Alternating Current Analysis 241
where
tan
1 ()^1
22
LC
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. ZT
b. VR, VL, VC, and I as phasors
ANALYTICAL Solution
Part a
ZT = 2 + j(6 − 10) = 2 – j 4 Ω
ZT 2422 ∠tan (^1 42 / )Ω
ZT = 4.46 ∠−63.4° Ω
Part b
I
V
ZT
530
446 634
112 30 634
∠
∠
∠
..
.( .)A
I = 1.12 ∠93.4° A
VR(.112 934∠∠∠. )*(..2 0) 224 934V
VL (.1 12 93 4∠∠ ∠. )*(). .6 90 6 72 183 4 V
VC(.1 12 93 4∠∠ ∠. )*().. 10 90 11 2 3 4V
V = 5∠ 30 °
I
XC = −j10
+ R = 2Ω XL = j6
−
FIGURE 3.12
Network of R.3.44.