$2-)$ The per$-$unit bus impedance matrix for the power system shown below is given by

$Z_{\text{b}\text{u}\text{s}}=\left[\begin{array}{cccc}j0\mathrm{.}150& j0\mathrm{.}075& j0\mathrm{.}140& j0\mathrm{.}135\\ j0\mathrm{.}075& j0\mathrm{.}1875& j0\mathrm{.}090& j0\mathrm{.}0975\\ j0\mathrm{.}140& j0\mathrm{.}090& j0\mathrm{.}2533& j0\mathrm{.}210\\ j0\mathrm{.}135& j0\mathrm{.}0975& j0\mathrm{.}210& j0\mathrm{.}2475\end{array}\right]$

The generator internal emfs and reactances are

$G1$: $E_1=\frac{1\mathrm{.}2}{{?}_0}p.u.,x_{G1}=j0\mathrm{.}2p.u.$

$G2$: $E_2=\frac{1\mathrm{.}25}{{?}_0}p.u.,x_{G2}=j0\mathrm{.}3p.u.$

An impedance $Z_b=0\mathrm{.}1+j0\mathrm{.}2$ is connected between buses $3$ and $4.$

$($a$)$ Calculate the new bus impedance matrix $Z_{\text{b}\text{u}\text{s}}^{(new)}.$

$($b$)$ Determine the new bus voltages at all the buses.

$($c$)$ Calculate the current in $Z_b.$