PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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.