Question

if radius of wire is halfved find the new resistance

Answer 1

Hello

When we change the area of cross-section of a wire its length changes in such a way that the volume of the wire remains constant.

Let, A and L be the initial area of cross-section and length of the wire.

The resistance initially is, R = ρL/A

When the area of cross-section is halved, then,

Volume of the wire = AL = (A/2)(L/)

[L/ is the new length]

Thus, L/ = 2L

So, the new resistance is,

R/ = ρL//(2A) = ρ(2L)/(A/2) = 4 ρL/A = 4R

Thus, resistance becomes 4 times.

Thank you !