CHAP. 4]

63

ANALYSIS METHODS

4.46

Loop Current Method. In the circuit of Fig. 4-51 write two loop equations using I1 and I2 as loop currents, then ﬁnd the currents and node voltages.   Loop 1: 4I1  I2 ¼ 2 I1 ¼ 1 A; I2 ¼ 2 A Ans: from which, Loop 2: I1 þ 2I2 ¼ 3 VA ¼ 9 V; VB ¼ 5 V; VC ¼ 2 V

4.47

Superposition. In the circuit of Fig. 4-51 ﬁnd the contribution of each source to VA , VB , VC , and show that they add up to values found in Problem 4.45.

Ans.

4.48

From the current source:

VA ¼ 7:429

VB ¼ 3:143

VC ¼ 1:429

From the voltage source:

VA ¼ 1:571

VB ¼ 1:857

VC ¼ 0:571

From both sources:

VA ¼ 9

VB ¼ 5

VC ¼ 2

(all in V)

Verify that the circuit of Fig. 4-52(a) is equivalent to the circuit of Fig. 4-51. Ans. Move node B in Fig. 4-51 to the outside of the loop.

Fig. 4-52

4.49

Find VA and VB in the circuit of Fig. 4-52(b).

4.50

Show that the three terminal circuits enclosed in the dashed boundaries of Fig. 4-52(a) and (b) are equivalent (i.e., in terms of their relation to other circuits). Hint: Use the linearity and superposition properties, along with the results of Problems 4.48 and 4.49.

Ans:

VA ¼ 9; VB ¼ 5, both in V

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An