boylistad

754 ⏐⏐⏐ METHODS OF ANALYSIS AND SELECTED TOPICS (ac)
+
E 1
–
+
E 1
–
R 1
R 2
Z 2
X L3
FIG. 17.20
Example 17.11
I 1
Z 1
Z 4
X L1
X L2
Z 3
–
+
–
E 2
E 2
FIG. 17.21
Assigning the mesh currents and subscripted
impedances for the network of Fig. 17.20.
I 3
I 2
+
Solution: The network is redrawn in Fig. 17.19. Again note the
reduced complexity and increased clarity provided by the use of subscripted
impedances:
Z1 � R1 � j XL1 Z4 � R3 � j XC2 Z2 � R2 � j XL2 Z5 � R4 Z 3 � j X C1
and I 1(Z 1 � Z 2) � I 2Z 2 � E 1
I 2(Z 2 � Z 3 � Z 4) � I 1Z 2 � I 3Z 4 � 0
I 3(Z 4 � Z 5) � I 2Z 4 � E 2
or I 1(Z 1 � Z 2) � I 2(Z 2) � 0 � E 1
I 1Z 2 � I 2(Z 2 � Z 3 � Z 4) � I 3(Z 4) � 0
0 � I 2(Z 4) � I 3(Z 4 � Z 5) � E 2
+
E 1
–
Z 1
+ –
I 1
+
–
Z 2
–
+
Z 3
+ –
I 2
+
–
Z 4
–
+
Z 5
+ –
FIG. 17.19
Assigning the mesh currents and subscripted impedances for the network of
Fig. 17.18.
EXAMPLE 17.11 Using the format approach, write the mesh equations
for the network of Fig. 17.20.
Solution: The network is redrawn as shown in Fig. 17.21, where
Z1 � R1 � j XL Z 1 3 � j XL2 Z2 � R2 Z4 � j XL3 and I1(Z2 � Z4) � I2Z2 � I3Z4 � E1 I2(Z1 � Z2 � Z3) � I1Z2 � I3Z3 � 0
I3(Z3 � Z4) � I2Z3 � I1Z4 � E2 or
I 1(Z 2 � Z 4) � I 2Z 2 � I 3Z 4 � E 1
�I 1Z 2 � I 2(Z 1 � Z 2 � Z 3) � I 3Z 3 � 0
�I 1Z 4 � I 2Z 3 � I 3(Z 3 � Z 4) � E 2
Note the symmetry about the diagonal axis; that is, note the location of
�Z 2, �Z 4, and �Z 3 off the diagonal.
17.5 NODAL ANALYSIS
General Approach
Independent Sources Before examining the application of the
method to ac networks, a review of the appropriate sections on nodal
I 3
N A
–
E 2
+