Page 73 - Schaum's Outline of Theory and Problems of Electric Circuits

ANALYSIS METHODS
62
4.42 Find The ´ venin equivalent of the circuit of Fig. 4-49 seen from terminals AB. [CHAP. 4
ans: V Th ¼ 12 V; R Th 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 I 1 , I 2 , and I 3 . Then find
the currents.
8
> Loop 1: 4I 1 þ 2I 2 þ I 3 ¼ 3
<
Ans: Loop 2: 2I 1 þ 5I 2 I 3 ¼ 2 From which I 1 ¼ 32=51; I 2 ¼ 9=51; I 3 ¼ 7=51 all in A
>
:
Loop 3: I 1 þ 2I 2 þ 2I 3 ¼ 0
4.44 Superposition. In the circuit of Fig. 4-50 find the contribution of each source to I 1 , I 2 , I 3 , and show that
they add up to values found in Problem 4.43.
From the source on the left: I 1 ¼ 36=51 I 2 ¼ 9=51 I 3 ¼ 27=51
Ans. From the source on the right: I 1 ¼ 4=51 I 2 ¼ 18=51 I 3 ¼ 20=51 (All in A)
From both sources: I 1 ¼ 32=51 I 2 ¼ 9=51 I 3 ¼ 7=51

4.45 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
8
> Node A: 9V A 7V B 2V C ¼ 42
<
Ans: Node B: 3V A þ 8V B 2V C ¼ 9 From which V A ¼ 9; V B ¼ 5; V C ¼ 2 all in V
>
:
Node C: 3V A 7V B þ 31V C ¼ 0