Problem $3.$ For the network shown in the following Figure, impedances labeled $1$ through $6$ are in per unit. $($a$)$ Determine $Y_{\text{b}\text{u}\text{s}},$ preserving all buses. $($b$)$ invert $Y_{\text{b}\text{u}\text{s}}$ to obtain $Z_{\text{b}\text{u}\text{s}}.$ Assume that bus $3$ has a symmetric fault, and the prefault bus voltage is $1\mathrm{.}0$ p$.$u$.,$ calculate the fault currents.

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