A given piece of wire of length l radius r and resistance R is stretched uniformly to a wire of radius r / 2. The new resistance is (A) 16 R (B)4 R (C) R/4 (D) R/1
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12th
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Current Electricity
Electrical Resistance & Resistivity
A wire of radius r has re...
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Asked on January 17, 2020 by
Yashwant Potnuru
A wire of radius r has resistance R. If it is stretched to a radius r/2, its resistance becomes:
A
0.5 R
B
2 R
C
4 R
D
16 R
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ANSWER
As we know,
R=
A
ρL
..........(i)
If you stretch the wire till it's radius is halved the previous value, then it's length will increase 4 times to keep the volume constant.
So, new values are,
L
2
=4L
A
2
=
4
A
where, L and A are the values of original length and area
Resistivity remains the same as it depends upon the material of the wire.
So, the new resistance will be,
R
1
=
A
ρL
R
1
=
A/2
ρ4L
R
1
=
A
16ρL
R
1
=16R
Answer:
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