# 6E4Z0008 Electrical Engineering- Magnetics and Capacitance

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1. Magnetics & Capacitance

(a) Assume an iron ring with a mean circumference of 50 cm and cross sectional area (c.s.a.) of 8 cm2 is wound with a coil of 110 turns and is required to have a flux of 800 μWb set up within the core. From the data shown in Table Q1a, calculate:

(i) The flux density in the core; (5 marks)
(ii) The required magnetising force; (5 marks)
(iii) The current required in the coil. (5 marks)

 Flux density, B, tesla 1 1.2 1.4 Magnetising force, H, ampere turns/metre 450 700 1350

Table Q1a

(b) For the parallel circuit shown in Figure Q1b, find the following

(i) The charge stored in each capacitor;  (5 marks)
(ii) The total charge; (5 marks)
(iii) The total capacitance; (5 marks)
(iv) If the capacitors are now connected in series, what would be the total capacitance? (5 marks)

Figure Q1b

(c) A capacitor is to be manufactured to have a capacitance value of 60μF. The dielectric to be used has a relative permittivity value of 50 and a maximum electric stress rating of 100 kV/cm. Calculate the minimum surface area of each plate of the capacitor for capacitor voltage ratings of 30V. (5 marks)

2. Resonance & Power in AC Circuits

(a) A series resonance network consisting of a resistor of 20Ω, a capacitor of 1uF and an inductor of 30mH, as shown in Figure Q2a, is connected across a sinusoidal supply voltage which has a constant output of 12V at all frequencies.

Figure Q2a

Calculate,

(i) The resonant frequency;  (3 marks)
(ii) The current at resonance;  (3 marks)
(iii) The inductive reactance at resonance XL; (3 marks)
(iv) The voltage across the inductor and capacitor at resonance;  (3 marks)
(v)The quality factor and the bandwidth of the circuit. (3 marks)

(b)  A light bulb (which can be assumed to be purely resistive) is rated at 80 W and is plugged into a mains power supply at 230V, 50Hz AC.

(i) Find the current that is drawn by the bulb. (3 marks)
(ii) If the light is left switched on for 30 minutes, calculate the total energy used. (4 marks)
(iii) Find the total current taken from the mains supply if an electric motor is operating at the same time as the light bulb. The motor consumes 2 A at a power factor of 0.5 lagging.        (4 marks)
(iv) Find the true power consumed by the overall load when the light bulb and the motor are operating simultaneously. (4 marks)