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Q1) A 1400 m, 2-core cable is used as a ring feeder supplied at both ends with 240 V. Loads of 100 A, 150 A, and 200 A are connected at points 400 m, 700 m, and 900 m, measured respectively from one end. The cable resistance (go+ return) is 0.2 Ω/km.

Calculate EACH of the following:

(a) sketch a labelled line diagram representing the distribution system; (2)

(b) the current in each cable section; (8)

(c) the voltage at each load point; (4)

(d) the total power delivered. (2)

Q2) A relay coil has a resistance of 200 Ω and the current required to operate the relay is 150 mA.

When the coil is connected to a 50 V d.c. supply it takes 40 ms for the relay to operate.

(a) Calculate EACH of the following:

(i) the steady state relay current; (2)

(ii) the time constant for the coil; (4)

(iii) the inductance of the coil. (4)

(b) To increase the operating time for the relay, a 50 Ω resistor is connected in series with the coil.

Determine the new operating time for the relay. (6)

Q3) THREE identical coils each having inductance 0.1 H and resistance 30 Ω are connected in delta to a three-phase, 440 V, 50 Hz supply. THRRE identical capacitors, arranged in star, are connected in parallel with the delta load to raise the power factor to 0.9 lagging.

Calculate EACH of the following:

(a) the value of each capacitor; (12)

(b) the percentage reduction in line current. (4)

Q4) A THREE-phase, 8-pole, 440 V, induction motor drives an 8-kW load at a power factor of 0.85 lagging with a shaft speed of 14.4 rev/s and a slip of 4%. The stator and rotational losses are 1 kW and 0.8 kW respectively.

(a) Determine EACG of the following:

(i) the supply frequency; (4)

(ii) the frequency of the rotor EMF; (2)

(iii) the input power to the motor; (4)

(iv) the supply current. (2)

(b) Insert the power values on the power-flow diagram provided in Worksheet Q4. (4)

Q5) A THREE-phase, 440 V, 60 Hz shaft-generator supplies the following loads:

(i) Incandescent lighting and heating 80 kW at unity pf;

(ii) Fluorescent lighting 60 kW at 0.9 pf lagging;

(iii) Navigation aids and miscellaneous 45 A at 0.85 pf lagging;

(iv) Induction motors 240 kW at 0.8 pf lagging.

(a) Determine the total kW, kVAr, kVA and the overall power factor of the ship’s load. (10)

(b) A THREE-phase synchronous motor which takes 70 kW is now connected to the power system. Determine EACH of the following:

(i) the required power factor of this motor to cause the shaft generator to operate at unity power factor; (3)

(ii) the current taken by the synchronous motor. (3)

Q6) With reference to a single-phase a.c. power transformer with natural air cooling:

(a) sketch a labelled diagram of the basic construction; (4)

(b) describe the principle of operation; (4)

(c) explain why it is rated in kVA; (3)

(d) explain why it may overheat if supplied below its rated frequency; (3)

(e) state how operation at a reduced frequency may be compensated to avoid Overheating. (2)

Q7) With reference to shipboard electrical distribution systems:

(a) describe the meaning of the term earth fault; (2)

(b) explain why insulated neutral is preferred for low voltage systems; (3)

(c) sketch a circuit diagram of one arrangement for detecting phase to earth faults in   a three-phase system supplied by a star connected generator with earthed neutral resistor (NER); (6)

(d) calculate the ohmic value of an NER to limit the earth fault current to the full load rating of a 2MW, 0.8 p.f., 3.3 kV, three-phase neutral earthed a.c generator. (5)

Q8) With reference to a three-phase, cage rotor induction motor:

(a) sketch a labelled cross-section of the motor; (8)

(b) describe how the motor develops torque; (5)

(c) explain why the motor cannot run at synchronous speed. (3)

Q9) A single-phase. 3:1 step-down transformer has a primary voltage of 230 V and supplies a half-wave rectifier circuit. The transformer has a secondary winding resistance of 1 Ω. The rectifier circuit has a resistive load of 680 Ω and the diode has a forward resistance of 14 Ω.

(a) Sketch EACH of the following:

(i) a labelled circuit diagram; (3)

(ii) the load voltage waveform indicating maximum and average voltage levels. (3)

(b) Calculate EACH of the following load values;

(i) the maximum current; (4)

(ii) the average current; (3)

(iii) the average voltage. (3)