P$15\mathrm{.}48.$ A permanent$-$magnet automotive fan motor draws $20$ A from a $12-$V source when the 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$).$