It is desired to make a `20Omega` coil of wire, which has a zero thermal coefficient of resistance. To do this, a carbon resistor of resistance `R_1` is placed in series with an iron resistor of resistance `R_2`. The proportions of iron and carbon are so chosen that `R_1 +R_2 = 20Omega` for all temperatures near `20^@C.` How long are `R_1 and R_2`? `alpha_(carbon) =- 0.5xx10^(-3).^@C^(-1), alpha_(iron) = 5xx10^(-3) .^@C(-1)`

Explanation

`R_1 = 1.25 Omega and R_2 = 18.75 Omega`