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JEE Main 30 June 2022 Shift 1 Solved Paper
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© examsnet.com
Question : 45
Total: 90
An electric cable of copper has just one wire of radius
9
mm
. Its resistance is
14
Ω
. If this single copper wire of the cable is replaced by seven identical well insulated copper wires each of radius
3
mm
connected in parallel, then the new resistance of the combination will be :
[30-Jun-2022-Shift-1]
9
Ω
18
Ω
28
Ω
126
Ω
Validate
Solution:
Initially, copper wire radius
(
r
1
)
=
9
mm
Resistance
(
R
)
=
14
Ω
We know,
R
=
ρ
L
A
=
ρ
L
π
r
1
2
=
14
Now this copper wire is replaced by 7 parallel copper wire of resistance
R
1
.
∴
Equivalent resistance of 7 parallel copper wire,
1
R
e
q
=
1
R
1
+
1
R
1
+
1
R
1
+
1
R
1
+
1
R
1
+
1
R
1
+
1
R
1
⇒
1
R
e
q
=
7
R
1
⇒
R
e
q
=
R
1
7
=
1
7
×
ρ
L
π
r
2
2
=
1
7
×
ρ
L
π
(
r
1
3
)
2
[
as
r
2
=
r
1
3
;
r
1
=
9
m
and
r
2
=
3
]
=
1
7
×
ρ
L
π
r
1
2
×
9
=
1
7
×
14
×
9
=
18
Ω
© examsnet.com
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