A 10-pole, 50 Hz, 240 V, single phase induction motor runs at 540 RPM while driving rated load. The frequency of induced rotor currents due to backward field is

The four stator conductors (A, A', B and B') of a rotating machine are carrying DC currents of the same value, the directions of which are shown in the figure (i). The rotor coils $$a$$-$$a'$$ and $$b$$-$$b'$$ are formed by connecting the back ends of conductors '$$a$$' and '$$a'$$' and '$$b$$' and '$$b'$$', respectively, as shown in figure (ii). The e.m.f. induced in coil $$a$$-$$a'$$ and coil $$b$$-$$b'$$ are denoted by $${E_{a - a'}}$$ and $${E_{b - b'}}$$, respectively. If the rotor is rotated at uniform angular speed $$\omega$$ rad/s in the clockwise direction then which of the following correctly describes the $${E_{a - a'}}$$ and $${E_{b - b'}}$$?

A separately excited DC motor rated 400 V, 15 A, 1500 RPM drives a constant torque load at rated speed operating from 400 V DC supply drawing rated current. The armature resistance is 1.2 $$\Omega$$. If the supply voltage drops by 10% with field current unaltered then the resultant speed of the motor in RPM is ____________ (Round off to the nearest integer).

A three-phase synchronous motor with synchronous impedance of 0.1+j0.3 per unit per phase has a static stability limit of 2.5 per unit. The corresponding excitation voltage in per unit is _________ (Round off to 2 decimal places).