Question

A resistance wire is stretched to double its length so that its area of cross section is halved.how will its resistance change will any change be observe in its resistivity?justify your answer

Answer 1

As we know that,   [R=Resistance , L=Length , A=Area , ρ=Resistivty] 
R=ρL/A;
Now According to question, The wire is stretched and the Length becomes i.e, L'=2L and new Area of Cross section i.e, A'=A/2
Original resistance of wire => R=ρL/A....(1) 
New resistance => R'=ρL'/A'
R'=ρ(2L) / [A/2]
R'=ρ(4L)/A......(2)
Now dividing eq (2) by (1)
R'/R = [ρ(4L)/A] / [ρ(L)/A]
R'/R = 4
R' = 4*R 

As the resistivity depends on the material of the conductor , resistivity in given case will remain unchanged , as the material of wire did not undergo any change.

Answer 2

Okay let's start!

First let's go through some variables:

Wire 1:

Length = l

Area of cross-section = a

Wire 2 (stretched):

Length = 2*original = 2l

Area of cross-section = a/2

Know we know,

R= constant* l

________

a

Now resistance of new wire:

R2 = constant * 2l

_________

a/2

= constant*4l

_________

a

= 4* constant *l

_______

a

= 4R. (R= constant *l )

_______

a

therefore,

The new resistance will be 4 times the original one!

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