Question

A wire of resistivity rho is stretched to double of its length. What will be its new resistance and resistivity?

Answer 1

Answer:

4 times

Explanation:

According to the given question,

p' = p and l' = 2l

Initial

R = resistance and p = resistivity

l = length and A = Area

Final

R' = resistance and p' = resistivity

l' = length and A' = Area

Volume is constant before and after stretching,

• A×l = A'×l'

• A/A' = l'/l

Putting the values we get

• A/A' = 2l/l

• A/A' = 2

We know,

• R = pl/A----------1)

• R' = p'×l'/A' -------2)

Dividing both equations we get,

• R'/R = l' × A/ l× A'

• R'/R = 2×2

• R'/R = 4

• R' = 4R

So resistance will be 4 times.