$2.$ You are given a DC motor with Kt$=0\mathrm{.}1$ N$-$m$/$A$,$ Ke $=10$V$/1000$ r$.$p$.$m$,$ Rarmature$=1$ ohm.

For an input voltage Vin$=20$ V find:

$($a$)$ No load speed $(5$ points$)$

$($b$)$ Stall current and Starting torque $(10$ points$)$

$($c$)$ Maximum Power $(5$ points$)$

$($d$)$ If Load Torque TL$=1$ N$-$m and Friction Torque TF$=0\mathrm{.}005$w find the equilibrium current $($I$)$

and motor speed w$.(10$ points$)$