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Question

A wire of radius r has resistance R. If it is stretched to a wire of radius r2, then the resistance becomes

A
2R
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B
4R
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C
16R
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D
zero
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Solution

The correct option is C 16R
Resistance of a conducting wire:
R=ρlA...(i)

As the volume of the wire remains constant.
Vi=Vf
πr21l1=πr22l2
[l2l1]=[r1r2]2=⎢ ⎢rr2⎥ ⎥2=4
A1A2=πr21πr22=4

Now, from equatuion (i)
R2R1=[l2l1][A1A2]

R2R1=[41][4]=16

R2=16R

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