Since,  i2
m and R are constants,
2
sin2
m
p
i R
ωt
=
<
>
[7 5(b)]
Using the trigonometric identity, sin2 wt =
1/2 (1– cos 2wt), we have < sin2 wt > = (1/2) (1– < cos 2wt >)
and since < cos2wt > = 0**, we have,
2
1
sin
2
ωt
<
> =
Thus,
212
m
p
i R
=
[7 5(c)]
To express ac power in the same form as dc power
(P = I2R), a special value of current is defined and used It is called, root mean square (rms) or effective current
(Fig