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amplitude of a sine wave.
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Expressions of Amplitude 153
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Root-Mean-Square Amplitude Often, it is necessary to express the effective amplitude of an ac wave. This is the voltage, current, or power that a dc source would have to produce in order to have the same general effect as a given ac wave. When you say a wall outlet provides 117 V, you mean 117 effective volts. This is not the same as the peak or peak-to-peak voltage. The most common expression for effective ac intensity is called the root-mean-square (rms) amplitude. The terminology reflects the fact that the ac wave is mathematically operated on by taking the square root of the mean (average) of the square of all its instantaneous amplitudes. In the case of a perfect ac sine wave, the rms value is equal to 0.707 times the peak value, or 0.354 times the peak-to-peak value. Conversely, the peak value is 1.414 times the rms value, and the peak-to-peak value is 2.828 times the rms value. The rms amplitude is often specified when talking about utility ac, radio-frequency (RF) ac, and audio-frequency (AF) ac. For a perfect square wave, the rms value is the same as the peak value, and half the peak-to-peak value. For sawtooth and irregular waves, the relationship between the rms value and the peak value depends on the exact shape of the wave. But the rms value is never greater than the peak value for any type of ac wave. Superimposed DC Sometimes a wave has components of both ac and dc. The simplest example of an ac/dc combination is illustrated by the connection of a dc voltage source, such as a battery, in series with an ac voltage source, like the utility mains. An example is shown in the schematic diagram of Fig. 9-12. Imagine connecting a 12-V automotive battery in series with the wall outlet. (Do not try this experiment in real life!) When this is done, the ac wave is displaced either positively or negatively by 12 V, depending on the polarity of the battery. This results in a sine wave at the output, but one peak is 24 V (twice the battery voltage) more than the other. Any ac wave can have dc components along with it. If the dc component exceeds the peak value of the ac wave, then fluctuating, or pulsating, dc will result. This would happen, for example, if a 200-V dc source were connected in series with the output of a common utility ac outlet, which has peak voltages of approximately 165 V. Pulsating dc would appear, with an average value of 200 V but with instantaneous values much higher and lower. The waveshape in this case is shown in Fig. 9-13.
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9-12 Connection of a dc
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source in series with an ac source.
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9-13 Waveform resulting
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from a 117-V ac sine-wave source connected in series with a +200-V dc source.
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Alternating current can be generated by a rotating coil of wire inside a powerful magnet, as shown in Fig. 9-14. An ac voltage appears between the ends of the wire coil. The ac voltage that a generator can produce depends on the strength of the magnet, the number of turns in the wire coil, and the speed at which the magnet or coil rotates. The ac frequency depends only on the speed of rota-
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9-14 A functional diagram
of an ac generator.
Why Alternating and Not Direct 155
tion. Normally, for utility ac, this speed is 3600 revolutions per minute (rpm), or 60 complete revolutions per second (rps), so the ac output frequency is 60 Hz. When a load, such as a light bulb or heater, is connected to an ac generator, it becomes more difficult, mechanically, to turn the generator shaft, compared to when there is nothing connected to the output. As the amount of electrical power demanded from a generator increases, so does the mechanical power required to drive it. This is why it is impossible to connect a generator to a stationary bicycle and pedal an entire city into electrification. There s no way to get something for nothing. The electrical power that comes out of a generator can never be more than the mechanical power driving it. In fact, there is always some energy lost, mainly as heat in the generator. Your legs might generate enough power to run a small radio or television set, but nowhere near enough to provide electricity for a household. The efficiency of a generator is the ratio of the electrical power output to the mechanical driving power, both measured in the same units (such as watts or kilowatts), multiplied by 100 to get a percentage. No generator is 100 percent efficient, but a good one can come fairly close. At power plants, generators are driven by massive turbines. The turbines are turned by various natural sources of energy such as moving water, steam heated by combustion of fossil fuels, or steam taken directly from deep inside the earth. These energy sources can provide tremendous mechanical power, and this is why power plants can produce megawatts of electrical power.
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