Download Problem 3.15 Use the supernode concept to find the current Ix in the

Problem 3.15
Fig. P3.15.
Use the supernode concept to find the current Ix in the circuit of
supernode
6V
+
V1
2A
V2
0.5 Ω
V3
_
Ix
4A
0.5 Ω
0.5 Ω
Figure P3.15: Circuit for Problem 3.15.
Solution: The presence of a voltage source between designated nodes 1 and 2 makes
the combination of nodes 1 and 2 a supernode. Hence,
V2 V2 −V3
V1
−2+
+
= 0.
0.5
0.5
0.5
(1)
V3 −V2
− 4 + 2 = 0,
0.5
(2)
V2 −V1 = 6.
(3)
For node 3,
and the auxiliary equation is
Combining the three equations leads to:
V1 = −2 V,
V2 = 4 V,
V3 = 5 V.
Hence,
Ix =
V2
4
=
= 8 A.
0.5 0.5
c
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