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9-9 A cycle is divided into
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360 equal parts, called degrees.
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Radians The other method of specifying phase is to divide the cycle into 2 equal parts, where (pi) is a geometric constant equal to the number of diameters of any circle that can be laid end to end around the circumference of that circle. This constant is approximately equal to 3.14159. A radian (rad) of phase is thus equal to about 57.3 . Sometimes, the frequency of an ac wave is measured in radians per second (rad/s) rather than in hertz. Because there are about 6.28 radians in a complete cycle of 360 , the angular frequency of a wave, in radians per second, is equal to about 6.28 times the frequency in hertz. Radians of phase are used mainly by physicists. Phase Difference Even if two ac waves have exactly the same frequency, they can have different effects because they are out of sync with each other. This is especially true when ac waves are added together to produce a third, or composite, wave. If two pure ac sine waves have identical frequencies and identical amplitudes but differ in phase by 180 (a half cycle), they cancel each other out, and the composite wave is zero; it ceases to exist! If the two waves are exactly in phase, the composite wave has the same frequency, but twice the amplitude, of either signal alone. If two pure ac sine waves have the same frequency but different amplitudes, and if they differ in phase by 180 , the composite signal has the same frequency as the originals, and an amplitude equal to the difference between the two. If two such waves are exactly in phase, the composite has the same frequency as the originals, and an amplitude equal to the sum of the two. If two pure ac sine waves have the same frequency but differ in phase by some odd amount such as 75 or 110 , the resulting signal has the same frequency, but does not have the same waveshape as either of the original signals. The variety of such cases is infinite. Household electricity from 117-V wall outlets consists of a 60-Hz sine wave with only one phase component. But the energy is transmitted over long distances in three phases, each differing by 120 or one-third of a cycle. This is what is meant by three-phase ac. Each of the three ac waves carries one-third of the total power in a utility transmission line.
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Amplitude is also called magnitude, level, strength, or intensity. Depending on the quantity being measured, the amplitude of an ac wave can be specified in amperes (for current), volts (for voltage), or watts (for power). In addition to this, there are several different ways in which amplitude can be expressed.
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Instantaneous Amplitude The instantaneous amplitude of an ac wave is the amplitude at some precise moment, or instant, in time. This constantly changes. The manner in which it varies depends on the waveform. Instantaneous amplitudes are represented by individual points on the wave curves. Peak Amplitude The peak (pk) amplitude of an ac wave is the maximum extent, either positive or negative, that the instantaneous amplitude attains. In many situations, the positive and negative peak amplitudes of
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9-10 A wave with unequal
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positive and negative peak amplitudes.
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an ac wave are the same. But sometimes they differ. Figure 9-9 is an example of a wave in which the positive peak amplitude is the same as the negative peak amplitude. Figure 9-10 is an illustration of a wave that has different positive and negative peak amplitudes.
Peak-to-Peak Amplitude The peak-to-peak (pk-pk) amplitude of a wave is the net difference between the positive peak amplitude and the negative peak amplitude (Fig. 9-11). The peak-to-peak amplitude is equal to the positive peak amplitude plus the negative peak amplitude. When the positive and negative peak amplitudes of an ac wave are equal, the peak-to-peak amplitude is exactly twice the peak amplitude.
9-11 Peak-to-peak (pk-pk)
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