Two wattmeter method is used for measurement of power in a balanced three-phase load supplied from a balanced three-phase system. If one of the wattmeters reads half of the other (both positive), then the power factor of the load is

A single-phase 100 kVA, 1000 V / 100 V, 50 Hz transformer has a voltage drop of 5% across its series impedance at full load. Of this, 3% is due to resistance. The percentage regulation of the transformer at full load with 0.8 lagging power factor is

A transformer with toroidal core of permeability $$\mu $$ is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius r $$ \ll $$ R, and neglecting any leakage flux, the best estimate for the mean radius R is

A separately excited dc motor has an armature resistance R_$$a$$ = 0.05⁡Ω. The field excitation is kept constant. At an armature voltage of 100 V, the motor produces a torque of 500 Nm at zero speed. Neglecting all mechanical losses, the no-load speed of the motor (in radian/s) for an armature voltage of 150 V is _____ (up to 2 decimal places).