Answer all questions showing all working out to show how answer was obtained.

1. For the circuit given in FIGURE 1 the power factor is 032 lagging and the power dissipated is 375 W.

FIG. I

Determine the:

(i) apparent power
(ii) reactive power
(iii) the magnitude of the current flowing in the circuit
(iv) the value of the impedance Z and state whether circuit is inductive or capacitive.

2. A 50 kW load operates from a 60 Hz 10 kV rms line with a power factor of 60% lagging. Determine the capacitance that must be placed in parallel with the load to achieve a 90% lagging power factor.

3. A series RLC circuit is connected to a 5 V supply, the frequency of the supply is adjusted to give a maximum current of 11.9 mA at 2.5 kHz. The Q factor is 70. Determine the component values of the circuit.

4. A single phase transformer has the following rating: 120 kVA, 2000 V/100 V, 60 Hz with 1000 primary turns.

Determine:

(a) the secondary turns
(b) the rated primary and secondary currents
(c) the maximum flux
(d) given a maximum flux density of 0.25 T, the cross-sectional area of the core.

5. An a.c. voltage, V, comprises of a fundamental voltage of 100 V rms at a frequency of 120 Hz, a 3rd harmonic which is 20% of the fundamental, a 5th harmonic which is 10% of the fundamental and at a phase angle of 1.2 radians lagging.

(i) Write down an expression for the voltage waveform.
(ii) Sketch the waveforms of the harmonic components.
(iii) Determine the voltage at 20 rns.
(iv) Given an ideal V= 100 V rms, what is the percentage error at 20 ms?