Load test data obtained from a $\backslash (120\backslash$mathrm$\{$~V$\},1\mathrm{.}2\backslash$mathrm$\{$~kW$\},1800\backslash$mathrm$\{$rpm$\}\backslash )$ separately excited DC generator is given below.

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|\}$

$\backslash$hline Torque input $($Nm$)$ & Speed input $($rpm$)$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Load voltage output $\backslash \backslash$

$($V$)$

$\backslash$end$\{$tabular$\}$ & $\backslash$begin$\{$tabular$\}\{$l$\}$

Load current output $\backslash \backslash$

$($A$)$

$\backslash$end$\{$tabular$\}\backslash \backslash$

$\backslash$hline $1$ & $1800$ & $130$ & $0\backslash \backslash$

$\backslash$hline $2$ & $1800$ & $128$ & $3\backslash \backslash$

$\backslash$hline $4$ & $1800$ & $125$ & $5\backslash \backslash$

$\backslash$hline $6$ & $1800$ & $122$ & $8\backslash \backslash$

$\backslash$hline $8$ & $1800$ & $120$ & $10\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Given this data, find the following:

a$)$ The efficiency of the generator at rated condition

b$)$ Voltage regulation of the DC generator.

c$)$ The armature resistance of the generator is Assuming that the excitation is constant.

d$)$ if the speed input is reduced to $1000$ rpm $,$ how does this change the no$-$load voltage?

e$)$ When the generator is operating at its rated condition, if the excitation current is reduced, what happens to load current and generator speed?