Question $3$

When a line is hit by a lightning surge of $100$ kV $,$ it behaves in specific ways. The line has a surge impedance of $500$ ohms and is connected to two parallel cables at its junction. These cables have a series inductance of $\backslash (400\backslash$mu $\backslash$mathrm$\{$H$\}\backslash )$ per phase per meter and a shunt capacitance of $\backslash (0\mathrm{.}1\backslash$mu $\backslash$mathrm$\{$~F$\}\backslash )$ per phase per meter. At the far end of the cables, there is an open$-$circuit situation.

$($a$)$ Calculate the total surge impedance of the two parallel cables and the surge speed in each cable. $(10$ marks$)$

$($b$)$ Calculate the surge current in each cable and the first reflective voltage at the cable end. $(10$ marks$)$

$($c$)$ Draw the surge voltage lattice diagram in the line and cable sections up to the second surge voltage enters the cable.