Question

If a wire of resistance R is melted and recast into a wire of 2/5th of its original length ,then find the resistance and resistivity of the new wire.

Answer 1

Explanation:

Answer

Correct option is

D

4

R

Resistance of wire R=

A

ρL

Also volume of wire V=AL

⟹ R=ρ

V

L

2

We get R∝L

2

(as volume of the wire remains the same when it is recasted)

Now the wire is melted and recasted to half of its length i.e. L

′

=

2

L

Thus new resistance of wire R

′

=R

L

2

(L

′

)

2

∴ R

′

=R

L

2

(L/2)

2

=

4

R