesh, apply KVL – Using Ohm’s law, write down the
equations in terms of mesh currents
Step 3
Solve mesh currents in equations obtained in step 2, simultaneously
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