PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

242 Practical MATLAB® Applications for Engineers

R.3.45 Let us evaluate now the current i(t) of the parallel RLC circuit diagram shown in
Figure 3.13, assuming that its voltage is v(t) = Vm cos(ωt)V.

ANALYTICAL Solution

Since v(t) = Im cos(ωt), then the current i(t) can be determined by i(t) = |Y|Vm cos(ωt + θ),
where

Y

R

C

L



^1122













  

and










tan^1 ()^1

1

CL

R









R.3.46 Power analysis of electrical AC circuits is done by means of a right triangle called
the power triangle, where the active power is given by P = [IRMS]^2 R, the reactive
power by Q = VRMS IRMS sin(θ), and the apparent power by S = VRMS IRMS (recall
that IRMS is the complex conjugate of IRMS) (Figure 3.14). A summary of useful
power relations are given as follows:

Active Power PI V I R

V

R

RMS RMScos( ) (^) RMS^2 RMS VIRMS RMS
2
real()∗
Reactive Power QI V I X

V

X

RMS RMSsin( ) (^) RMS^2 XRMS VIRMS RMS
2
 imag()∗
Apparent Power SP jQ P Q QP

IZ

V

Z

RMS ZRMS VIRMS RMS





22 1

2

2

∠

()

tan

abs ∗

Power Factor PF

R

Z

P

S

cos( )

R.3.47 The following example is used to illustrate the construction of the power triangle
for the series circuit shown in Figure 3.15.

v(t) = Vm cos(ωt) R L C

i(t)

FIGURE 3.13
RLC parallel circuit diagram of R.3.45.