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CHAP. 4]

61

ANALYSIS METHODS

Fig. 4-47 4.36

Node Voltage Method. In the circuit of Fig. 4-48 write three node equations for nodes A, B, and C, with node D as the reference, and find the node voltages. 8 5VA  2VB  3VC ¼ 30 > < Node A: Ans: from which VA ¼ 17; VB ¼ 9; VC ¼ 12:33 all in V Node B: VA þ 6VB  3VC ¼ 0 > : Node C: VA  2VB þ 3VC ¼ 2

Fig. 4-48 4.37

In the circuit of Fig. 4-48 note that the current through the 3- resistor is 3 A giving rise to VB ¼ 9 V. Apply KVL around the mesh on the upper part of the circuit to find current I coming out of the voltage source, then find VA and VC . Ans: I ¼ 1=3 A; VA ¼ 17 V; VC ¼ 37=3 V

4.38

Superposition. In the circuit of Fig. 4-48 find contribution of each source to VA , VB , VC , and show that they add up to values found in Problems 4.36 and 4.37.

Ans.

Contribution of the voltage source:

VA ¼ 3

VB ¼ 0

VC ¼ 1

Contribution of the 1 A current source:

VA ¼ 6

VB ¼ 3

VC ¼ 4

Contribution of the 2 A current source:

VA ¼ 8

VB ¼ 6

VC ¼ 28=3

Contribution of all sources:

VA ¼ 17

VB ¼ 9

VC ¼ 37=3

(All in V)

4.39

In the circuit of Fig. 4-48 remove the 2-A current source and then find the voltage Vo:c: between the opencircuited nodes C and D. Ans: Vo:c: ¼ 3 V

4.40

Use the values for VC and Vo:c: obtained in Problems 4.36 and 4.39 to find the The´venin equivalent of the circuit of Fig. 4-48 seen by the 2-A current source. Ans: VTh ¼ 3 V; RTh ¼ 14=3 

4.41

In the circuit of Fig. 4-48 remove the 2-A current source and set the other two sources to zero, reducing the circuit to a source-free resistive circuit. Find R, the equivalent resistance seen from terminals CD, and note that the answer is equal to the The´venin resistance obtained in Problem 4.40. Ans: R ¼ 14=3 

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