Q$3.(35$ piv$)$ Conatder that an armature consisis of two coils which are connected in series, This armature is replaced betweent twe eurved pole faces. The two ends of the armature are connected to two commutator segments and there are atso twe brushes. Each goil cansists of $10$ turns. Each pole generates a flux of $0\mathrm{.}09$ Wb $.$ A $48-V$ bgttery is connected to the krukhes through a resiataneg of S$-$ohm. Answer the following questions by Ignoring the armature resistance:

a$)$ Find the no$-$load specid of the armature.

b$)$ Suppose that a forgue of $10$ Nm is applied at the opposite direction of rotation, calculate the batery current,

e$)$ Under the cendition in part $($b$),$ how much power is the battery consuming or producing?

d$)$ How much tarque must we apply to the armature under no$-$load to make lits speed to be equal to $2-$times of no$-$load speed?