$7\mathrm{.}2$ An ungrounded $4\mathrm{.}16$ kV system has a capacitance to ground of $0\mathrm{.}4$ F per phase. In this system, do the following:

a$.$ Calculate the normal charging current in amperes per phase.

b$.$ Calculate the fault current for a phase$-$a$-$to$-$ground fault.

c$.$ Will this fault current operate a ground overcurrent relay set at $0\mathrm{.}5$ A pickup and connected to $100$:$5$ CT or a ground sensor connected to a toroidal$-$type CT with a primary pickup of $5$ A$?$

d$.$ It has been decided to ground this system with a zigzag transformer and neutral resistor. The source to the $4\mathrm{.}16$ kV bus has X$1=10\%$ on $5000$ kVA. If in this system X$1$ is $2\mathrm{.}4\%$ on the zigzag bank rating, what is the kVA of the zigzag bank?

e$.$ In order to limit the overvoltage on the unfaulted phases to a maximum of $250\%$ for possible restriking ground faults, it is necessary that