There are two wires of copper and iron of the same length but difference radii .When equal potential difference between the ends of each wire, the same current flows in them. What the ratio of their radii .Specific resistance of copper and irons are `1.6 xx 10^(-8) Omega m and 1.0 xx 10^(-7) Omega m` respectively

Answer

`(2)/(5)`

Explanation

As, under the the same potential difference across the two wires, the same current flow in them to the resistance of two wires must be same
Now,`R = (rhol)/(pi r^(2))` ,
So `R_(Cu) = (rho_(Cu)l)/(pi r_(Cu)^(2)) and R_(I) = (rho_(I)l)/(pi r_(I)^(2))`
As `R_(Cu) = R_(I)` so `(rho_(Cu)l)/(pi r_(Cu)^(2)) = (rho_(I)l)/(pi r_(I)^(2))`
or `(rho_(Cu))/(rho_(I)) = (r_(Cu)^(2))/(r_(I)^(2))`
or `(r_(Cu))/(r_(I)) = sqrt((rho_(Cu))/(rho_(I))) = sqrt((1.6 xx 10^(-8))/(1.0 xx 10^(-7))) = 0.4 = (2)/(5)`