# Need help on the electrical resistances of semiconductors and metals and their dependance on temperature

So I was doing some problems and this came up : -

Two resistors $A$ and $B$ having resistances $R_1$ and $R_2$ respectively at $0^{\circ}C$ and temperature coefficients $α_1$ and $α_2$ are joined in series. If this combination gives the same resistance at all temperatures, then one possible correct choice is

(a) $A$ is a metal, $B$ is a semiconductor

(b) $A$ and $B$ both are metals

(C) $A$ and $B$ both are semiconductors.

Can anyone explain me the difference between electrical resistances of semiconductors and metals and their dependance on temperature.

Get as detailed as you can. And also any hint on the problem would be awesome.

(1) Semiconductors have so called a band gap $E_{\Delta}$ with the fermi level sitting somewhere between the valence and conducting band. A semiconductor conducts via hole/electron excitations that jump to the conducting band. The number of free electrons/holes in the conducting band is suppressed by the boltzmann factor $e^{-\Delta E \over kT}$ where $\Delta E = E_{conducting}- \epsilon_{F}$, the difference between conducting and fermi energies.