2233 Alternating Current Analysis .............................................................................
The task of Science is both to expand the range of our experience and to reduce it to
order.
Niels Bohr3.1 Introduction ...............................................................................................................
DC is a network in which its currents and voltages have a fi xed or constant magnitude
and direction except when transients occur. AC networks, in contrast, are electrical net-
works where the currents and voltages are characterized by time-dependent alternating
waveforms.
The majority of the AC signals in real life are sinusoids and they represent voltages or
currents that in general are expressed instantaneously by the following equations:
vt() V cos tmm( ) V sin t2
it() I sin tmm( ) I cos t 2
The choice of sine or cosine-based calculations is a matter of taste, and the conversions are
rather simple algebraic manipulations. However, it is imperative that the same choice be
used throughout a problem.
The term alternating waveform, in general, refers to periodic waves of time-varying
polarity. Therefore, alternating waveforms include a large family of waves such as square
waves, saw-tooth waves, and triangular waves.
Most of the equipment and appliances used in homes, industries, and commercial and
residential buildings operate with AC. The AC wave delivered to the consuming public by
the utilities companies is the sinusoid and is the most common modern form of electric
energy.
The three-phase AC is used in industries and commercial buildings, whereas the single
phase is commonly used in homes and residences.
In general, AC principles and applications discussed in this book are used in power
distribution, lighting, industrial systems, and consumer appliances and products.
The vast majority of AC problems deal with sinusoids, and because of it, mainly
sinusoidal waves will be considered in this chapter. If the wave is not sinusoidal, it
can always be approximated by sinusoids by means of a Fourier (trigonometric) series
expansion (see Chapter 4 for additional information).