Applying single phase AC Theory to solve electrical and electronic engineering problems.

The design and development department associated with a power generation plant has various issues which require resolving. You are now asked to provide a series of written solutions on the analysis of these issues with respect to the questions detailed below.

Task 1: Recognise a variety of complex waveforms and explain how they are produced from sinusoidal waveforms.

A triangular waveform can be rep esented by the following series:

v = sinωt + [1/9] sin(3ωt - Π) + [1/25] sin5ωt

Discuss the relationships between the component waveforms and the fundamental, include the effects of frequency, amplitude and phase shift. Predict the next few terms in the series. Synthesise, graphically by hand, the triangular waveform, using the first three terms only.

Task 2: Apply AC theory to solve problems on R, L & C circuits and components

2. A tuned circuit is shown below, for the circuit find:-

a) the resonant frequency

b) the Q factor at resonance.

Two induction motors are connected in parallel and take the following loads from an a.c. supply: 2kW at a power factor of 0.8 lagging, 5kW at a power factor of 0.6 lagging.

Calculate the true power, the reactive power, the apparent power and the power factor.

Task 3. Apply AC theory to solve problems involving transformers

(i) An ideal transformer has a turns ratio of 10:3. If there is an a.c input of 250V to the primary and a resistance of 150 across the secondary, determine:

a) the secondary e.m.f;

b) the secondary current;

c) the primary current; and

d) the power input.

4 (ii) A transformer with a primary impedance of 1.2 kΩ and a secondary circuit of impedance 100. Determine the tums ratio of the transformer which will enable maximum power transfer between the circuits.