Just like the Resistor, the Capacitor, sometimes
referred to as a Condenser, is a passive device. It is one of the three basic
passive devices which include resistors, capacitors, and inductors.
basic form, a capacitor consists of two conductive (metal) plates which are not
connected or touch each other, but are electrically separated either by air or
by some form of insulating material such as paper, mica, ceramic or
plastic. This insulating material spans
the entire area of the plates and is called a Dielectric.
The plates have
terminals on each one for connection, and they don’t have to be flat, but could
be formed as cylinders, spherical shapes, etc. For larger capacitor values, the
"plates" may be strips of metal foil, sandwiched around a flexible
insulating medium and rolled up for compactness. As long as there are two
conductive areas separated by a dielectric, it could be considered a capacitor.
When a voltage is applied to the two terminals of
a capacitor, there is a rapid inrush of current that is similar to
short-circuiting a battery. However, this is only a short pulse of current that
allows a certain amount of charge to build up across the plates because of the
interaction of the electric field generated between the plates.
operates in a manner very similar to a battery. The capacitor can be “charged”
by applying voltage to it through a current limiting resistor. When the voltage is then removed, a capacitor
will hold the charge indefinitely unless there is a resistive load between the
As voltage is applied to the terminals, a concentrated
field flux is generated between the plates, which allows a significant difference
of charge (free electrons) to develop between the two plates. Capacitors store
the potential energy of accumulated charge (or electrons) in the form of an
electric field between the plates.
This field is sometimes called an
"electrostatic field". Energy storage in a capacitor is a function of
the voltage between the plates, and has nothing to do with current, because
current can’t flow in a dielectric, as this is where the energy is stored. This
behavior is quite different than resistors, which dissipate energy in the form
of heat. Capacitors don’t dissipate any energy except through a small leakage
current through the dielectric, which is a resistive element.
The currents in a
capacitor are mainly for charging and discharging the capacitor by increasing
or decreasing the voltage across its terminals. As energy is stored by
increasing the voltage, that same energy is released through resistive loads as
the voltage is decreased of removed.
ability of a capacitor to store charge on its plates in the form of an
electrostatic field as a function of voltage is called the Capacitance of the
Capacitance is also is also a measure of the ability to resist
changes in the voltage applied. In other words, it is a tendency to try to
maintain voltage at a constant level. Capacitance is measured in Farads, where
one Farad is defined as the capacitance when one Coulomb is stored on the
plates when one volt is applied. This is
a very large unit, and not very practical, so micro-Farad (uF), nano-Farad (nF)
and pico-Farad (pF, 10-12 Farads) are generally used instead as a
measure of capacitance.
a capacitor has stored energy there is a charge built up on both plates, and
these charges are equal but with opposite polarity. The capacitor's capacitance
(C) is a measure of the amount of charge (Q) stored on each plate for a given
potential difference or voltage (V) which appears between the plates:
C = Q / V
The amount of capacitance within a capacitor is a
function three basic dimensions of the capacitor’s construction. These factors
will determine capacitance by affecting how much electric charge can be stored
on the two plates for a given voltage as the dimension is varied.
Plate area: The amount of capacitance is directly
proportional to plate area, so that a larger plate are means higher
capacitance, and less plate area means less.
The reasoning for this is that the amount of field flux (charge
collected on the plates) generated increases with plate size for a given
voltage between the plates, as this provides more area for charge to build up.
Plate spacing: The
amount of capacitance is inversely proportional to plate spacing, so wide
spacing gives less capacitance, while closer plate spacing gives greater
capacitance. This is because the field flux is proportional to the voltage
across the capacitor divided by the distance between the plates. A greater
field flux will allow more charge to build up on the plates, which results in a
larger capacitance value.
