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750 ⏐⏐⏐ METHODS OF ANALYSIS AND SELECTED TOPICS (ac)
E 1
+
–
Z 1
I 1
I
–
E 2 +
I 2
Z 2
FIG. 17.13
Applying mesh analysis to a network with an
independent current source.
E 1
+
–
I
Z 1
I 1
kI
Z 2
E 2
+
FIG. 17.14
Applying mesh analysis to a network with a
current-controlled current source.
I 2
–
The result is two equations and two unknowns.
E 1 � I 1R 1 � R 2(I � I 2) � 0
R 2(I 2 � I 1) � mR 2(I 1 � I 2) � I 2R 3 � 0
Independent Current Sources For independent current sources,
the procedure is modified as follows:
1. Steps 1 and 2 are the same as those applied for independent
sources.
2. Step 3 is modified as follows: Treat each current source as an
open circuit (recall the supermesh designation of Chapter 8), and
write the mesh equations for each remaining independent path.
Then relate the chosen mesh currents to the dependent sources to
ensure that the unknowns of the final equations are limited simply
to the mesh currents.
3. Step 4 is as before.
EXAMPLE 17.7 Write the mesh currents for the network of Fig. 17.13
having an independent current source.
Solution:
Steps 1 and 2 are defined on Fig. 17.13.
Step 3: E1 � I1Z1 � E2 � I2Z2 � 0 (only remaining independent
path)
with I1 � I � I2 The result is two equations and two unknowns.
Dependent Current Sources For dependent current sources, the
procedure is modified as follows:
1. Steps 1 and 2 are the same as those applied for independent
sources.
2. Step 3 is modified as follows: The procedure is essentially the
same as that applied for independent current sources, except now
the dependent sources have to be defined in terms of the chosen
mesh currents to ensure that the final equations have only mesh
currents as the unknown quantities.
3. Step 4 is as before.
EXAMPLE 17.8 Write the mesh currents for the network of Fig. 17.14
having a dependent current source.
Solution:
Steps 1 and 2 are defined on Fig. 17.14.
Step 3: E1 � I1Z1 � I2Z2 � E2 � 0
and kI � I1 � I2 Now I � I1 so that kI1 � I1 � I2 or I2 � I1(1 � k)
The result is two equations and two unknowns.
N A