PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

248 Practical MATLAB® Applications for Engineers

for DC circuits can easily be extended to include AC circuits. To use the mesh analy-

sis technique it is required that all the forcing functions be sinusoidals (either sines

or cosines) having the same frequency. The mesh equations are then expressed in

terms of phasor currents, voltages, and impedances. The passive elements such as

resistances, capacitances, and inductances can be combined using the standard

complex algebra, presented in Chapter 6 of the book titled Practical MATLAB® Basics

for Engineers.

R.3.57 The circuit diagram shown in Figure 3.21 is used to illustrate the general approach
in the construction of the loop equations. First, we recognize the existence of three
independent loops, then loop currents are assigned to each loop, thus we write the
three independent loop equations and fi nally solve for each unknown loop current
(I 1 , I 2 , and I 3 ), as illustrated as follows:

ANALYTICAL Solution

Observe that ω = 10 rad/s (from the forcing function), the three loop currents are
labeled assuming a clockwise direction, then all the network reactances are evaluated
as indicated as follows:

X

jC j

C

 j





11

10 1 20

2

 ()( )

XjLjL

 ()10 
j

1

2

5

The circuit of Figure 3.21 is then redrawn with the network elements, replaced by their

respective impedances and the source voltage, by a phasor, as shown in Figure 3.22.

The three independent loop equations are then given by

(8 − j2)I 1 − 3I 2 + 0I 3 = 10

−3I 1 + (8 + j5)I 2 − 5I 3 = 0

+0I 1 − 5I 2 + (7 − j2)I 3 = 0

I 1 I 2 I 3

3 Ω 5 Ω

2 Ω

1/20 F

5 Ω 1/20 F 1/2 H

+

v 1 (t) = 10 sin10t V

FIGURE 3.21
Network of R.3.57.