The operating region of the developed torque ( $T_{\mathrm{em}}$ ) and speed ( $\omega$ ) of an induction motor drive is given by the shaded region OQRE in the figure. The load torque $\left(T_L\right)$ characteristic is also shown. The motor drive moves from the initial operating point O to the final operating point S . Which one of the following trajectories will take the shortes time?

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