please use the image to solve to full completion

A $5$ kW with a lagging power factor of $0\mathrm{.}5$ is connected to the low$-$voltage terminals of the transformer. Assuming rated voltage across the load:

$($i$)$ Calculate the current and voltage on the high$-$voltage side and the voltage regulation of the transformer $(\backslash (5\backslash$mathbf$\{$m k s$\}\backslash )).$

$($ii$)$ Explain why you can neglect the excitation branch in your calculations $(2$mks$).$

$($iii$)$ Determine the transformer efficiency $(2$mks$).$

$($iv$)$ Calculate the reactive power consumed by the transformer and indicate its proportion in $\backslash \%$ with respect to the total apparent power drawn from the supply $(4$mks$).$

$($c$)$ State three advantages of an autotransformer $(3$mks$)$

$($d$)$ You are given a $\backslash (25\backslash$mathrm$\{$~kW$\},230\backslash$mathrm$\{$~V$\}\backslash )$ DC shunt motor with armature resistance, $\backslash (\backslash$mathrm$\{$Ra$\}=0\mathrm{.}14\backslash$Omega $\backslash ).$ The no load speed of the motor at rated voltage is $1980$ rpm and armature current is $8\mathrm{.}2$ A $.$ The field resistance is $\backslash (120\backslash$Omega $\backslash ).$ When the machine is operated at full load $($rated voltage$),$ its armature current is $160$ A but its flux is $\backslash (7\mathrm{.}5\backslash \%\backslash )$ less than the no load value.

$($i$)$ Sketch the diagram for the shunt connected motor, showing clearly the direction of armature current, and the field resistance $(2$mks$).$

$($ii$)$ Calculate the values of induced voltage, Ea$,$ for the no load and full load cases $(\backslash (\backslash$mathbf$\{4$ m k s$\}\backslash )).$

$($iii$)$ By using the ratio of voltages$/$ speeds and considering the flux decrease, determine the speed at full load $(3$mks$)$