PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

244 Practical MATLAB® Applications for Engineers

or

SV I


RMS RMS*(10 0∠∠)( 2 53 13. )20 53 13∠.va

The power triangle for the circuit diagram of Figure 3.15 is shown in Figure 3.16.

R.3.48 Evaluate the active power P, apparent power S, the reactive power Q, and the PF,
if the impedance of a given circuit is Z = 7. 0 5 + j9.7 Ω and the voltage across it is
Vm = 60 V.

ANALYTICAL Solution

Zj

 705 97 705  97 

97

705

....tan22 1.

.

∠ 







Ω

Z = 12 ∠54° 

I

V

m Z




m^60

12

5A

VRMS = 0.707 * 60 = 42.42 V

IRMS = 0.707 * 5 = 3.535 A

Taking the current I as reference, the phasor diagram that relates the current I to the

voltage V is shown in Figure 3.17.

PF = cos(54°) = 0.588

sin(54°) = 0.809

then

S = 42.42 * 3.535 = 150 va

P = |S|c o s ( ) = (^150) * 0.588 = 88.1 W
S = 20 va
P = 12 W
QL = 16 var
 = 53.13°
FIGURE 3.16
Power triangle of the circuit in Figure 3.15.
V = 42.42 ∠ 54 °
I = 3.535 ∠ 0 °
 = 54°
FIGURE 3.17
Phasor diagram of R.3.48.