I.$$ A $250$MVA, $25$kV$,3-$phase turbo$-$alternator has a synchronous reactance of $1\mathrm{.}6$pu and a direct axis transient reactance of $0\mathrm{.}23$pu$.$ While supplying full$-$load at a power factor of $0\mathrm{.}9$ lagging, a short$-$circuit occurs at a point on the line close to the terminals of the generator. Determine the induced voltage before short$-$circuit, the initial and the final value of the short$-$circuit current if the circuit breaker fails to open.

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