Question

What will be the effect on the resistance of a wire if its radius is reduced to 1/3 of its initial value.​

Answer 1

We know that resistance is given by

$R=\rho \frac{l}{A} \\hence \:as \:result \: of \:indirect\: proportionality\:\\if\:radius \:decreases\:i.e,\:area\:decreases\:resistance \: increases$

area becomes 1/9 times original as area is given by

A=πr^2

so dur to inverse proportionality resistance becomes 9 times

$R1/R2=A/9 \: \div \; A\\R2=9R1$