Translated Statement:

The selected cable can carry an effective current of $200$ A$.$ It powers a three$-$phase load network with a line$-$to$-$line effective voltage of $1$ kV and a frequency of $60$ Hz$.$ There are three loads connected to the line.

Load $1$ consists of three inductors of $8$ mH connected in delta $().$

Load $2$ consists of three capacitors of $1\mathrm{.}5$ mF connected in star $($Y$).$

Load $3$ consumes an active power of $100$ kW$.$

Finally, a synchronous machine operating in motor mode is connected at the end of the line. It delivers a power of $50$ kW and is connected in star $($Y$).$ It has $8$ poles and a synchronous reactance of $0\mathrm{.}88.$

a$)$ If the synchronous machine operates at a unity power factor, determine if the selected cable's $200-$ampere capacity is adequate. Support your choice with all required calculations.

b$)$ If the synchronous machine has a constant KK of $9\mathrm{.}5,$ the flux $(\backslash$Phi$)$ is $450$ mWb$,$ and the active power provided by this machine remains constant at $50$ kW$,$ determine whether the conductor's capacity is exceeded. Support your choice with all required calculations.

c$)$ If the machine's flux $(\backslash$Phi$)$ produced by the excitation current $($ifi$\_$f$)$ is given by the equation:

$($if$)=(0\mathrm{.}05)($if$)+0\mathrm{.}25($Wb$),\backslash$Phi$($i$\_$f$)=(0\mathrm{.}05)($i$\_$f$)+0\mathrm{.}25\backslash ,\backslash$text$\{($Wb$)\},$

determine the value of the excitation current allowing the selection of the smallest wire gauge. Assume that the synchronous machine still provides $50$ kW of power and that the constant KK is $9\mathrm{.}5.$ Support your choice with all required calculations.

i already done question a i juste need b and c