PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

232 Practical MATLAB® Applications for Engineers

since T = 1/f, then

W

VI

R f


 RMS RMS (in joules)

R.3.22 The reactive power Q is defi ned as Q = A sin(θ) with units given by volt-ampere-
reactive (var)

Then,

Q

VImm




2









sin( )

or

Q = (VRMS IRMS)sin( ) = imaginary(VRMS IRMS*)

where θ is the phase angle between V and I.
The reactive power Q can be either inductive or capacitive. Then,

QVIL


RMS RMS IXVXL RMS L

2 2

QVIC


RMS RMS IXVXC RMS C

22

and the respective energies are

W

VI T

L

RMS RMS LI

2 

(^2) (in joules)

W

VI T

C

RMS RMS CV

2 

(^2) (in joules)
R.3.23 The complex or apparent power S is defi ned as
SV I
RMS RMS with units in volt-ampere ( )va

SI Z

V

Z


  RMS^2 RMS PjQ absV IRMS RMS

2

()*

(Recall that * denotes the complex conjugate of IRMS.)

R.3.24 The PF is defi ned by

PF = cos( ) = P/S = R/Z

R.3.25 Observe that if the current through a resistance R is

iR(t) = Im sin(t)

Its voltage drop is then

vR(t) = RIm sin(t) = Vm sin(t)

where Vm = RIm.