
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
RMS
and voltage
RMS
multiplied together.
ANSWER
The instantaneous power is given by
2
2
pvi
v
Ri== =
and in a cycle the real power corresponds to
11 1
sin
2
2sin
2
2
2
2
T
pdt
T
Ri dt
T
RI wt dt
RI
T
wt dt
TT T
M
M
T
∫∫
[]
==
2
1cos 2
2
0
P
T
pdt
T
Ri dt
T
RI wt dt
RI
T
wt dt
RI
T
wt dt
M
T
∫
)
(
=−
with
2
. Solving, we obtain
2
PR
I
M
=
but the RMS value of a sinusoidal waveform is