The resistances of an iron wire and a copper wire at `20^(@)C`are `3.9(Omega)`and `4.1(Omega)`respectively. At what temperature will the resistances be equal?Temperature coefficient of resistivity for iron is `5.0xx10^(-3)K^(-1)`and for copper it is `4.0xx10^(-3)k^(-1).`Neglect any thermal expansion.

Explanation

`R'_Fe = R_Fe xx (1 + alpha _Fe xx Delta theta )`
` R'_(Cu) = R_(Cu) (1+ alpha_(cu) xx Delta theta)`
` R'_Fe = R'_Cu `
` rArr R_Fe xx (1+ alpha_(Fe) xx Delta theta )`
` =R_(Cu)(1+alpha_(Cu) xx Delta theta)`
` rArr 3.9 xx [1+5 xx (10^-3)(20-theta)]`
` = 4.1 [1+4 xx (10^-3)(20-theta)]`
` rArr 3.9 + 3.9 xx 5 xx (10^-3)(20-theta)`
` = 4.1 xx 4.1 xx 4 xx (10^-3)(20-theta)`
` 4.1 xx 4 xx (10^-3)(20-theta)- 3.9 xx 5 xx (10^-3)`
`(20 - theta)`
` = 4.1 xx 3.9`
` rArr 16.4 (20-theta) - 19.5 (20 -theta)`
` = 0.2 xx(10^3)`
` rArr (20 - theta)(-3.1) = 0.2 xx (10^3) `
` rArr theta - 20 = 64.5 `
` rArr theta = 84.5^@C` .