$12\mathrm{.}25$ An industrial load is connected across a three$-$phase, Y$-$connected source of a $4\mathrm{.}5$ kV $($line$-$to$-$line$).$ The real power of the load is $160$ kW$,$ and its power factor is $0\mathrm{.}8$ lagging: a$.$ Compute the reactive power of the load. b$.$ A synchronous motor is connected across the load to improve the total power factor to unity. The synchronous motor is running unloaded $($no mechanical load$).$ If the synchronous reactance of the motor is $10$ Ohms, compute the equivalent field voltage of the motor.