`1kg` piece of copper is drawn into a wire `1mm` thick and another piece into a wire `2mm` thick. Compare the resistance of these wires.

Answer

`16: 1`

Explanation

Let `d` be the meterial of copper wire Let `l_(1) and l_(2)` be length of copper wires of diameter `1mm and 2 mm` respectively. As mass = volume `xx` density `[(piD^(2)//4)xxl]d`, so
`1 = (pi (10^(-3))^(2))/(4) l_(1) xx d = (pi( 2xx 10^(-3))^(2))/(4)l_(2) xx d`
or `l_(1) = 4 l_(2)`
`:. R_(1) = (rhol_(1))/(piD_(1)^(2)//4) = (rho4l_(2))/(pi(10^(-3))^(2)//4)`
or `R_(2) = (rhol_(2))/(piD_(2)^(2)//4) = (rhol_(2))/(pi(2 xx 10^(-3))^(2)//4)`
so `(R_(1))/(R_(2)) = 16 or R_(1) = 16 R_(2)`