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pends on the dielectric constant of the material between the plates. A vacuum has a dielectric constant of 1; some substances have dielectric constants that multiply the effective capacitance many times.
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The Unit of Capacitance
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When a battery is connected between the plates of a capacitor, the potential difference between the plates builds up at a rate that depends on the capacitance. The greater the capacitance, the slower the rate of change of voltage in the plates. The unit of capacitance is an expression of the ratio between the current that flows and the rate of voltage change between the plates as the plates become charged. A capacitance of 1 farad (1 F) represents a current flow of 1 A while there is a voltage increase of 1 V/s. A capacitance of 1 F also results in 1 V of potential difference for an electric charge of 1 C. The farad is a huge unit of capacitance. You ll almost never see a capacitor with a value of 1 F. Commonly employed units of capacitance are the microfarad ( F) and the picofarad (pF). A capacitance of 1 F represents 0.000001 (10 6) F, and 1 pF is a millionth of a microfarad, or 0.000000000001 (10 12) F. Physically small components can be made to have fairly large capacitance values. Conversely, some capacitors with small values take up large physical volumes. The physical size of a capacitor, if all other factors are held constant, is proportional to the voltage that it can handle. The higher the rated voltage, the bigger the component.
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With capacitors, there is rarely any mutual interaction. This makes capacitors easier to work with than inductors. We don t have to worry about mutual capacitance very often, the way we have to be concerned about mutual inductance when working with wire coils. Capacitors in series add together like resistors or inductors in parallel. Suppose you have several capacitors with values C1, C2, C3, . . . , Cn connected in series. You can find the reciprocal of the total capacitance, 1/C, using the following formula: 1/C = 1/C1 + 1/C2 + 1/C3 + . . . + 1/Cn The net capacitance of the series combination, C, is found by taking the reciprocal of the number you get for 1/C. If two or more capacitors are connected in series, and one of them has a value that is tiny compared with the values of all the others, the net capacitance is roughly equal to the smallest capacitance.
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Problem 11-1 Suppose two capacitors, with values of C1 = 0.10 F and C2 = 0.050 F, are connected in series (Fig. 11-3). What is the net capacitance Using the preceding formula, first find the reciprocals of the values. They are 1/C1 = 10 and 1/C2 = 20. Then 1/C = 10 + 20 = 30, and C = 1/30 = 0.033 F. Note that we can work with reciprocal capacitances in this calculation only because the values of the components are specified in the same units.
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178 Capacitance
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11-3 Capacitors in series.
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Illustration for Problem 11-1.
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Problem 11-2 Suppose two capacitors with values of 0.0010 F and 100 pF are connected in series. What is the net capacitance In this case, you must convert to the same size units before doing any calculations. A value of 100 pF represents 0.000100 F. Thus, C1 = 0.0010 F and C2 = 0.000100 F. The reciprocals are 1/C1 = 1000 and 1/C2 = 10,000. Therefore, 1/C = 1000 + 10,000 = 11,000, so C = 1/11,000 = 0.000091 F. (You might rather say it s 91 pF.) Problem 11-3 Suppose five capacitors, each of 100 pF, are in series. What is the total capacitance If there are n capacitors in series, all of the same value so that C1 = C2 = C3 = . . . = Cn, the net capacitance C is equal to 1/n of the capacitance of any of the components alone. Because there are five 100-pF capacitors here, the total is C = 100/5 = 20.0 pF.
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