Instruments required to synchronize an alternator to the grid is/are

The induced emf in a 3.3 kV , 4-pole, 3-phase, star-connected synchronous motor is considered to be equal and in phase with the terminal voltage under no load condition. On application of a mechanical load, the induced emf phasor is deflected by an angle of $2^{\circ}$ mechanical with respect to the terminal voltage phasor. If the synchronous reactance is $2 \Omega$, and stator resistance is negligible, then the motor armature current magnitude, in ampere, during loaded condition, is closest to __________ . (round off to two decimal places)

A DC series motor with negligible series resistance is running at a certain speed driving a load, where the load torque varies as cube of the speed. The motor is fed from a 400 V DC source and draws 40 A armature current. Assume linear magnetic circuit. The external resistance, in $\Omega$, that must be connected in series with the armature to reduce the speed of the motor by half, is closest to

A 3-phase, $400 \mathrm{~V}, 4$ pole, 50 Hz star connected induction motor has the following parameters referred to the stator :

$$ R_r^{\prime}=1 \Omega, X_S=X_r^{\prime}=2 \Omega $$

Stator resistance, magnetizing reactance and core loss of the motor are neglected. The motor is run with constant V/f control from a drive. For maximum starting torque, the voltage and frequency output, respectively, from the drive, is closest to,