62

4.42

ANALYSIS METHODS

[CHAP. 4

Find The´venin equivalent of the circuit of Fig. 4-49 seen from terminals AB. ans: VTh ¼ 12 V; RTh ¼ 17 

Fig. 4-49 Fig. 4-50

4.43

Loop Current Method. In the circuit of Fig. 4-50 write three loop equations using I1 , I2 , and I3 . the currents. 8 4I1 þ 2I2 þ I3 ¼ 3 > < Loop 1: Loop 2: 2I1 þ 5I2  I3 ¼ 2 From which I1 ¼ 32=51; I2 ¼ 9=51; I3 ¼ 7=51 all in A Ans: > : Loop 3: I1 þ 2I2 þ 2I3 ¼ 0

4.44

Superposition. In the circuit of Fig. 4-50 ﬁnd the contribution of each source to I1 , I2 , I3 , and show that they add up to values found in Problem 4.43.

Ans.

4.45

From the source on the left:

I1 ¼ 36=51

I2 ¼ 9=51

I3 ¼ 27=51

From the source on the right:

I1 ¼ 4=51

I2 ¼ 18=51

I3 ¼ 20=51

From both sources:

I1 ¼ 32=51

I2 ¼ 9=51

I3 ¼ 7=51

Then ﬁnd

(All in A)

Node Voltage Method. In the circuit of Fig. 4-51 write three node equations for nodes A, B, and C, with node D as the reference, and ﬁnd the node voltages.

Fig. 4-51

Ans:

8 > < Node A: Node B: > : Node C:

9VA  7VB 

2VC ¼ 42

3VA þ 8VB  2VC ¼ 9 3VA  7VB þ 31VC ¼ 0

From which VA ¼ 9; VB ¼ 5; VC ¼ 2 all in V

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
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