PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Direct Current and Transient Analysis 213

The ∆-to-Y transformation equations are

R

RR

A RRR



12

123

*

R

RR

B RRR



13

123

*

R

RR

C RRR



23

123

*

Calculate the voltage VXY in the circuit shown in Figure 2.114 by

a. Applying the ∆-to-Y transformation to loop I only

b. Applying the ∆-to-Y transformation to loop II only

c. Using loop equations (with no transformations)

d. Applying Thevenin’s theorem (assuming that the load is R = 30)

FIGURE 2.115

Current iC of P.2.19.

t (seconds)

0 5

1 mA

iC

FIGURE 2.116

Volt age vL of P.2.20.

t (seconds)

0

1 V

vL

e. Using node equations (with no transformations)

f. Applying Norton’s theorem (assuming that the load is R = 30)

Assume that all the resistors are given in ohms.

P.2.18 From the equations for RA, RB, and RC defi ned in P.2.17, obtain expressions for R 1 ,

R 2 , and R 3 for the Y-to-∆ transformations by hand and by using MATLAB symbolic

techniques.