Q12. For the circuit shown in Fig, determine EACH of the following:
(a) the value and direction, positive or negative, of currents I2, I3 and I4. (10)
(b) the voltage of Battery 1. (2)
(c) the power delivered by Battery 2. (4)
Q13. (a) A 68 μF capacitor is charged from a 110 V d.c. supply via a 75 kΩ resistor for 5 seconds. This capacitor is then disconnected from the supply and a 47 μF capacitor is charged from the same supply via the same resistor for 7 seconds.
Calculate EACH of the following:
(i) the voltage to which each capacitor has charged. (7)
(ii) the charge stored in each capacitor. (3)
(b) The charged capacitors in Q2(a) are connected in parallel.
Calculate the final voltage across the parallel circuit. (6)
Q14. A three-phase, 690 V, four wire unbalanced system has the following currents:
IR = 6 A, 0.8 lead IΓ = 8 A, 0.6 lag IN = 3 A leading VRN by 30°
(a) Calculate EACH of the following:
(i) the current in the s phase; (6)
(ii) the phase angle of the S phase current with respect to the S phase voltage; (2)
(iii) the total reactive power. (3)
(b) Sketch, approximately to scale, a labelled phasor diagram to show the relationship between all phase voltages and all currents. (5)
Q15. A three-phase, 2 MVA, 6.6 kV generator is driven at constant speed and has a synchronous reactance of 10 Ω/phase.
The generator supplies full-load current at 0.85 power factor lag and rated terminal voltage.
(a) Sketch a labelled phaser diagram to show the relationship between the e.m.f. generated, the terminal voltage and the load current. (4)
(b) Calculate the full-load voltage regulation. (6)
(c) Sketch the terminal voltage/load current characteristic for the generator to show the change in voltage, from rated terminal voltage at full-load, 0.85 lag, when the load is disconnected. Indicate full-load voltage and current and the generated e.m.f.
(d) Using the axes in Q7(c), sketch the characteristics for disconnection of full -load at rated terminal voltage for the following load power factors, indicating the generated e.m.f. in EACH case:
• unity
• 0.85 lead. (2)
Q16. a) Fig shows a simple voltage regulator circuit. The unregulated supply Vs can vary between 21 V and 24 V and the minimum diode current for stable operation is 7 mA.
Calculate EACH of the following for protection of the diode and to stable load voltage:
(i) the minimum value of Rs (3)
(if) the minimum power rating of Rs (2)
(iii) the minimum value of RL (3)
b) Fig shows a simplified equivalent circuit for a single-phase transformer ignoring the no-load current.
The winding resistances are assumed to be negligible, and the reactance of the secondary has been referred to the primary to give a value equivalent to the reactance effects of both windings.
The transformer has a turns ratio of 5:1 and delivers 105∠-30° A at 86 V.
(i) Sketch a labelled phasor diagram, to show all voltages, currents and angles. (4)
(ii) Calculate EACH of the following:
→ The supply voltage V1
→ The voltage regulation. (8)
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