Nodal Analysis One problem - Supermesh

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Tutorial 6: Focus
 Nodal Analysis
 One problem - Supermesh

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T6_Problem 1: Supermesh
Note: This is problem 48 on page 118, Figure 4.73 in the Ref 1 book (by Hayt)
 Find i1 and Power supplied by 1V:
- 1+ 4i1 + 3(i1 -i2) + 1(i1 -i3) = 0
3(i2 - i1) – 8 + 2i3 + 1(i3 - i1) = 0
8i1 - 3i2 - i3 = 1
KVL for the mesh with i1 :
supermesh combining i2 and i3 :
-4i1 + 3i2+ 3i3 = 8
5i1= i2 – i3
How many meshes are there? 3
What is 5i1 in terms of mesh currents?
5i1= i2 – i3 i3= i2 – 5i1
8i1 - 3i2 – (i2 – 5i1)= 1
8i1 - 4i2 + 5i1 = 1 13i1 - 4i2 = 1
-4i1 + 3i2+ 3(i2 – 5i1) = 8
-19i1 + 6i2 = 8

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T6_Problem 1: Supermesh
Note: This is problem 48 on page 118, Figure 4.73 in the Ref 1 book (by Hayt)
 Find i1 and Power supplied by 1V:
Solving these two equations:
i1 = 19 A
P1V = (i1 * 1) = 19 W
13i1 - 4i2 = 1
-19i1 + 6i2 = 8
---- (2)
---- (1)
-38 i1 + 12 i2 = 8(1) * 2 
(2) * 3  39 i1 - 12 i2 = 3
i1 = 19 A
P1V = 19 W

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References
Ref 1 Ref 2