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Standard XII
Physics
NCERT
Question
Variation of voltage with time is shown in the above figure.
The rms voltage is found to be
N
√
2
3
V
. Find
N
.
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Solution
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V
2
r
m
s
=
1
4
∫
4
0
V
2
d
t
=
1
4
[
∫
1
0
4
2
d
t
+
∫
2
1
(
−
4
(
t
−
1
)
)
2
d
t
+
∫
3
2
4
2
d
t
+
∫
4
3
(
−
4
(
t
−
3
)
)
2
d
t
]
=
1
4
[
∫
1
0
16
d
t
+
∫
2
1
16
(
t
2
−
2
t
+
1
)
d
t
+
∫
3
2
16
d
t
+
∫
4
3
16
(
t
2
−
6
t
+
9
)
d
t
]
=
1
4
[
16
+
16
(
8
−
1
3
−
2
×
4
−
1
2
+
1
)
+
16
+
16
(
64
−
27
3
−
6
×
16
−
9
2
+
9
)
]
=
32
3
V
r
m
s
=
4
√
6
3
=
4
√
2
√
3
V
N=4
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