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
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