Direct Current and Transient Analysis
213
The ∆-to-Y transformation equations are
R
R R
R
R
R
A ϭ
ϩ ϩ
1
2
1
2
3
*
R
R R
R
R
R
B ϭ
ϩ ϩ
1
3
1
2
3
*
R
R R
R
R
R
C ϭ
ϩ ϩ
2
3
1
2
3
*
Calculate the voltage V XY 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 i C of P.2.19.
t (seconds)
5
0
1 mA
i C
FIGURE 2.116
Voltage v L of P.2.20.
t (seconds)
0
1 V
v L
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 R A , R B , and R C 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.
CRC_47760_CH002.indd 213
CRC_47760_CH002.indd 213
7/23/2008 1:39:03 PM
7/23/2008 1:39:03 PM