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Inductance and Capacitance
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Problem 108 The inductance of a certain coil is 0.62 henrys. Find the magnitude of the selfinduced voltage during a 1-second time interval in which (a) the current increases linearly from 1 ampere to 3 amperes, (b) the current increases linearly from 28 amperes to 30 amperes. Problem 109 Suppose, in problem 108, that the self-induced voltage is 5.52 volts at a certain instant of time. How fast is the current changing at that particular instant Problem 110 Suppose the current in a certain coil is increasing at the rate of 76 amp/sec at a certain instant of time. If the self-induced voltage is 0.048 volts at that instant, nd the inductance of the coil in microhenrys.
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Capacitors and Capacitance
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We have learned that an INDUCTOR is a passive electrical circuit device that utilizes a magnetic eld. A CAPACITOR, on the other hand, is a passive electrical circuit device that utilizes an electric eld instead of a magnetic eld. Physically, a capacitor consists of two conducting surfaces called the PLATES, which are separated by an electrical insulating material called the DIELECTRIC. In electrical drawings, capacitors are indicated by either of the symbols shown below, where the vertical lines represent the two plates of the capacitor and the horizontal lines represent the wires used to connect the capacitor to the rest of the circuit.
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Usually the symbol using the curved line, on the right, is preferred, because the one on the left is the same as the symbol used to denote a set of relay contacts. Capacitors have the ability to store electric charge, the amount of such charge depending upon the amount of voltage between the plates and a quantity called the CAPACITANCE of the capacitor, which we ll de ne a little later on. The physical construction of a capacitor depends upon the amount of capacitance required, the amount of voltage that will appear between the plates, and the type of circuit it is to be used in. For example, in very-high-frequency work a simple arrangement of parallel aluminum or copper plates separated by air dielectric might be used, as in Fig. 121, where s is the separation between the plates.
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Fig. 121.
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(w, w are wires used to connect the capacitor into the circuit).
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CHAPTER 7 Inductance and Capacitance
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When a potential di erence exists between the plates of a capacitor electrical energy is stored in the electric eld between the plates, the amount of such stored energy being 1. directly proportional to the plate area A, 2. inversely proportional to the distance s between the plates, 3. directly proportional to the dielectric constant K of the material between the plates, 4. directly proportional to the square of the potential di erence between the plates. A brief discussion of these four items follows, beginning with the plate area A and the plate separation s. From (1) and (2) it follows that, to get maximum energy storage, the plate area A should be large and the plate separation s should be small. To meet these requirements, practical capacitors are often made of alternate strips of aluminum foil and paper dielectric, as illustrated in the side view in the gure to the left below, where the dashed lines represent the edges of the strips of paper dielectric.
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After the layers of aluminum foil and paper are in place, the whole assembly is then rolled tightly into the form of a cylinder, thus producing a capacitor having large plate area and small plate separation. Wire leads are then soldered to the aluminum plates, after which the unit is enclosed in a protective cardboard cover. The required technical information is then printed on the cover, producing a nished capacitor of the form shown in the gure to the right, above. Such capacitors are convenient to use and have a large amount of capacitance, relatively, in comparison with the amount of space they occupy. Next, concerning item (3), the dielectric constant K of a material is de ned as the ratio of the capacitance of a capacitor with the material between the plates to the capacitance with vacuum between the plates, where K 1 for vacuum (also, K 1 for air, for all practical purposes). In the de nition of K, it s assumed that the dielectric material completely lls the space between the plates. Finally, in connection with item (4) we have the problem of voltage breakdown of the dielectric material, which limits the amount of potential di erence (volts) that can be safely applied between the plates of a given capacitor. Let us de ne that the DIELECTRIC STRENGTH of a material is the maximum value of ELECTRIC FIELD STRENGTH that the material can withstand without breaking down and permitting the passage of current. From the de nition of electric eld strength (volts per meter), it follows that the eld strength, E, between the plates of a capacitor is equal to the potential di erence in volts, divided by the plate separation in meters; that is E v=s volts per meter 183
where v is the potential di erence in volts between the plates, and s is the plate separation in meters. For example, suppose v 100 volts. If s 0:01 meter (1 centimeter), then E 100=0:01 10,000 volts per meter, but if s 0:001 meter (1 millimeter), then E 100=0:001 100,000 volts per meter, and so on. Equation (183) is simply a numerical
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