Biomedical Engineering Reference
In-Depth Information
EXAMPLE PROBLEM 9.7
For the following circuit, find
V
3
.
1/5
Ω
1/4
Ω
+
1 V
2 A
1/2
Ω
1/3
Ω
1 A
1/2
Ω
V
3
-
Solution
The circuit has three essential nodes, two of which are connected to an independent voltage
source and form a supernode. We label the essential nodes as 1, 2, and 3 in the redrawn circuit,
with the reference node at the bottom of the circuit and three node voltages,
V
1
,
V
2
, and
V
3
as indi-
cated.
1/5
Ω
1
2
3
1/4
Ω
+
+
+
1 V
2 A
1/2
Ω
V
1
1/3
Ω
1 A
V
2
1/2
Ω
V
3
-
-
-
Summing the currents leaving node 1 gives
2
þ
2
V
1
þ
5
ð
V
1
V
3
Þ þ
4
ð
V
1
V
2
Þ ¼
0
Simplifying gives
11
V
1
4
V
2
5
V
3
¼
2
