$3)$ Consider the single$-$line diagram for a power system depicted in the figure below $(\backslash (\backslash$mathbf$\{50\}\backslash )$ points$).$

a$)$ Draw the positive, negative, and zero sequence equivalent $($reactance$)$ circuits. All reactances must be represented explicitly $(10$ points$)$

b$)$ The numerical values of the reactances are given in the table.

b$\mathrm{.}1)$ Compute the three$-$phase short circuit current analytically $(20$ points$).$

b$\mathrm{.}2)$ Compute the single$-$line$-$to$-$ground fault current analytically $(20$ points$).$