Question

Resistance of a wire is r ohms.the wire is stretched to double its length, and its radius is halfed then its resistance in ohms is

Answer 1

let the initial length and radius of the wire =l and r respectively

area, a= (pi)r^2

let resistance be R= rho l/a

now the final length and radius be = L and r1 respectively

L=2l

r1= r/2

area A=(pi) r1^2

= (pi)(r/2)^2

=a/4

resistance R1= rho*L/A

R1= rho* 2l/a/4

R1= 8. rho l/A

R1= 8R