19.5 Capacitors and dielectrics

Learning objectives

By the end of this section, you will be able to:

• 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 [link] . (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, $+Q$ and $–Q$ , are separated into its two plates. The capacitor remains neutral overall, but we refer to it as storing a charge $Q$ in this circumstance.

The amount of charge $Q$ 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 [link] , 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 [link] . 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 $Q$ .