$(1)$ Two single$-$phase transformers A and B have the same rated voltage $\backslash (220/110\backslash$mathrm$\{$~V$\}\backslash )$ and their highvoltage windings have the same number of turns. During open$-$circuit tests, their measured excitation currents have the relationship of $\backslash ($ I$\_\{$O A$\}=2$ I$\_\{$O B$\}\backslash ).$

$(1-1)$ Find the relationship of their reluctances.

$(1-2)$ If the high$-$voltage windings are connected in series and supplied with $440$ V voltage, calculate their voltages of secondary sides respectively.

$(2)$ Suppose that the stator of a synchronous generator is supplied with a three$-$phase symmetrical voltage source, and the supplied voltage is kept unchanged, compare, with brief explanation, the stator currents in the following two cases:

$($i$)$ the rotor is physically removed;

$($ii$)$ the rotor rotates at the rated speed with zero excitation current.