Question: A permanent-magnet DC motor has armature resistance Ra = 2 ohms, armature voltage Va = 200 V, and operates under no-load conditions at a speed of N rpm drawing armature current Ia of 0.5 A

1. A permanent-magnet DC motor has armature resistance Ra = 2 ohms, armature voltage Va = 200 V, and operates under no-load 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).

2. A balanced 3-phase 360-V 50-Hz source supplies power to a 3-phase induction motor, a balanced star- connected load with per-phase impedance of 50/30^o Ω, and a delta-connected 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:

1. 1. Line current for each load (12.5 marks)
   2. Phase current for each load (12.5 marks)
   3. Source line current (10 marks)
   4. Active power taken by each load (12.5 marks)
   5. Reactive power taken by each load (12.5 marks)
   6. 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)

3. A 50-Hz 20-kVA 2400/360-V transformer has the following equivalent-circuit 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
• Core-loss 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).

4. A certain eight-pole 360-V 50-Hz delta-connected three-phase 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 no-load and locked-rotor tests on this motor are as follows:

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

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