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JEE Advanced 2017 Paper 2
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© examsnet.com
Question : 12
Total: 54
The instantaneous voltages at three terminals marked X, Y and Z are given by
V
X
=
V
0
s
i
n
ω
t
V
Y
=
V
0
s
i
n
(
ω
t
+
2
π
3
)
and
V
Z
=
V
0
s
i
n
(
ω
t
+
4
π
3
)
An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points X and Y and then between Y and Z. The reading(s) of the voltmeter will be
V
Y
Z
r
m
s
=
V
0
√
1
2
V
Y
Z
r
m
s
=
V
0
√
3
2
V
Y
Z
r
m
s
=
V
0
independent of the choice of the two terminals
Validate
Solution:
If connected across X and Y :
V
X
Y
=
V
X
−
V
Y
=
V
0
s
i
n
(
ω
t
+
2
π
3
)
=
V
0
[
s
i
n
ω
t
−
s
i
n
ω
t
c
o
s
ω
t
2
π
3
−
c
o
s
ω
t
s
i
n
2
π
3
]
=
V
0
[
s
i
n
ω
t
+
1
2
s
i
n
ω
t
−
√
3
2
c
o
s
ω
t
]
=
√
3
V
0
[
√
3
2
s
i
n
ω
t
−
1
2
c
o
s
ω
t
]
=
√
3
V
0
s
i
n
n
(
ω
t
−
π
3
)
∴
V
X
Y
r
m
s
=
√
3
V
0
√
2
=
√
3
2
V
0
If connected across X and Z.
V
X
Z
=
V
X
−
V
Z
=
V
0
s
i
n
ω
t
−
V
0
s
i
n
(
ω
t
+
4
π
3
)
=
√
3
V
0
s
i
n
(
ω
+
π
6
)
If connected across Y and Z
V
Y
Z
=
V
Y
−
V
Z
=
V
0
s
i
n
(
ω
t
+
2
π
3
)
−
V
0
s
i
n
(
ω
t
+
4
π
3
)
=
√
3
V
0
c
o
s
ω
t
∴
V
r
m
s
is same if the voltmeter is connected across an
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