P$15\mathrm{.}48.$ A permanent$-$magnet automotive fan motor draws $20$ A from a $12-$V source when the VT$=240$ V RA$=1\mathrm{.}5.$ RF$+$Radj$=240.$ IL$=50$ A$.$ RA$=0\mathrm{.}05$ RF$+$Radj$=100.$ RA$=1\mathrm{.}3$ VT$=220$ V$.$ nm$=950$ rpm IA$=12\mathrm{.}2$ A$.$ RA$,$ VT$=200$ V$,$ IL$=23\mathrm{.}3$ A$,$ nm$=1500$ rpm$.$ IF$=$ RA$=0\mathrm{.}4.$ rotor is locked $($i$.$e$.,$ held motionless$).$ a$.$ Find the armature resistance. b$.$ Find the maximum developed power that this motor can produce when operated from a $12-$V source. c$.$ Repeat part $($b$)$ for operation at $10$ V $($this represents a nearly dead battery$)$ and at $14$ V $($this is the terminal voltage during charging of the battery after the engine is started$).$