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  • 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 dielectric.
  • Determine capacitance given charge and voltage.

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 size 12{Q} {} and Q size 12{Q} {} , are separated into its two plates. The capacitor remains neutral overall, but we refer to it as storing a charge Q size 12{Q} {} in this circumstance.

Capacitor

A capacitor is a device used to store electric charge.

Part a of the figure shows a charged parallel plate capacitor and part b of the figure shows a charged rolled capacitor. In the parallel plate capacitor, two rectangular plates are kept vertically facing each other separated by a distance d. These two plates are the conducting parts of the capacitor. One plate is connected to the positive terminal of the battery, and the other is connected to the negative terminal of the battery. One plate has a positive charge, plus Q, and the other plate has a negative charge, negative Q. The rolled capacitor has conducting parts in the form of a spiral coil. Between the two conducting parts is insulating material, also in the form of a coil. The conducting and insulating materials of the capacitor are rolled together to form a spiral. The outer conducting coil is connected to the positive terminal of the battery, and the inner coil is connected to the negative terminal of the battery.
Both capacitors shown here were initially uncharged before being connected to a battery. They now have separated charges of + Q size 12{Q} {} and Q size 12{Q} {} on their two halves. (a) A parallel plate capacitor. (b) A rolled capacitor with an insulating material between its two conducting sheets.

The amount of charge Q size 12{Q} {} 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 Q size 12{Q} {} A capacitor can store

The amount of charge Q size 12{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 size 12{Q} {} .

Two metal plates are positioned vertically facing each other. The plates are the conducting parts of a capacitor. The plate on the left-hand side is connected to the positive terminal of a battery, and the plate on the right-hand side is connected to the negative terminal of the battery. There is an electric field between the two plates of the capacitor. The electric field lines emanate from the positively charged plate and end on the negatively charged plate. The electric field E is proportional to the charge Q.
Electric field lines in this parallel plate capacitor, as always, start on positive charges and end on negative charges. Since the 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:

E Q , size 12{E prop Q} {}

where the symbol size 12{prop} {} means “proportional to.” From the discussion in Electric Potential in a Uniform Electric Field , we know that the voltage across parallel plates is V = Ed size 12{V= ital "Ed"} {} . Thus,

V E . size 12{V prop E} {}

It follows, then, that V ∝ Q size 12{Va`Q} {} , and conversely,

Q V . size 12{Q prop V} {}

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     C size 12{C} {} to be such that the charge Q size 12{C} {} stored in a capacitor is proportional to C size 12{C} {} . The charge stored in a capacitor is given by

Practice Key Terms 6

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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