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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:
stored charge in C
C = --------
C= capacitance in F (1F = 1C/1V)
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
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.
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:
C = epsilon --- Farads
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
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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