Consider a semiconductor that is uniformly doped with Nd $=1014$ cm$-3$ and Na $=0,$ with an applied electric field of E $=100$ V$/$cm$.$ Assume that $$n $=1000$ cm$2/$V$-$s and $$p $=0.$ Also assume the following parameters: NC $=2$ x $1019($T$/300)3/2$ cm$-3,$ NV $=1$ x $1019($T$/300)3/2$ cm$-3,$ Eg$=1\mathrm{.}1$ eV$.($a$)$ Calculate the electric$-$current density at T $=300$ K$.($b$)$ At what temperature will this current increase by $5$ percent? $($Assume the mobilities are independent of temperature.$)$