Question

A piece of wire is redrawn by pulling it until its length is doubled compare the new resistance with the original value

Answer 1

R = ¶L/A

If

L' =2L then

A'=A/2

So

R'= ¶2L/ A/2

R'= 4¶L/A

R'= 4 R

On comparing

R'/R = 4R /R

= 4: 1

Answer 2

A piece of wire is redrawn by pulling it until its length is doubled. Compare the new resistance with the original value.

Volume of the material of wire remains same. So, when length is doubled its area of cross-section will get halfed.

So, if l & a are the original length & area of cross-section of the wire,

0riginal value of Resistance,

R = p × l / a

New value of Resistance,

R' = p × 2l / a/2

  = p l/a × 4

  = 4R ...