Show that Irms = 0.707Io of an AC where symbols have their usual meaning
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Current i=
T
2i
o
t
Since, areas of i-t graph are equal but with opposite signs in first and second half cycle. So, net area is zero in full cycle.
Thus mean value of current is zero.
Mean value of square of current <i
2
>=
T
∫
0
T
i
2
dt
Or <i
2
>=
T
∫
0
T
(
T
2i
o
t)
2
dt
=
T
3
4i
o
2
∫
0
T
t
2
dt
Or <i
2
>=
T
3
4i
o
2
×
3
T
3
=
3
4i
o
2
Rms value of current, i
rms
=
<I
2
>
=
3
2
i
o
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