**Introduction**

Direct current (dc) can be expressed in terms of two variables: the *polarity* (or direction) and the *amplitude* . Alternating current (ac) is more complicated. There are additional variables: the *period* (and its reciprocal, the *frequency)* , the *waveform* , and the *phase* .

**Definition of Alternating Current**

Direct current has a polarity, or direction, that stays the same over a long period of time. Although the amplitude can vary—the number of amperes, volts, or watts can fluctuate—the charge carriers always flow in the same direction through the circuit. In ac, the polarity reverses repeatedly.

**Period**

In a *aperiodic ac wave* , the kind discussed in this chapter, the mathematical function of amplitude versus time repeats precisely and indefinitely; the same pattern recurs countless times. 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. 13-1 for a simple ac wave.

**Fig. 13-1** . A sine wave. The period is the length of time required for one cycle to be completed.

The period of a wave, in theory, can be anywhere from a minuscule fraction of a second to many centuries. Some electromagnetic (EM) 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. Period, when measured in seconds, is symbolized *T* .** **

**Frequency**

The frequency, denoted *f* , of a wave is the reciprocal of the period. That is, *f* = 1/ *T* , and *T* = 1/ *f* . In the olden days (prior to the 1970s), frequency was specified 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 given in *kilohertz* (kHz), *megahertz* (MHz), *gigahertz* (GHz), and *terahertz* (THz). The relationships are

1 kHz = 1,000 Hz = 10 ^{3} Hz

1 MHz = 1,000 kHz = 10 ^{6} Hz

1 GHz = 1,000 MHz = 10 ^{9} Hz

1 THz = 1,000 GHz = 10 ^{12} Hz

**Alternating Current Practice Problem**

**Alternating Current Practice Problem**

**Problem**

The period of an ac wave is 5.000 × 10 ^{−6} s. What is the frequency in hertz? In kilohertz? In megahertz?

**Solution**

First, find the frequency *f* _{Hz} in hertz by taking the reciprocal of the period in seconds:

*f* _{Hz} = 1/(5.000 × 10 ^{−6} ) = 2.000 × 10 ^{5} Hz

Next, divide *f* _{Hz} by 1,000 or 10 ^{3} to get the frequency *f* _{kHz} in kilohertz:

*f* _{kHz} = *f* _{Hz} /10 ^{3} = 2.000 × 10 ^{5} /10 ^{3} = 200.0 kHz

Finally, divide *f* _{kHz} by 1,000 or 10 ^{3} to get the frequency *f* _{MHz} in megahertz:

*f* _{MHz} = *f* _{kHz} /10 ^{3} = 200.0/10 ^{3} = 0.2000 MHz

Practice problems of these concepts can be found at: Alternating Current Practice Test

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