An open circuit test is performed on 50 Hz transformer, using variable frequency source and keeping V/f ratio constant, to separate its eddy current and hysteresis losses. The variation of core loss/frequency as function of frequency is shown in the figure The hysteresis and eddy current losses of the transformer at 25 Hz respectively are

The load shown in the figure absorbs 4 kW at a power factor of 0.89 lagging. Assuming the transformer to be ideal, the value of the reactance X to improve the input power factor to unity is ___________.

A single phase induction motor is provided with capacitor and centrifugal switch in series with auxiliary winding. The switch is expected to operate at a speed of 0.7 Ns, but due to malfunctioning the switch fails to operate. The torque-speed characteristic of the motor is represented by

The torque-speed characteristics of motor ($$T_M$$) and load ($$T_L$$) for two cases are shown in the figures (a) and (b). The load torque is equal to motor torque at points P, Q, R and S The stable operating points are