Question $3$

In a high$-$voltage overhead transmission line system as shown in Figure Q$3,$ having a switching voltage surge of $90$ kV traveling in a surge impedance of $\backslash (500\backslash$Omega $\backslash ),$ arrives at a junction where it branches into two lines with surge impedances of $\backslash (600\backslash$Omega $\backslash )$ and $\backslash (300\backslash$Omega $\backslash )$ respectively.

Figure Q$3$

$($a$)$ Determine the surge voltage $\backslash ((\backslash$mathrm$\{$V$\})\backslash )$ and currents $\backslash (\backslash$left$(\backslash$mathrm$\{$I$\}\_\{2\}\backslash$right$.\backslash )$ and $\backslash (\backslash$left$.\backslash$mathrm$\{$I$\}\_\{3\}\backslash$right$)\backslash )$ transmitted into each branch line. $(10$ marks$)$

$($b$)$ A power company received an enquiry from a consumer who is supplied by the above overhead transmission line network and find some of his equipment burnt from time to time. Explain ONE possible reason and suggest ONE mitigation measure for the customer and ONE mitigation measure for the power company.

$(9$ marks$)$

$($c$)$ As high$-$voltage overhead line systems are prone to lightning surges, why is high$-$voltage overhead line are still preferred for transmission of large amount of energy? Give TWO reasons.