A balanced three$-$phase $\backslash (\backslash$Delta $\backslash )-$connected source is shown in figure below:

a$)$ Find the $\backslash ($ Y $\backslash )-$connected equivalent circuit. $(25$ points$)$

b$)$ Show that the $\backslash ($ Y $\backslash )-$connected equivalent circuit delivers the same open$-$circuit voltage as the original $\backslash (\backslash$Delta $\backslash )-$connected source. $(25$ points$)$

c$)$ Apply an external short circuit to the terminals $\backslash (\backslash$mathrm$\{$A$\},\backslash$mathrm$\{$B$\}\backslash ),$ and C $.$ Use the A $-$connected source to find the three line currents laA, lbB$,$ and IcC. $(25$ points$)$

d$)$ Repeat $($c$)$ but use the Y$-$equivalent source to find the three line currents. $(25$ points$)$