$4\mathrm{.}9$ The dc machine in Problem $4\mathrm{.}6$ is self$-$excited.

$($a$)$ Determine the maximum and minimum values of the no$-$load terminal voltage.

$($b$)$ Rfc is adjusted to provide a no$-$load terminal voltage of $120$ V$.$ Determine the value of Rfc$.$

$($i$)$ Assume no armature reaction. Determine the terminal voltage at rated armature current.

Determine the maximum current the armature can deliver. What is the terminal

voltage for this situation?

$($ii$)$ Assume that If$.$AR$.=0$:$1$ A at Ia $=50$ A and consider armature reaction proportional to

armature current. Repeat part $($i$).$