Q$3)$

A $480-V,100-kW,50-Hz,$ four$-$pole, Y$-$connected synchronous motor has a rated power factor of $0\mathrm{.}85$ leading. At full load, the efficiency is $91$ percent. The armature resistance is $0\mathrm{.}08,$ and the synchronous reactance is $1\mathrm{.}0.$ Find the following quantities for this machine when it is operating at full load:

$($a$)$ Output torque

$($b$)$ Input power

$($c$)n_m$

$($d$)E_A$

$($e$)|I_A|$

$($f$)P_{\text{c}\text{o}\text{n}\text{v}}$

$($g$)P_{\text{m}\text{e}\text{c}\text{h}}+P_{\text{c}\text{o}\text{r}\text{e}}+P_{\text{s}\text{t}\text{r}\text{a}\text{y}}$