For an induction motor, operating at a slip 's', the ratio of gross power output to air gap power is equal to:

Which three-phase connection can be used in a transformer to introduce a phase difference of 30° between its output and corresponding input line voltages

A 50 kW dc shunt motor is loaded to draw rated armature current at any given speed. When driven
(i) at half the rated speed by armature voltage control and
(ii) at 1.5 times the rated speed by field control, the respective output powers delivered by the motor are approximately

In relation to DC machines, match the following and choose the correct combination.

Group-I(Performance variables)
(P) Armature emf (E)
(Q) Developed torque (T)
(R) Developed power (P)

Group-II(Proportional to)
1.Flux ($$\phi$$), speed ($$\omega$$) and armature current ($$I_a$$)
2.$$\phi$$ and $$\omega$$ only
3.$$\phi$$ and $$I_a$$ only
4.$$I_a$$ and $$\omega$$ only
5.$$I_a$$ only