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 0-1 Ampere moving iron ammeter has an internal resistance of 50 m$$\Omega $$ and inductance of 0.1 mH. A shunt coil is connected to extend its range to 0-10 Ampere for all operating frequencies. The time constant in milliseconds and resistance in m$$\Omega $$ of the shunt coil respectively are

The equivalent circuit of a single phase induction motor is shown in the figure, where the parameters are

R₁ = R₂^' = X_l1 = X_l2^' = 12 $$\Omega $$, X_m = 240 $$\Omega $$

and s is the slip. At no-load, the motor speed can be approximated to be the synchronous speed. The no-load lagging power factor of the motor is___________ (up to 3 decimal places).

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).