Question

A copper wire is cut into two segment in the ratio of 2:3 in respect of length. find the ratio of resistance and resistivity of two segment.

Answer 1

their resistance will be in the same ratio of the length in which they are cut bcoz Resistance is directly proportional to length of the conductor
so the ratio of resistance of the two segments will be 2:3
but resistivity is the materialistic property of a substance and doesn't depend on the size of conductor so the ratio of resistivity of the two segments will be1:1

Answer 2

As the formula of resistance R is = (¿ × L)/A
so ,
so let's take after cutting the copper wire the length of first Regiment become 2 X and the length of another segment became 3x.

so now by using the resistance formula

R1 = (¿ × 2x)/A
R2 = ( ¿× 3x)/A

show the ratio of resistance R1 to R2

R1/R2= (¿× 2x /A)/(¿× 3x/A)

=( ¿×2x/A)×(A/3x× ¿)

R1/R2 = 2/3

R1:R2 = 2:3

and as
resistivity is also inversely proportional to the length of wire.
i.e.
¿= R×A/L

¿ = 1/ L

ratio will be also inversly
which be
¿1 / ¿2 = 3/2