A wire of mass `10g` radius `1mm` is compressed to its length by `10 %` Calculate percentage change in its resistance.

Answer

`19%`

Explanation

Let `l`, A and B be the length area of cross-section and density of wire of mass m then
`m = A l d or A = m//ld`
Resistance `R = (rhol)/(A) = (rhol)/(m//ld) = (rhol^(2)d)/(m)` i.e. `R prop l^(2)`
`:. (R')/(R ) = (l'^(2))/(l^(2)) = ((1 - (10)/(100) l )^(2))/(l^(2)) = (1 - (1)/(10))^(2) = (81)/(100) = 0.81`
`R = 0.81 R`
% decrease in resistance `= ((R - R')/(R)) xx 100`
`= ((R - 0.81R)/(R )) xx 100 = 19%`