A $3$ phase, $\backslash (380\backslash$mathrm$\{$kV$\},50\backslash$mathrm$\{$~Hz$\},100\backslash$mathrm$\{$~km$\}\backslash )$ long completely transposed line is built with three bundle ACSR Pheasant conductor. ACSR Pheasant conductor has an outside diameter of $35\mathrm{.}1$ mm and GMR of $13\mathrm{.}66$ mm $.$ the conductors in bundles are equally spaced with $50$ cm $.$ A horizontal tower configuration is used with a phase spacing of $12$ m $.$ The height of conductors is $40$ m from the earth level.

$-$ Determine the per phase inductance of the transmission line for three phase balanced conditions.

$-$ Determine the per phase capacitance of the transmission line for three phase balanced conditions by neglecting the earth effect.

$-$ Determine the per phase capacitance of the transmission line for three phase balanced conditions by taking account of earth effect. Assume that the earth surface is perfectly conducting horizontal plane.