Practice problem 3.1: Find the voltages at the three nonreference nodes in the circult Figure below. 41 Answer: Vi = 80 V, v2 =-64 V, v3 = 156 V. 1 し -> 10 A 40 I3 1 ww

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If we need the currents, we can easily cal
= 3.333A
i = 5 A, iz = 1-2 = -1.6667 A, iz =
6. 666A, i4 = 10 A, iz =2 =
%3D
%3D
The foct that ia is negative shows that the current flows in the direction opposite to the one
assumed.
Practice problem 3.1: Find the voltages at the three nonreference nodes in the circuit of
Figure below.
Answer: V1 = 80 V, v2 =-64 V, v3 = 156 V.
41,
2
1
10 A
I3
3. NODAL ANALYSIS WITH VOLTAGE SOURCES
W w. consider how voltage sources affect nodal analysis, We use the
3.4 for illustration. Consider the following two possibilities.
van n Fig.
CASE 1: If a voltage source is connected between the reference node and a nonreference
node, we simply set the voltage at the nonreference node equal to the voltage of the voltage
source. In Fig. 3.4, for example,
V1 = 10 V
(3.10)
Thus our analysis is somewhat simplified by this knowledge of the voltage at this node.
ạl engme
Supernode
10 V
Biom
Figure 3.4 A circuit with a supernode.
CASE 2: If the voltage source (dependent or independent) is connected between two
nonreference nodes, the two nonreference nodes form a generalized node or supernode; we
apply both KCL and KVL to determine the node voltages.
A supernode is formed by enclosing a (dependent or independent) voltage source connected
between two nonreference nodes and any elements connected in parallel with it.
ww.
Transcribed Image Text:If we need the currents, we can easily cal = 3.333A i = 5 A, iz = 1-2 = -1.6667 A, iz = 6. 666A, i4 = 10 A, iz =2 = %3D %3D The foct that ia is negative shows that the current flows in the direction opposite to the one assumed. Practice problem 3.1: Find the voltages at the three nonreference nodes in the circuit of Figure below. Answer: V1 = 80 V, v2 =-64 V, v3 = 156 V. 41, 2 1 10 A I3 3. NODAL ANALYSIS WITH VOLTAGE SOURCES W w. consider how voltage sources affect nodal analysis, We use the 3.4 for illustration. Consider the following two possibilities. van n Fig. CASE 1: If a voltage source is connected between the reference node and a nonreference node, we simply set the voltage at the nonreference node equal to the voltage of the voltage source. In Fig. 3.4, for example, V1 = 10 V (3.10) Thus our analysis is somewhat simplified by this knowledge of the voltage at this node. ạl engme Supernode 10 V Biom Figure 3.4 A circuit with a supernode. CASE 2: If the voltage source (dependent or independent) is connected between two nonreference nodes, the two nonreference nodes form a generalized node or supernode; we apply both KCL and KVL to determine the node voltages. A supernode is formed by enclosing a (dependent or independent) voltage source connected between two nonreference nodes and any elements connected in parallel with it. ww.
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