Question

a wire of resistivity p is stretched to double its length. why will be its new resistance

Answer 1

The Resistivity of the wire will not change with the change in length. Resistivity is a property of the wire, it doesn't depend upon it's length or cross-sectional area. However, If you are asking about Resistance, it willincrease to 4 times it's initial value.

Answer 2

By the formula R=pl/A

where R=resistance

p=resistivity

l=length

A=cross sectional area

We can say that R is directly proportional to length

Thus the resistance will increase by a factor of 4.

Now why 4 why not 2 ??

Because with change in length its area will also change .

initial area=pi*r²l

final area=pi*R²(2l) (new length=2l)

we get r=R/√2

new area will be 1/2 of initial area

Now putting in the equation

R=p(2l)*2/A, R=4pl/A

Thus Rnew=4Rold