This is about the same line, shown in'one$-$line format in Figure $11\mathrm{.}8.$ The buses at each end, represented as voltage sources, have the same voltage magnitude: $138kV,RMS,$ line$-$line. Now, however, model the line as having an impedance to balanced currents of $Z_1=j40+4.$ Assume the sending end has a phase advance over the receiving end of angle $.$

$($a$)$ What is real power flow into the receiving end of the line for $=10?$

$($b$)$ What is real power flow out of the sending end of the line for $=10?$

$($c$)$ What is real power flow into the receiving end of the line for $=30?$

$($d$)$ What is real power flow out of the sending end of the line for $=30?$

$($e$)$ What angle $$ results in a real power flow into the receiving end of $100$ MW $?$

$($f$)$ When $100$ MW is flowing into the receiving end of the line, how much real power is flowing out of the sending end?

$($g$)$ With $100$ MW flowing into the receiving end, what is reactive power at the sending and receiving ends?