Alternating Current Analysis 257
R.3.64 The superposition principle for the AC case follows closely to the DC case discussed
in Chapter 2, that is, in a linear network containing n sources (not necessarily with
the same frequencies) any network current or voltage is the algebraic sum of the
responses or contributions due to each of the n sources acting separately by forcing
all the remaining n – 1 sources to zero.
R.3.65 The circuit shown in Figure 3.34 uses the superposition principle to evaluate each
current (I 1 , I 2 , and I 3 ). Observe that one source is DC and the other is AC (with ω =
10 rad/s).
ANALYTICAL Solution
The circuit of Figure 3.34 is redrawn into the circuit shown in Figure 3.35, by setting
VB = 0 (short), and solving for all the currents contributed by the voltage source VA.
Note that because ω = 0, XL = jωL = 0 (short), then the currents IA1, IA2, and IA3 are
IA 1
10
2
5 A
IA 2 0 A
IA 3 5 A
VTH =
() 9
100
9
300
9
8
9
44
)7( * jj +j +
−
+ =+
ZL=^469 −j 98
ZTH=
9
8
9
(^44) +j
IL
FIGURE 3.33
Thevenin’s equivalent circuit of Figure 3.28.
VB = 4 cos(10t)υ
VA = 10 V
I 3
I 2
L = 100 mH
2 Ω
2 Ω
I 1
- −
−
FIGURE 3.34
Network of R.3.65.