Question

Find the ratio of the diameter of copper to iron wire, if they have the same resistance per unit length (as they might in household wiring). dCu dFe =

Answer 1

The ratio of diameter of copper wire to the iron wire is 0.42.

Step-by-step explanation:

length of both the wires is same as L and resistance is R.

resistivity of copper = 1.7 x 10^-8 ohm m

resistivity of iron = 9.7 x 10^-8 ohm m

Let the diameter of copper is d and for iron is d'.

The formula of the resistance is

`R = \rho*(L)/(A)\\\\R = \rho*(4L)/(\pi d^2).... (1)\\And\\ R = \rho'*(4L)/(\pi d'^2).... (2)\\\\comparing (1) by (2)\\\\1.7*10^(-8)*(4L)/(\pi d^2)=9.7*10^(-8)*(4L)/(\pi d'^2)\\\\d : d' = 0.42`