PHYS208 PHYS208 3/9 Class

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Capacitors

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Introduction to Capacitance

A capacitor is comprised of two insulated conductors. Electrical energy may be stored in a system of two conductors by moving charge from one conductor to the other with a battery. While the net charge of the system is still zero, the charge on one conductor is +Q and on the other -Q. The capacitor is said to be charged to +Q.

System of two conductors
Each conductor is an equipotential region, with the conductor charged to +Q at the higher potential. Thus there will be a definite potential difference between the conductors, which is conventionally represented by V.

We will find, via several examples in the homework and for the parallel plate capacitor today, that the potential difference is always proportional to the charge on either conductor, where the proportionality constant depends only on geometric terms: 1) the shape of the conductors and 2) their relative position. [Next class we will see that an additional parameter, known as the dielectric constant, will also enter via the insulating material surrounding the conductors.]

Definition of capacitance

The proportionality constant is called the capacitance of the system of two conductors. The capacitance is a measure of how much charge per unit volt may be stored in the system of two conductors, the capacity of the system for storing charge, hence its name.

Capacitance has dimensions of [Q] / [V]; the SI unit coulomb/volt has been given the name farad. This unit is large for typical use; more often capacitors found in the laboratory will have values expressed in microfarads (10-6 F) or picofarads (10-12 F). [Note: nanofarad is also an acceptable unit, although it is rarely used in electronics literature; 1 nF = 1000 pF = 0.001 microF.)

The capacitor has many uses -- some of these we will consider as the semester progresses:

In a few days we will consider circuits involving both capacitors and resistors.

Concept Check

Calculation of Capacitance

  1. Consider the system of two conductors, placing a charge +Q on one conductor and -Q on the other.
  2. Evaluate the electric field everywhere along some path joining the two conductors. Typically in PHYS208, this will involve a calculation using Gauss's law.
    Gauss's law
  3. Evaluate the potential difference along that same path using the relationship between V and E. Pick a path over which the line integral will be the simplest to evaluate; i.e. one in which the line integral reduces to a simple integral.
    Formula relating V to E
  4. The capacitance is the ratio of the charge deposited on one conductor to the potential difference between the two. (Convert charge density to total charge Q if needed.)

The Parallel-Plate Capacitor

Parallel-plate capacitor

The parallel-plate capacitor consists of two parallel conducting plates. Generally both plates are considered to have the same shape and area A and are separated by a distance d. The circuit schematic for the capacitor reflects this geometry.

Capacitor schematic element

To the chalkboard for
Evaluation of the Capacitance of a Parallel-Plate Capacitor
Capacitance of a parallel-plate capacitor

Demonstration of Alumnium Foil/Wax Paper Capacitor


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Last updated March 10, 1998.
Copyright George Watson, Univ. of Delaware, 1997.