PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

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.