The reactance data for the power system shown in figure in pu on a common base is as follows : G$1$ and G$2$ : $x1=x2=0\mathrm{.}10$;$x0=0\mathrm{.}05$;$T1$ and $T2$:$x1=x2=x0=0\mathrm{.}25$; Line $1-2$:$x1=x2=0\mathrm{.}30$;$x0=0\mathrm{.}50.$ Compute the fault current in pu for a$)$ a bolted three phase fault at bus $1$ and b$)$ a bolted single line to ground fault at bus $1.$