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posted by  Altima on 11/3/2009 6:29:33 AM  |  status: Closed  |  Earned Karma: 0

What's i1, i2, and i3 by using mesh analysis?

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Electrical Engineering Fundamentals of Electric Circuits (4th) by Alexander, Sadiku 3 52 11/4/2009 at 4:00:00 PM
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posted by Shree_vani(MNK) on 11/3/2009 12:01:02 PM  |  status: Live
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Response Details:
Applying KVL to loop 1
12 = I1 (2+4) - I2(2) -I3(4)
6I1 - 2I2 - 4I3 = 12 ------- (1)
But
I3 - I2 = 3
I3 = 3 + I2
Substituting in (1)
6I1 - 2I2 - 4(3-I2 ) = 12
6I1 + 2I2 - 12 = 12
6I1 + 2I2  = 24 --------- (2)
Applying KVL to the supermesh
12 = 8I2 +2Vo
But
Vo = 2(I1 - I2)
12 = 8I2 + 2[2(I1 - I2)]
12 = 8I2 + 4I1 - 4I2
4I1 + 4I2 = 12
I1 + I2 = 3 ---------- (2)
Solving (1) and (2)
6I1 + 2I2  = 24
2I1 + 2I2  = 6
----------------
4I1 = 18
I1 = 4.5A
I2 = 3 - I1 = 3 - 4.5
I2 = -1.5A
Vo = 2[4.5-(-1.5)]
Vo = 12V
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