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Principles of Analog Electronics
book

Principles of Analog Electronics

by Giovanni Saggio
January 2014
Intermediate to advanced content levelIntermediate to advanced
567 pages
23h 13m
English
CRC Press
Content preview from Principles of Analog Electronics
Principles of Analog Electronics
148
EXERCISE 4
Demonstrate that the power dissipated by a resistor of resistance R,
across which there is a sinusoidal voltage
sinvwtV wt
M
))
((
=
, is obtained
by the RMS values of current
I
RMS
and voltage
V
RMS
multiplied together.
ANSWER
The instantaneous power is given by
2
2
pvi
v
R
Ri== =
and in a cycle the real power corresponds to
11 1
sin
2
2sin
2
1cos 2
00
2
0
2
2
0
2
2
0
P
T
pdt
T
Ri dt
T
RI wt dt
RI
T
wt dt
RI
T
wt dt
TT T
M
M
T
M
T
∫∫
∫∫
[]
[]
)) )
(((
==
===−
11 1
sin
2
2sin
2
1cos 2
00
2
0
2
2
0
2
2
0
P
T
pdt
T
Ri dt
T
RI wt dt
RI
T
wt dt
RI
T
wt dt
TT T
M
M
T
M
T
∫∫ ∫∫
[] []
))
)
((
(
== ==
=−
with
cos2 12sin
2
xx
)
(
)
(
=−
. Solving, we obtain
2
2
PR
I
M
=
but the RMS value of a sinusoidal waveform is
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Publisher Resources

ISBN: 9781466582026