The resistance of iron and copper wires at `20^@C` are `4.1Omega` and `4.3Omega` respectively. At what temperature will the resistance be equal ? Temperature coefficient of resistance for iron is `5.0xx10^(-3)K^(-1)` and for copper is `4.0xx10^(-3) K^(-1)`. Neglect any thermal expansion.

Explanation

For iron, `R_(20)=4.1Omega, alpha=5.0 xx10^(-3)K^(-1)`
From copper, `R'_(20) =4.3 Omega, alpha'=4.0 xx 10^(-3)K^(-1)`
Let at temperature `t^@C`, the resistance of iron wire be equal to the resistance of copper wire. So
`R_(20)[1+alpha( t-20)]=R'_(20)(1+alpha'(t-20)]`
or `4.1[1+5.0 xx 10^(-3)(t-20)]=4.3[1+4.0 xx10^(-3)xx(t-20)]`
`(t - 20) xx 10^(-3)[4.1 xx 5.0 - 4.3 xx 4.0]=4.3-4.1`
or `t-20 = (0.2)/(3.3xx10^(-3)) =60.6`
`t=20+60.6=80.6^@C`