# Tag: AC Waveforms

• ## 2.8 Some Examples with AC Circuits

Let’s connect three AC voltage sources in series and use complex numbers to determine additive voltages. All the rules and laws learned in the study of DC circuits apply to AC circuits as well (Ohm’s Law, Kirchhoff’s Laws, network analysis methods), with the exception of power calculations (Joule’s Law). The only qualification is that all…

• ## 2.7 More on AC polarity

Complex numbers are useful for AC circuit analysis because they provide a convenient method of symbolically denoting phase shift between AC quantities like voltage and current. However, for most people, the equivalence between abstract vectors and real circuit quantities is not an easy one to grasp. Earlier in this chapter, we saw how AC voltage…

• ## 2.6 Complex Number Arithmetic

Since complex numbers are legitimate mathematical entities, just like scalar numbers, they can be added, subtracted, multiplied, divided, squared, inverted, and such, just like any other kind of number. Some scientific calculators are programmed to directly perform these operations on two or more complex numbers, but these operations can also be done “by hand.” This…

• ## 2.5 Polar Form and Rectangular Form Notation for Complex Numbers

In order to work with complex numbers without drawing vectors, we first need some kind of standard mathematical notation. There are two basic forms of complex number notation: polar and rectangular. Polar Form of a Complex Number The polar form is where a complex number is denoted by the length (otherwise known as the magnitude,…

• ## 2.4 Complex Vector Addition

If vectors with uncommon angles are added, their magnitudes (lengths) add up quite differently than that of scalar magnitudes: (Figure below) Vector magnitudes do not directly add for unequal angles. If two AC voltages—90° out of phase—are added together by being connected in series, their voltage magnitudes do not directly add or subtract as with…

• ## 2.3 Simple Vector Addition

Remember that vectors are mathematical objects just like numbers on a number line: they can be added, subtracted, multiplied, and divided. Addition is perhaps the easiest vector operation to visualize, so we’ll begin with that. If vectors with common angles are added, their magnitudes (lengths) add up just like regular scalar quantities: (Figure below) Similarly,…

• ## 2.2 Vectors and AC Waveforms

OK, so how exactly can we represent AC quantities of voltage or current in the form of a vector? The length of the vector represents the magnitude (or amplitude) of the waveform, like this: (Figure below) The greater the amplitude of the waveform, the greater the length of its corresponding vector. The angle of the…

• ## 2.1 Introduction to Complex Numbers

If I needed to describe the distance between two cities, I could provide an answer consisting of a single number in miles, kilometers, or some other unit of linear measurement. However, if I were to describe how to travel from one city to another, I would have to provide more information than just the distance…

• ## 1.6 Principles of Radio

One of the more fascinating applications of electricity is in the generation of invisible ripples of energy called radio waves. The limited scope of this lesson on alternating current does not permit full exploration of the concept, some of the basic principles will be covered. With Oersted’s accidental discovery of electromagnetism, it was realized that…

• ## 1.5 AC phase

Things start to get complicated when we need to relate two or more AC voltages or currents that are out of step with each other. By “out of step,” I mean that the two waveforms are not synchronized: that their peaks and zero points do not match up at the same points in time. The…

• ## 1.4 Simple AC Circuit Calculations

Over the course of the next few chapters, you will learn that AC circuit measurements and calculations can get very complicated due to the complex nature of alternating current in circuits with inductance and capacitance. However, with simple circuits (figure below) involving nothing more than an AC power source and resistance, the same laws and rules of…

• ## 1.3 Measurements of AC Magnitude

So far we know that AC voltage alternates in polarity and AC current alternates in direction. We also know that AC can alternate in a variety of different ways, and by tracing the alternation over time we can plot it as a “waveform.” We can measure the rate of alternation by measuring the time it…

• ## 1.2 AC Waveforms

When an alternator produces AC voltage, the voltage switches polarity over time, but does so in a very particular manner. When graphed over time, the “wave” traced by this voltage of alternating polarity from an alternator takes on a distinct shape, known as a sine wave: Figure below Graph of AC voltage over time (the…

• ## 1.1 What is Alternating Current (AC)?

Most students of electricity begin their study with what is known as direct current (DC), which is electricity flowing in a constant direction, and/or possessing a voltage with constant polarity. DC is the kind of electricity made by a battery (with definite positive and negative terminals), or the kind of charge generated by rubbing certain…