Question

A metal wire of circular cross-section has a
resistance R1. The wire is now stretched
without breaking so that its length is doubled
and the density is assumed to remain the same
If the resistance of the wire now becomes R2
then R2:R1​

Answer 1

As we know that, R

1

=ρ

a

l

=ρ

V

l

2

,

where l= length of wire, a= area of cross-section of the wire and V= volume of the wire.

So, R

1

∝l

2

⇒

R

2

R

1

=(

l

2

l

1

)

2

=(

2

1

)

2

⇒R

2

:R

1

=4:1