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326 ⏐⏐⏐ NETWORK THEOREMS
I
6 mA
R 1
R 3
6 k�
14 k�
FIG. 9.16
Example 9.4.
9 V R 2
E
R 4
I 2
12 k�
35 k�
Obviously, x � y � z, or 24 W � 216 W � 384 W, and superposition
does not hold. However, for a linear relationship, such as that
between the voltage and current of the fixed-type 6-� resistor, superposition
can be applied, as demonstrated by the graph of Fig. 9.15,
where a � b � c, or 2 A � 6 A � 8 A.
b
This results because 2 A � 6 A � 8 A, but
(2 A) 2 � (6 A) 2 � (8 A) 2
As mentioned previously, the superposition principle is not applicable
to power effects since power is proportional to the square of the current
or voltage (I 2 R or V 2 /R).
Figure 9.14 is a plot of the power delivered to the 6-� resistor versus
current.
400
300
200
P (W)
FIG. 9.14
Plotting the power delivered to the 6-� resistor versus current through the
resistor.
10
9
8
7
6
5
4
3
2
a 1
0
z
100 y
Nonlinear curve
x{
0 1 2 3 4 5 6 7 8 I6Ω (A)
I (A)
c
Linear curve
Th
12 24 36 48 V 6Ω (V)
FIG. 9.15
Plotting I versus V for the 6-� resistor.
EXAMPLE 9.4 Using the principle of superposition, find the current
I2 through the 12-k� resistor of Fig. 9.16.
Solution: Considering the effect of the 6-mA current source (Fig.
9.17):