A $490-$kV$,125-$km$,60-$Hz$,$ three$-$phase overhead transmission line, assumed to be lossless, has a series inductance of $0\mathrm{.}910$ mH$/$km per phase and a shunt capacitance of $0\mathrm{.}0123$F$/$km per phase. $($Due to the nature of this problem, do not use rounded intermediate values$$including answers submitted in WebAssign$$in your calculations.$)$

$($a$)$

Determine the phase constant $($in rad$/$km$),$ the surge impedance Zc $($in $),$ velocity of propagation v $($in km$/$s$),$ and the wavelength $($in km$)$ of the line.

$=$ rad$/$kmZc$=$v$=$ km$/$s$=$ km

$($b$)$

The receiving$-$end load is $800$ MW at $0\mathrm{.}8$ power factor lagging and at $490$ kV$.$ At the sending end, determine the line$-$to$-$line voltage $($in kVLL$),$ current $($in A$),$ real power $($in MW$),$ and reactive power $($in Mvar$).($Enter the magnitudes.$)$

voltage kVLLcurrent Areal power MWreactive power Mvar

Determine the percent voltage regulation of the line.