Dielectric material: The
larger the permittivity of the dielectric, the larger the capacitance. And less
permittivity dielectric allows less capacitance. The permittivity of a
dielectric in a capacitor is the relation between the field flux and the
voltage applied, which is very similar to the relation between current and
voltage in a resistor (conductivity). Some materials have greater permittivity
than others, which allows more field flux to be generated for a given amount of
field force (applied voltage). This will then allow more capacitance with the
given plate dimensions, and allow more charge to collect on the plates. More
will be explained on this later.
These three factors can be combined into one
equation which will provide an approximation of capacitance: C = εA/d,
where ε =Permittivity of dielectric, A=area of the plate in square meters, and
d=distance between plates in meters.
There is a definite mathematical relationship
between voltage and current for a capacitor, even as there is a relationship
between voltage and current for a resistor.
For a resistor, this is essentially
a linear relationship; whereas in a capacitor, it’s not. There is no
“resistance” or “conductivity” in a capacitor like there is in a resistor.
capacitor, the current is proportional to the change in the voltage
applied instead of the voltage itself. So for a resistor, the equation would be
I = V/R, while for a capacitor, the equation becomes: I = C x dV/dt,
where I = Current through the capacitor, C = Capacitance in Farads,
dV/dt = Rate of voltage change (volts
The “time” variable becomes an important factor for capacitors,
while it has no effect on resistors. This equation can be derived from the
basic equation C = Q/V by assuming that I = dQ/dt, so C x dV = dQ, and C x
dV/dt = dQ/dt, which reduces to I = C x dV/dt.
The amount of energy stored within the
electrostatic field or a capacitor is derived below. The power (P) is derived
from the equation for current, and the power integrated over a time when
voltage is applied to build up charge yields the energy stored in the
The same result would be obtained if the energy
was derived from the equation C = Q/V, and integrating over charge instead of
Whenever an electric voltage exists between two
separated conductors, an electric field is present within the space between
those conductors which stores the potential energy. This field doesn’t even
have to have any mass, and could even be empty vacuum.
Electric fields have two
units of measure: a field force and a field flux. Field force and flux are
roughly analogous to voltage and current through a conductor, respectively.
space between the two conductors has a certain amount of opposition to the
field flux as the field force is applied, similar to the opposition a resistor
has to current (flow of electrons) when voltage is applied. The amount of field
flux that develops in a material is proportional to the amount of field force
applied, divided by the amount of opposition to flux, similar to the I = V/R
equation for a resistor, although flux can even exist in empty space, and
currents must have a conductive material to pass through.
Just as the type of conducting material
determines its resistance to electric current in a resistor, the type of
insulating material separating two conductors determines the specific opposition
to field flux.
The value of permittivity used in the above
equation (C = εA/d) is a measure of this opposition to field flux. The
resistance value of a resistor is calculated in the same way from a value for
conductivity. For empty space (vacuum), the value for permittivity (ε) is 8.84
x 10-12 F/m. A vacuum would
not be practical for use as a dielectric, so other insulating materials with a
relatively high permittivity are used instead. Some of the more common
materials are air, paper, polyester, polypropylene, Mylar, ceramic, glass, oil,
The factor by which the dielectric material, or
insulator, increases the capacitance of the capacitor compared to a pure vacuum
is called the Dielectric Constant. This
is a dimensionless quantity, since it is relative to a vacuum, and the
dielectric constant for a few common materials would be: Pure Vacuum = 1.0000,
Air = 1.0005, Paper = 2.5 to 3.5, Glass = 3 to 10, Mica = 5 to 7, and Metal
Oxide Powders = 6 to 20.
Since a capacitor
can store electricity, or electrical energy, and resist voltage change, it can
perform many useful functions in variety of circuits. Its main use is as a
filter, as it tends to pass alternating current (AC) and block direct current
(DC). From the current equation, it is easily shown that for AC circuits
(sinusoidal waveforms), there is a phase shift, as the voltage "lags"
the current by 90 degrees. It can be shown that a capacitor has an impedance on
the imaginary axis on a complex number plane, while a resistor has an impedance
along the real axis.
The next article on
capacitors will discuss the various types of capacitors and what kinds of
circuits they are typically used for.