Question

A given wire of resistance 1 2 is stretched to double
its length. What will be its new resistance ?​

Answer 1

Answer:

thanks for free points

Answer 2

Given: a wire of resistance 1Ωis stretched  to double its length.

To find the new resistance

Solution:

Here,

R=1Ω,Length=L,Cross sectional area, CSA=A

The formula used is,

R=ρAL​⟹ρAL​=1..........(i)

The new length, L′=2L

And new CSA = A′

So we have,

Volume of the wire= AL

Now after the act of stretching the volume remains constant.

Therefore, AL=A′L′

⟹AL=2LA′⟹A′=2A​

Now the new resistance of the wire becomes

Rnew​=ρA′L′​⟹Rnew​=ρ2A​2L​⟹Rnew​=4ρAL​

Rnew​=4×1 by using equation (i)

Therefore the new resistance is 4Ω