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Chapter 3
Methods of Analysis
Example 3.3
For the circuit shown in Fig. 3.9, find the node voltages.
10 Q
Solution:
The supemode contains the 2-V source, nodes 1 and 2, and the 10-N
resistor. Applying KCL to the supernode as shown in Fig. 3.10(a) gives
2 = i, + iz + 7
2A
4Ως
(+ 7A
Expressing i, and iz in terms of the node voltages
U2
8 = 2v, + v2 + 28
Figure 3.9
For Example 3.3.
or
v2 = -20 - 2v,
(3.3.1)
To get the relationship between vị and v2, we apply KVL to the circuit
in Fig. 3.10(b). Going around the loop, we obtain
-u, - 2 + v2 = 0
U2 = v, + 2
(3.3.2)
From Eqs. (3.3.1) and (3.3.2), we write
Uz = v, + 2 = - 20 – 2v,
or
3v, = -22
v, = -7.333 V
and v2 = v, + 2 = -5.333 V. Note that the 10-2 resistor does not
make any difference because it is connected across the supernode.
2 A
7A
2 A (4
4Ω
) 7A
(b)
(a)
Figure 3.10
Applying: (a) KCL to the supernode, (b) KVL to the loop.
Practice Problem 3.3
Find v and i in the circuit of Fig. 3.11.
Answer: -400 mV, 2.8 A.
14 V
3Ω
2Ω3
Figure 3.11
For Practice Prob. 3.3.
H....(Càn u help me for this question?)
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