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

The core loss of a single phase, 230/115 V, 50 Hz power transformer is measured from 230 V side by feeding the primary (230 V side) from a variable voltage variable frequency source while keeping the secondary open circuited. The core loss is measured to be 1050 W for 230 V, 50 Hz input. The core loss is again measured to be 500W for 138 V, 30 Hz input. The hysteresis and eddy current losses of the transformer for 230 V, 50 Hz input are respectively.

A 3 phase, 50 Hz, 6 pole induction motor has a rotor resistance of 0.1 Ω and reactance of 0.92 Ω. Neglect the voltage drop in stator and assume that the rotor resistance is constant. Given that the full load slip is 3%, the ratio of maximum torque to full load torque is

A star connected 400 V, 50 Hz, 4 pole synchronous machine gave the following open circuit and short circuit test results:
Open circuit test: V_OC = 400 V (rms, line–to–line) at field current, I_f = 2.3 A
Short circuit test: I_SC = 10 A(rms, phase) at field current, I_f =1.5 A
The value of per phase synchronous impedance in Ω at rated voltage is __________.