Given that 'average' traction current is $3$ kA $,$ the total length of the parallelism is $20$ km and the soil resistivity is $\backslash (300\backslash$Omega$-\backslash$mathrm$\{$m$\}\backslash ),$ calculate the induced voltage on the telecommunication cable if the propulsion current returns the traction substation via:

$($i$)$ a remote$-$return path

$($ii$)$ the outer rail

$($iii$)$ the earth wire, by means of booster transformers

In case $($ii$),$ if the induced voltage cannot exceed $430$ V $,$ estimate the minimum thickness required for the screening lead$-$sheath of a $\backslash (3-\backslash$mathrm$\{$cm$\}\backslash )$ diameter telecommunication cable.

$($Resistivity of lead is $\backslash (2\mathrm{.}83\backslash$times $10^\{-8\}\backslash$Omega$-\backslash$mathrm$\{$m$\}\backslash )).$

$(20$ marks$)$

Q$9$ Ans: Refer to tutorial