A 3-phase, 4-pole, 400 V, 50 Hz squirrel-cage induction motor is operating at a slip of 0.02. The speed of the rotor flux in mechanical rad/sec, sensed by a stationary observer, is closest to

A star-connected, 12.5 kW, 208 V (line), 3-phase, 60 Hz squirrel cage induction motor has following equivalent circuit parameters per phase referred to the stator. R₁ = 0.3 Ω, R₂ = 0.3 Ω, X₁ = 0.41 Ω, X₂ = 0.41 Ω. Neglect shunt branch in the equivalent circuit. The starting current (in Ampere) for this motor when connected to an 80 V (line), 20 Hz, 3- phase AC source is __________.

If a synchronous motor is running at a leading power factor, its excitation induced voltage (E_r) is

A $$3$$-phase, $$2$$-pole, $$50$$ $$Hz,$$ synchronous generator has a rating of $$250$$ $$MVA,$$ $$0.8$$ $$pf$$ lagging. The kinetic energy of the machine at synchronous speed is $$100$$ $$MJ.$$ The machine is running steadily at synchronous speed and delivering $$60$$ $$MW$$ power at a power angle of $$10$$ electrical degrees. If the load is suddenly removed, assuming the acceleration is constant for $$10$$ cycles, the value of the power angle after $$5$$ cycles is ________ electrical degrees.