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.