Network Analysis and Synthesis, 1st Edition by Pearson

102 Network Analysis and Synthesis

The expression for the voltage and current in series R–L circuit is as follows:

vV t

iI

tI

V

=

=−

m

m

as lags

sin

sin( ),

w

wf

The power is the product of instantaneous values of the voltage and the current,

pvi

VtIt

VI tt

VI

=×

=×−

=−

=

mm

mm

mm

sinsin ()

[sin sin( )]

[c

wwf

wwf

1

2

2

1

2

oos cos( )]

co

sc

os

()

fwf

fw

f

−−

=− −

2

1

2

1

2

2

t

VI VI t

mm mm

The average power over a complete cycle is calculated as follows:

PVItdt

VI dt

av mm

mm

=−−

=

∫

1

2

1

2

2

1

2

1

2

0

2

p

fwfw

p

fw

p

[cos cos( )] ()

cos()

−

−−

∫∫

1

2

1

2

2

0

2

0

2

p

wfw

pp

VI tdt

mm

cos( )( )

Now, the second term is a cosine term whose average value over a complete cycle is zero.

Hence, the average power consumed is calculated as follo ...