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17. A series circuit has 99.0 of resistance and 88.0 of inductive reactance. An ac rms voltage of 117 V is applied to this series network. What is the current A. 1.18 A. B. 1.13 A. C. 0.886 A. D. 0.846 A. 18. What is the voltage across the reactance in the above example A. 78.0 V. B. 55.1 V. C. 99.4 V. D. 74.4 V. 19. A parallel circuit has 10 ohms of resistance and 15 of reactance. An ac rms voltage of 20 V is applied across it. What is the total current A. 2.00 A. B. 2.40 A. C. 1.33 A. D. 0.800 A. 20. What is the current through the resistance in the above example A. 2.00 A. B. 2.40 A. C. 1.33 A. D. 0.800 A.
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CHAPTER
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Power and resonance in ac circuits
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YOU HAVE LEARNED HOW CURRENT, VOLTAGE, AND RESISTANCE BEHAVE IN ac circuits. How can all this theoretical knowledge be put to practical use One of the engineer s biggest challenges is the problem of efficient energy transfer. This is a major concern at radio frequencies. But audio design engineers, and even the utility companies, need to be concerned with ac circuit efficiency because it translates into energy conservation. The first two-thirds of this chapter is devoted to this subject. Another important phenomenon, especially for the radio-frequency engineer, is resonance. This is an electrical analog of the reverberation you re familiar with if you ve ever played a musical instrument. The last third of this chapter discusses resonance in series and parallel circuits.
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What is power
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There are several different ways to define power. The applicable definition depends on the kind of circuit or device in use.
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The most all-encompassing definition of power, and the one commonly used by physicists, is this: Power is the rate at which energy is expended. The standard unit of power is the watt, abbreviated W; it is equivalent to one joule per second. This definition can be applied to motion, chemical effects, electricity, radio waves, sound, heat, light, ultraviolet, and X rays. In all cases, the energy is used up somehow, converted from one form into another form at a certain rate. This expression of power refers to an event that takes place at some definite place or places. Sometimes power is given as kilowatts (kW or thousands of watts), megawatts (MW or millions of watts) or gigawatts (GW or billions of watts). It might be given as milliwatts
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306 Power and resonance in ac circuits (mW or thousandths of watts), microwatts ( W or millionths of watts), or nanowatts (nW or billionths of watts).
Volt-amperes
In dc circuits, and also in ac circuits having no reactance, power can be defined this way: Power is the product of the voltage across a circuit or component, times the current through it. Mathematically this is written P EI. If E is in volts and I is in amperes, then P is in volt-amperes (VA). This translates into watts when there is no reactance in the circuit (Fig. 17-1). The root-mean-square (rms) values for voltage and current are always used to derive the effective, or average, power.
17-1 When there is no reactance in a circuit, the power, P, is the product of the voltage E and the current I.
Like joules per second, volt-amperes, also called VA power or apparent power, can take various forms. A resistor converts electrical energy into heat energy, at a rate that depends on the value of the resistance and the current through it. A light bulb converts electricity into light and heat. A radio antenna converts high-frequency ac into radio waves. A speaker converts low-frequency ac into sound waves. The power in these forms is a measure of the intensity of the heat, light, radio waves, or sound waves. The VA power can have a meaning that the rate-of-energy-expenditure definition does not encompass. This is reactive or imaginary power, discussed shortly.
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