Capacitors and Dielectrics Quiz

PDF page 910: A capacitor is a device used to store electric charge. Capacitors have applications ranging from filtering static out of radio reception to energy storage in heart defibrillators. Typically, commercial capacitors have two conducting parts close to one another, but not touching, such as those in Figure 19.12. (Most of the time an insulator is used between the two plates to provide separation—see the discussion on dielectrics below.) When battery terminals are connected to an initially uncharged capacitor, equal amounts of positive and negative charge, and , are separated into its two plates. The capacitor remains neutral overall, but we refer to it as storing a charge in this circumstance.

PDF page 910: A capacitor is a device used to store electric charge.

PDF page 910: A capacitor is a device used to store electric charge. Capacitors have applications ranging from filtering static out of radio reception to energy storage in heart defibrillators. Typically, commercial capacitors have two conducting parts close to one another, but not touching, such as those in Figure 19.12. (Most of the time an insulator is used between the two plates to provide separation—see the discussion on dielectrics below.) When battery terminals are connected to an initially uncharged capacitor, equal amounts of positive and negative charge, and , are separated into its two plates. The capacitor remains neutral overall, but we refer to it as storing a charge in this circumstance.

PDF page 911: A system composed of two identical, parallel conducting plates separated by a distance, as in Figure 19.13, is called a parallel plate capacitor. It is easy to see the relationship between the voltage and the stored charge for a parallel plate capacitor, as shown in Figure 19.13. Each electric field line starts on an individual positive charge and ends on a negative one, so that there will be more field lines if there is more charge. (Drawing a single field line per charge is a convenience, only. We can draw many field lines for each charge, but the total number is proportional to the number of charges.) The electric field strength is, thus, directly proportional to .

PDF page 911: electric field strength is proportional to the density of field lines, it is also proportional to the amount of charge on the capacitor. The field is proportional to the charge: 19.45 where the symbol means “proportional to.” From the discussion in Electric Potential in a Uniform Electric Field, we know that the voltage across parallel plates is . Thus, 19.46

PDF page 911: . The charge stored in a capacitor is given by 19.48 This equation expresses the two major factors affecting the amount of charge stored. Those factors are the physical characteristics of the capacitor, , and the voltage, . Rearranging the equation, we see that capacitance is the amount of charge stored per volt, or

PDF page 912: Capacitance is the amount of charge stored per volt, or

PDF page 912: The unit of capacitance is the farad (F), named for Michael Faraday (1791–1867), an English scientist who contributed to the fields of electromagnetism and electrochemistry. Since capacitance is charge per unit voltage, we see that a farad is a coulomb per volt, or

PDF page 912: The unit of capacitance is the farad (F), named for Michael Faraday (1791–1867), an English scientist who contributed to the fields of electromagnetism and electrochemistry. Since capacitance is charge per unit voltage, we see that a farad is a coulomb per volt, or

PDF page 912: A 1-farad capacitor would be able to store 1 coulomb (a very large amount of charge) with the application of only 1 volt. One farad is, thus, a very large capacitance. Typical capacitors range from fractions of a picofarad to millifarads .

PDF page 912: A 1-farad capacitor would be able to store 1 coulomb (a very large amount of charge) with the application of only 1 volt. One farad is, thus, a very large capacitance. Typical capacitors range from fractions of a picofarad to millifarads .

PDF page 913: It can be shown that for a parallel plate capacitor there are only two factors ( and ) that affect its capacitance . The capacitance of a parallel plate capacitor in equation form is given by

PDF page 913: is the area of one plate in square meters, and is the distance between the plates in meters. The constant is the permittivity of free space; its numerical value in SI units is . The units of F/m are equivalent to . The small numerical value of is related to the large size of the farad. A parallel plate capacitor must have a large area to have a capacitance approaching a farad. (Note that the above equation is valid when the parallel plates are separated by air or free space. When another material is placed between the plates, the equation is modified, as discussed below.)

PDF page 912: The parallel plate capacitor shown in Figure 19.15 has two identical conducting plates, each having a surface area , separated by a distance (with no material between the plates). When a voltage is applied to the capacitor, it stores a charge , as shown. We can see how its capacitance depends on and by considering the characteristics of the Coulomb force. We know that like charges repel, unlike charges attract, and the force between charges decreases with distance. So it seems quite reasonable that the bigger the plates are, the more charge they can store—because the charges can spread out more. Thus should be greater for larger . Similarly, the closer the plates are together, the greater the attraction of the opposite charges on them. So should be greater for smaller .

PDF page 912: depending upon purpose and size. Insulating materials, called dielectrics, are commonly used in their construction, as discussed below.

PDF page 914: The previous example highlights the difficulty of storing a large amount of charge in capacitors. If is made smaller to produce a larger capacitance, then the maximum voltage must be reduced proportionally to avoid breakdown (since ). An important solution to this difficulty is to put an insulating material, called a dielectric, between the plates of a capacitor and allow to be as small as possible. Not only does the smaller make the capacitance greater, but many insulators can withstand greater electric fields than air before breaking down. There is another benefit to using a dielectric in a capacitor. Depending on the material used, the capacitance is greater than that given by the equation by a factor , called the dielectric constant. A parallel plate capacitor with a dielectric between its plates has a capacitance given by

PDF page 914: Values of the dielectric constant for various materials are given in Table 19.1. Note that for vacuum is exactly 1, and so the above equation is valid in that case, too. If a dielectric is used, perhaps by placing Teflon between the plates of the capacitor in Example 19.8, then the capacitance is greater by the factor , which for Teflon is 2.1.