Learning Objectives
By the end of this section, you will be able to do the following:
- Describe the action of a capacitor and define capacitance
- Explain parallel plate capacitors and their capacitances
- Discuss the process of increasing the capacitance of a capacitor with a dielectric
- Determine capacitance given charge and voltage
The information presented in this section supports the following AP® learning objectives and science pracitces:
- 4.E.4.1 The student is able to make predictions about the properties of resistors and/or capacitors when placed in a simple circuit based on the geometry of the circuit element and supported by scientific theories and mathematical relationships. (S.P. 2.2, 6.4)
- 4.E.4.2 The student is able to design a plan for the collection of data to determine the effect of changing the geometry and/or materials on the resistance or capacitance of a circuit element and relate results to the basic properties of resistors and capacitors. (S.P. 4.1, 4.2)
- 4.E.4.3 The student is able to analyze data to determine the effect of changing the geometry and/or materials on the resistance or capacitance of a circuit element and relate results to the basic properties of resistors and capacitors. (S.P. 5.1)
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 2.18. 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.
Capacitor
A capacitor is a device used to store electric charge.
The amount of charge a capacitor can store depends on two major factors—the voltage applied and the capacitor’s physical characteristics, such as its size.
The Amount of Charge QQ size 12{Q} {} a Capacitor Can Store
The amount of charge a capacitor can store depends on two major factors—the voltage applied and the capacitor’s physical characteristics, such as its size.
A system composed of two identical, parallel conducting plates separated by a distance, as in Figure 2.19, 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 2.19. 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
The field is proportional to the charge
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,
It follows, then, that and conversely,
This is true in general: The greater the voltage applied to any capacitor, the greater the charge stored in it.
Different capacitors will store different amounts of charge for the same applied voltage, depending on their physical characteristics. We define their capacitance to be such that the charge stored in a capacitor is proportional to The charge stored in a capacitor is given by
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
Capacitance
Capacitance is the amount of charge stored per volt, or
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
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
Figure 2.20 shows some common capacitors. Capacitors are primarily made of ceramic, glass, or plastic, depending upon purpose and size. Insulating materials, called dielectrics, are commonly used in their construction, as discussed below.