 A permanentmagnet DC motor has armature resistance Ra = 2 ohms, armature voltage Va = 200 V, and operates under noload conditions at a speed of N rpm drawing armature current Ia of 0.5 A. When load is connected, the motor speed drops by 20%. Determine the power efficiency of the motor under the loaded conditions. Assume that the motor losses consist solely of heating of Ra and frictional loss torque that is independent of speed. For N value in rpm take the last four digits of your student ID number. (100 marks).
 A balanced 3phase 360V 50Hz source supplies power to a 3phase induction motor, a balanced star connected load with perphase impedance of 50/30^{o} Ω, and a deltaconnected resistive load with 10 Ω per phase impedance. The motor draws a total of 5 kVA at power factor of 0.7.
Sketch a circuit diagram for the entire system of three loads. (5 marks)
Determine the following parameters:

 Line current for each load (12.5 marks)
 Phase current for each load (12.5 marks)
 Source line current (10 marks)
 Active power taken by each load (12.5 marks)
 Reactive power taken by each load (12.5 marks)
 Overall power factor of the system (10 marks)
Design a capacitor bank required to correct the overall power factor to 100%. Specify the values of the capacitors and show their connection on the circuit diagram. (25 marks)
 A 50Hz 20kVA 2400/360V transformer has the following equivalentcircuit parameters:
 Primary winding resistance 5 Ω
 Secondary winding resistance 0.1 Ω
 Primary winding leakage reactance 4.5 Ω
 Secondary winding leakage reactance 0.1 Ω
 Magnetizing reactance 30 kΩ
 Coreloss equivalent resistance 50 kΩ
Find the percentage regulation (35 marks) and power efficiency for the transformer (35 marks) for the rated load having a lagging power factor of 0.8. Plot phasor diagrams for the voltage and current at the source (15 marks) and at the load (15 marks).
 A certain eightpole 360V 50Hz deltaconnected threephase induction motor operates at slip 4% at full load and has rotational losses (windage + friction) of 100 W. The stator resistance per phase is 0.2 Ohm. The results of noload and lockedrotor tests on this motor are as follows:

Noload test

Lockedrotor test

Linetoline input voltage:

360 V

50 V

Input active power:

1500 W

1800 W

Input line current:

15 A

45 A

Using the tests data, determine parameters of the perphase equivalent circuit. (20 marks) Plot the perphase equivalent circuit diagram with all parameters indicated. (5 marks) Using the obtained equivalent circuit, determine the following parameters of the motor:

 Speed at full load (3 marks)
 Frequency of the stator currents at full load (3 marks)
 Frequency of the rotor currents at full load (4 marks)