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# Alternating Current Help

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## Introduction to Alternating Current

Trigonometry is important in electricity and electronics, particularly in the analysis of alternating current (AC) and waves.

In electrical applications, direct current (DC) has a polarity, or direction, that stays the same over a long period of time. Although the intensity of the current might vary from moment to moment, the electrons always flow in the same direction through the circuit. In alternating current (AC), the polarity reverses repeatedly and periodically. The electrons move back and forth; the current ebbs and flows.

## Period and Frequency

### Period

In a periodic AC wave, the kind discussed in this chapter, the mathematical function of the amplitude (the level of current, voltage, power, magnetic-field intensity, or some other variable quantity) versus time repeats precisely and indefinitely. The period is the length of time between one repetition of the pattern, or one wave cycle, and the next. This is illustrated in Fig. 9-1 for a simple AC wave.

Fig. 9–1. The period of an AC wave is the time it takes for exactly one complete cycle to occur.

The period of an alternating wave can be as short as a minuscule fraction of a second, or as long as thousands of centuries. Some electromagnetic fields have periods measured in quadrillionths of a second or smaller. The charged particles held captive by the magnetic field of the sun reverse their direction over periods measured in years, and large galaxies may have magnetic fields that reverse their polarity every few million years. The period of an AC wave, when expressed in seconds, is symbolized T .

### Frequency

The frequency of an AC wave, denoted f , is the reciprocal of the period. That is, f = 1 /T , and T = 1 /f . Prior to the 1970s, frequency was expressed in cycles per second , abbreviated cps. High frequencies were expressed in kilocycles, megacycles , or gigacycles , representing thousands, millions, or billions of cycles per second. Nowadays, the standard unit of frequency is known as the hertz , abbreviated Hz. Thus, 1 Hz = 1 cps, 10 Hz = 10 cps, and so on.

Higher frequencies are expressed in kilohertz (kHz), megahertz (MHz), gigahertz (GHz), and terahertz (THz). The relationships are:

1 kHz = 1000 Hz = 10 3 Hz

1 MHz = 1000 kHz = 10 6 Hz

1 GHz = 1000 MHz = 10 9 Hz

1 THz = 1000 GHz = 10 12 Hz

## The Sine Wave

In its purest form, alternating current has a sine-wave, or sinusoidal, nature. The waveform in Fig. 9-1 is a sine wave. Any AC wave that concentrates all of its energy at a single frequency has a perfect sine-wave shape. Conversely, any perfect sine-wave electrical signal contains one, and only one, component frequency.

Fig. 9–1. The period of an AC wave is the time it takes for exactly one complete cycle to occur.

In practice, a wave can be so close to a sine wave that it looks exactly like the sine function on an oscilloscope, when in reality there are traces of signals at other frequencies present. The imperfections in a signal are often too small to see using an oscilloscope, although there are other instruments that can detect and measure them. Utility AC in the United States has an almost perfect sine-wave shape, with a frequency of 60 Hz.

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