Two parallel connected, three-phase, $$50Hz,$$ $$11kV,$$ star-connected synchronous machines $$A$$ and $$B,$$ are operating as synchronous condensers. They together supply $$50$$ $$MVAR$$ to a $$11$$ $$kV$$ grid. Current supplied by both the machines are equal. Synchronous reactances of machine $$A$$ and machine $$B$$ are $$1\,\,\Omega $$ and $$3\,\,\Omega ,$$ respectively. Assuming the magnetic circuit to be linear, the ratio of excitation current of machine $$A$$ to that of machine $$B$$ is ____________. (Give the answer up to two decimal places).

A three-phase, $$50$$ $$Hz$$ salient-pole synchronous motor has a per-phase direct-axis reactance $$\left( {{X_d}} \right)$$ of $$0.8$$ $$pu$$ and a per-phase quadrature-axis reactance $$\left( {{X_q}} \right)$$ of $$0.6$$ $$pu.$$ Resistance of the machine is negligible. It is drawing full-load current at $$0.8$$ $$pf$$ (leading). When the terminal voltage is $$1$$ $$pu,$$ per-phase induced voltage, in $$pu,$$ is ______________.

A three-phase, $$11$$ $$kV,$$ $$50$$ $$Hz,$$ $$2$$ pole, star connected, cylindrical rotor synchronous motor is connected to an $$11$$ $$kV,$$ $$50$$ $$Hz$$ source. Its synchronous reactance is $$50\Omega $$ per phase, and its stator resistance is negligible. The motor has a constant field excitation. At a particular load torque, its stator current is $$100$$ $$A$$ at unity power factor. If the load torque is increased so that the stator current is $$120$$ $$A,$$ then the load angle (in degrees) at this load is ____________.

A $$20$$-pole alternator is having $$180$$ identical stator slots with $$6$$ conductors in each slot. All the coils of a phase are in series. If the coils are connected to realize single-phase winding, the generated voltage is $${V_1}.$$ If the coils are reconnected to realize three-phase star-connected winding, the generated phase voltage is $${V_ 2}.$$ Assuming full pitch, single-layer winding, the ratio $${V_1}/{V_2}$$ is