#
PHYS208 3/9 Class

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## Capacitors

### 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*.

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.]

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:

- energy storage
- power conversion
- filter circuits
- timing circuits

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

### Calculation of Capacitance

- Consider the system of two conductors,
placing a charge
*+Q* on one conductor and *-Q* on the other.
- Evaluate the electric field everywhere along some path joining the two conductors.
Typically in PHYS208, this will involve a calculation using Gauss's law.

- 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.

- 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

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.

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Comments, suggestions, or requests to
ghw@udel.edu.
"http://www.physics.udel.edu/~watson/phys208/clas0309.html"

Last updated March 10, 1998.

Copyright George Watson, Univ. of Delaware, 1997.