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Q1. Fig Q1 shows a 220 V ring main. The cable resistance (go+ return) is 0.003 Ω / m.

Calculate EACH of the following:

(a) the resistance of each cable section AB, BC, CD and DE. (4)

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

(c) the voltage at each load. (4)

Q2. A 56 μF capacitor and a 68 kΩ resistor are connected in series to a 15 V d.c. power supply.

(a) Calculate EACH of the following:

(i) the instantaneous current when the supply is switched on; (2)

(ii) the capacitor voltage 3 seconds after switch-on; (3)

(iii) the energy stored in the capacitor 3 seconds after switch-on. (2)

(b) After 3 seconds of charging the supply is switched off and the capacitor is discharged through a 39 kΩ resistor.

(i) Calculate the time taken for the capacitor voltage to fall to 6 v. (3)

(ii) Using approximately scaled axes, sketch graphs of capacitor voltage against time for charge and discharge indicating:

• the supply voltage and the voltage 3 seconds after switch-on

• initial discharge voltage and the time when the voltage is 6 V (6)

Q3. A THREE-phase, 440 V, 60 Hz shaft generator supplies the following loads.

• induction motors    200 kW, 0. 7 lag

• fluorescent lighting          14 kVA, 0.86 lag

• incandescent lighting       5 kW, u.p.f.

• navigation aids                27 A, 0.9 lag

(a) Calculate EACH of the following:

(i) the total active power supplied. (4)

(ii) the generator power factor. (6)

(b) A THREE-phase synchronous motor is connected to the supply to raise the generator power factor to unity. The synchronous motor has an input power of 50 kW.

Calculate EACH of the following for the synchronous motor:

(i) the power factor; (4)

(ii) the current. (2)

Q4. The alarm circuit in Fig shows a silicon transistor, a relay and a klaxon.

(a) With reference to current flow, describe the operation of the circuit when S is closed.

(b) State EACH of the following:

(i) the type of transistor;

(ii) ONE marine application for this circuit.

(c) Sis closed and VeE = -0.7 V, VcE = -0.3 V.

Calculate EACH of the following:

(i) the power dissipated by the relay coil;

(ii) the current gain of the transistor;

(iii) the power supplied to the circuit.