Alternating Current Analysis
241
where
ϭ
Ϫ ր
Ϫ Յ Յϩ
Ϫ
tan
(
)
1
1
2
2
L
C
R

 

 
for
Clearly,
a. If ωL > 1/ωC, then θ is positive, meaning that the voltage leads the current and the
equivalent circuit is RL.
b. If on the other hand, ωL < 1/ωC, then θ is negative, meaning that the voltage lags the
current and the equivalent circuit is RC.
R.3.44 For example, evaluate for the circuit diagram shown in Figure 3.12 the following:
a. Z T
b. V R , V L , V C , and I as phasors
ANALYTICAL Solution
Part a
Z T = 2 + j(6 − 10) = 2 – j4 Ω
Z T ϭ
ϩ
Ϫ
Ϫ
2
4
4 2
2
2
1
∠ tan ( / ) Ω
Z T = 4.46 ∠−63.4° Ω
Part b
I
V
Z T
ϭ
ϭ
Њ
Ϫ
Њ
ϭ
Њϩ
Њ
5 30
4 46
63 4
1 12 30
63 4
∠
∠
∠
.
.
.
(
. )A
I = 1.12 ∠93.4° A
V R ϭ
Њ
Њϭ
Њ
( .
. ) * (
.
.
1 12 93 4
2 0
2 24 93 4
∠
∠
∠
)
V
V L ϭ
Њ
Њϭ
Њ
( .
. ) * (
)
.
.
1 12 93 4
6 90
6 72 183 4
∠
∠
∠
V
V C ϭ
Њ
Ϫ Њϭ
Њ
( .
. ) * (
)
.
.
1 12 93 4
10
90
11 2 3 4
∠
∠
∠
V
V = 5∠30°
I
X C = −j10
R = 2Ω
X L = j6
+
−
FIGURE 3.12
Network of R.3.44.
CRC_47760_CH003.indd 241
CRC_47760_CH003.indd 241
7/23/2008 1:27:34 PM
7/23/2008 1:27:34 PM