Question

if a wire of length l, cross-section A & resistance
r is melted & recast to half its length. calculate
the new residence
of
the wire
​

Answer 1

Answer:

Let, length of wire is l and area of cross section is A .

Given, it's resistance is r

so, r = rho l/A .....(1)

since, wire is melted and recast to half its length .

so, it's area of cross become double

such that , new length l' = l/2 and new area of cross section is A' = 2A

therefore , new resistance R is

R = rho l'/A'

=> R = rho l/2/2A

=> R = 1/4 × rho l/A

=> R = 1/4r (from 1)

hence, new resistance is 1/4 r

Explanation: