Biomedical Engineering Reference
In-Depth Information
If one of the branches located between an essential node and the reference node contains
an independent or dependent voltage source, we do not write a node equation for this node
because the node voltage is known. This reduces the number of independent node equa-
tions by one and the amount of work in solving for the node voltages. In writing the node
equations for the other nodes, we write the value of the independent voltage source in those
equations. Consider Figure 9.20a and assume the voltage
V
2
results from an independent
voltage source of 5 V. Since the node voltage is known, we do not write a node-voltage
equation for node 2 in this case. When writing the node-voltage equation for node 1, the
I
A
¼
V
5
1
current
I
A
is written as
:
Example Problem 9.5 further illustrates this case.
R
EXAMPLE PROBLEM 9.5
Find
V
1
using the node-voltage method.
1/2
1/2
Ω
Ω
+
+
−
5 V
1/3
Ω
1/4
Ω
3 A
V
1
-
Solution
This circuit has two essential nodes, labeled 1 and 2 in the redrawn circuit that follows, with
the reference node and two node voltages,
V
2
, indicated. The node involving the 5 V volt-
age source has a known node voltage, and therefore we do not write a node equation for it.
V
1
and
1/2
Ω
1
1/2
Ω
2
+
+
+
−
5 V
1/3
Ω
1/4
Ω
3 A
V
1
V
2
−
−
