Power consumed by a balanced $$3$$-phase, $$3$$-wire load is measured by the two wattmeter method. The first wattmeter reads twice that of the second. Then the load impedance angle in radians is

In an oscilloscope screen, linear sweep is applied at the

A 15kW, 230V dc shunt motor has armature circuit resistance of 0.4 $$\Omega$$ and field circuit resistance of 230 $$\Omega$$. At no load and rated voltage, the motor runs at 1400 rpm and the line current drawn by the motor is 5 A. At full load, the motor draws a line current of 70 A. Neglect armature reaction. The full load speed of the motor in rpm is ________________

For a specified input voltage and frequency, if the equivalent radius of the core of a transformer is reduced by half, the factor by which the number of turns in the primary should change to maintain the same no load current is