A wire of length L and resistance R is stretched so that its length is doubled and the area of cross-section is halved. How will its:
(a) resistance change?
(b) resistivity change?
Justify your answer in each case.

Explanation

(a) Here, length is doubled and area of cross-section is halved. Thus, a wire of length l and area of cross-section A becomes a wire of length 2l and area of cross-section `(A)/(2)`
Using `R= rho (l)/(A)`
New resistance `R_(l)=rho (2l)/(A//2)`
`R_(l) = (4rhol)/(A)= 4 xx R`
i.e., resistance becomes four times
(b) Resistivity of a substance does not depend on its length or area of cross-section. It depends on the nature of the material and temperature. Hence there is no change.