$1.$ The synchronous generator is delivering $0\mathrm{.}8$pu real power when both the terminal voltage of the machine and the voltage of the infinite$-$bus are $1\mathrm{.}0$ per unit. Determine: a$.$ The internal voltage of the generator. b$.$ The power$-$angle equation for the system during the specified operating conditions. $2.$ A three$-$phase fault occurs on the system at point P$,$ located at a distance of $30\%$ of the line length away from the sending$-$end of the terminal of the line. Find the equation for the electric power as a function of the angle during the fault. $3.$ The fault in $2.$ is cleared by permanently opening circuit breakers B$13$ and B$31.$ Determine the equation for the electric power delivered by the for the system in that configuration. $4.$ A generator with H $=6$ MJ$/$MVA is delivering $1\mathrm{.}0$ per unit of real power to an infinite bus through a purely reactive network when a fault reduces the generator output to zero. The maximum power that could be delivered is $2\mathrm{.}5$ per unit. When the fault is cleared, the original network is restored. Determine the critical clearing angle and time.