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So far, our electrons have owed as a current from one place to another, not unlike a river owing downstream. You might say it ows directly from one position in a circuit to another, making it direct current (DC). If you were to watch the voltage level at one point in a DC circuit, it might look like the 5-volt trace in Fig. 10-1. Simple DC has its place, but most circuits are going to involve changes in their current and voltage. The stereotypical changing current, or alternating current (AC), is the sine wave (Fig. 10-2). The sine is the most e cient waveform for power transmission. The electricity in your walls is in this shape.
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Fig. 10-1.
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5-volt signal.
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CHAPTER 10 Capacitance
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Fig. 10-2.
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5-volt sinusoidal signal.
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Note that though we are talking about current, voltage follows the current so a current reversal involves a voltage reversal as well. In most circuits our attention is on the voltage and not the current, so we normally show voltage measurements. There are cases where the current and voltage do not exactly match, but these subtleties don t concern us here. Not all AC signals are sinusoidal (sine-like). They can be any shape. Most of the mathematics, however, describes sinusoidal signals. The sine wave is the shape that is traced out by a point on the edge of a rolling wheel, and this AC pattern is created naturally by a spinning generator. There are several new attributes we can measure on a periodic signal: its period, for example, and its frequency and amplitude (Fig. 10-3). It is only fair to give a math warning here. The following discussion uses a number of mathematical equations, including trigonometric functions. These equations are needed to provide a complete description. However, to get a feel for the subject you can work with the gures and the text and skim over the equations. Unfortunately for the math-phobic among us, mathematics is required for a detailed understanding of how most technologies work. A periodic waveform is one that repeats itself, over and over again, coving the same voltage territory in more or less the same way over time. A period, then, is one cycle of the waveform. This period takes a certain amount of time (T). Frequency ( f ) is the number of cycles that occur in one second, and is measured in hertz (Hz). Like most physical constants, the hertz is named after a scientist who made signi cant contributions to the eld the constant
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Fig. 10-3.
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AC measurements.
applies to. In this case, Heinrich Rudolf Hertz, a German scientist who worked with electromagnetism and radio waves. One hertz is one cycle in one second. A waveform s frequency and period are reciprocals: f 1 T 10-1
The amplitude (A) of the signal is the extreme voltage level it reaches, either above or below zero. The peak-to-peak amplitude is the total voltage spanned by the waveform and, for waveforms that are symmetrical around 0 V: VP P 2 A 10-2
The voltage in our sinusoidal signal is characterized by the sine function: Vt A sin 2  f t 10-3
The magic number (2 ) is the number of radians spanned by one circle. A radian is a measurement of angle, like the more familiar degree. Where there are 360 degrees in a circle, there are (2 ) radians. Therefore, there are (2  f ) cycles per time unit t. There is one last question. How much power is represented by this waveform For a DC signal, power is the voltage times the current. But for AC the voltage is constantly changing. To calculate the average power for a
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