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Capacitance

One of the commonly used devices in electronic circuits is the capacitor. It can be used to store charge, block direct current, construct a filter, etc. Such capacitors are usually just two conductors separated by some dielectric medium. On this page, I will try to explain what capacitance is, why it comes about, and then do a quick review of the steps used to calculate capacitance.

What is capacitance ?

Capacitance is formally defined as the ratio of stored charge to the voltage applied to a device(often a set of parallel plates). This is:

           Q                    Q= stored charge in C
C = --------              C= capacitance in F (1F = 1C/1V)
           V                     V= applied voltage in V

Capacitance, then, can be viewed as the ability of a device to store charge, It is usually constant, depending only upon the geometry of the device in question -- not upon the applied voltage -- up to the point where the device beings to break down. Since the capacitance is constant, the stored charge must increase when the applied voltage increases.

Why does capacitance exist?

In order for a device to have a capacitance, it must be able to store a rather large group of like charges. Since like charges tend to repel one another, we must apply a force to the particles in order for the storage to be effective. Without this outside force, the particles would simply disperse.

The outside force used is the applied voltage, V. If you recall, a voltage indicates the presence of an electric field, and an electric field is a field of force. This electric field, which is caused by the opposite charges that appear on the plates of the capacitor, is the energy that the capacitor stores. The capacitance of an object is a measure of how much energy can be stored in this way before the repulsive forces between like particles on each plate balance the attractive forces between particles on different plates.

Calculating Capacitance

The main point to remember when calculating the capacitance for a given system is that capacitance, in general, is determined by geometry. Thus, we can derive relationships for a generic situation of a given geometry and use this formula for specific problems.

For example, the capacitance of a parallel plate capacitor that consists of two plates of surface area S seperated by a distance d with a dielectric material with permittivity epsilon is given by:

                  S
C = epsilon ---  Farads
                  d

Knowing this, you can solve a great number of problems involving parallel plate capacitors. But you need to know how to derive this result. A good procedure for calculating capacitace appears in David K. Cheng's Fundamentals of Engineering Electromagnetics:

Ę—Choose an appropriate coordinate system.
Ę—Assume +Q and -Q charges on the conductors.
Ę—Find the electric field E by some convenient means (like Gauss's Law)
Ę—Find the voltage V between the two surfaces by using the definition of the electrical potential by integrating from the -Q surface to the +Q surface.
Ę—Find C = Q/V

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