PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Alternating Current Analysis 229

Note that

AVm t dt A dt A T

TT

sin() 

 0 ,

0

22

∫∫ (^0)
and
V t dt V t dt

V

dt

V

T

m

T

m

T

mm

22

0

2

0

22

0

1

2

1

2

2

22

∫∫sin ()  cos( )









TT

∫

Then

V

T

AT

V

T

A

V

A

V

RMS

m

mm






1

2

2 2

2

2

2

2

2

2

















Note that

V

m VVmRMSAC

2

∗0 707. 

Then

VAVRMS

^22 RMS AC ,()forvtAVtmsin()

If

v( )tAV
mm11 2 2sin( tV) sin( t V)
mnnsin( t)

then

VA

V

RMS mk AV

k

n

RMS

n

2

2

1

22

(^21)
∑∑k
k
for k AC sources and one DC source (A).
R.3.12 The power dissipated by a resistor R, having a current i(t) over an interval of time
[t 1 , t 2 ], is given by

P

tt

Ri t dt

t

t






1

21

2

1

2

∫ ()