238
Practical MATLAB
® Applications for Engineers
Part b
V
I
Y
T
T
ϭ
ϭ
Њ
Њ
ϭ
Ϫ Њ
Ϫ
15 20
89 10
26 6
168
6 6
3
∠
∠
∠
*
.
.
I
V
R
R ϭ ϭ
Ϫ Њ
Њ
ϭ
Ϫ Њ
168
6 6
12 5 0
13 4
6 6
∠
∠
∠
.
.
.
.
I
V
X
C
C
ϭ
ϭ
Ϫ Њ
Ϫ Њ
ϭ
Њ
168
6 6
25
90
6 72 83 4
∠
∠
∠
.
.
.
R.3.39 Let us analyze now the RC series case. Evaluate the voltage v(t) of the series RC
circuit, shown in Figure 3.8, assuming that the current is given by
i(t) = I m cos(t)
then
v(t) = I m |Z|cos(t + )
where
Z = R –
j
___
C
Z
R
C
C R
C R
ϭ
ϩ
ϭ
Ϫ
ϭϪ
Ϫ
Ϫ
2
2
1
1
1
1
1

 

 

 

 

 

 
and
tan
tan
Clearly, in a series RC circuit the voltage lags the current by a phase angle
bounded by 0 ≤ θ ≤ (π/2).
R.3.40 Let us analyze the series LC circuit diagram shown in Figure 3.9, and assume that
the current is given by
i (t) = I m cos(t)
then the voltage
v(t) = v L (t) + v C (t) (KVL)
FIGURE 3.7
Network of R.3.38.
I T = 15 20°
I R
I C
R = 12.5Ω
X C = 25Ω
V
FIGURE 3.8
Network of R.3.39.
+ C –
i(t ) = I m cos (t )
v(t)
+ R –
–
+
CRC_47760_CH003.indd 238
CRC_47760_CH003.indd 238
7/23/2008 1:27:33 PM
7/23/2008 1:27:33 PM