Inductance is the property of a coil that causes energy to be stored in a
magnetic field about the coil. The energy is stored so as to oppose any change
in current. Capacitance is similar to inductance because it also causes a
storage of energy. A capacitor is a device that stores energy in an
electrostatic field. The energy is stored so as to oppose any change in voltage.
This chapter explains the principles of an electrostatic field as it is applied
to capacitance and how capacitance opposes a change in voltage.
Opposite charges attract each other, while like electrical charges repel
each other. The reason for this is the existence of an electrostatic field. Any
charged particle is surrounded by invisible lines of force, called electrostatic
lines of force. These lines of force have some interesting characteristics:
They are polarized from positive to negative.
They radiate from a charged particle in straight lines and do not form
They have the ability to pass through any known material.
They have the ability to distort the orbits of tightly bound electrons.
An electrostatic charge can only exist in an insulator.
Figure 7-1 represents two unlike charges surrounded by
their electrostatic field. Because an electrostatic field is polarized positive
to negative, arrows are shown radiating away from the positive charge and toward
the negative charge. Stated another way, the field from the positive charge is
pushing, while the field from the negative charge is pulling. The effect of the
field is to push and pull the unlike charges together.
Figure 7-2 shows two like charges with their
surrounding electrostatic field. The effect of the electrostatic field is to
push the charges apart.
If two unlike charges are placed on opposite sides of an
atom whose outermost electrons cannot escape their orbits, the orbits of the
electrons are distorted. Figure 7-3 view A shows the
normal orbit. View B shows the same orbit in the presence
of charged particles. Since the electron is a negative charge, the positive
charge attracts the electrons, pulling the electrons closer to the positive
charge. The negative charge repels the electrons, pushing them further from the
negative charge. It is this ability of an electrostatic field to attract and to
repel charges that allows the capacitor to store energy.
A simple capacitor consists of two metal plates separated
by an insulating material called a dielectric (Figure 7-4).
One plate is connected to the positive terminal of a battery. The other plate is
connected to the negative terminal of the battery. An insulator is a material
whose electrons cannot easily escape their orbits. Due to the battery voltage, plate
A is charged positively, and plate B is charged
negatively. Thus, an electrostatic field is set up between the positive and
negative plates. The electrons on the negative plate (plate B)
are attracted to the positive charges on the positive plate (plate
View A shows an uncharged capacitor connected to a
four-position switch. With the switch in position 1, the
circuit is open, and no voltage is applied to the capacitor. Initially, each
plate of the capacitor is a neutral body. Until a difference in potential is
impressed (or a voltage applied) across the capacitor, no electrostatic field
can exist between the plates.
To charge the capacitor, the switch must be thrown to position
2, which places the capacitor across the terminals of the battery. Under the
assumed perfect conditions, the capacitor would reach full charge
instantaneously. However, in the following discussion, the charging action is
spread out over a period of time for a step-by-step analysis.
At the instant the switch is thrown to position 2 (view B),
a displacement of electrons occurs simultaneously in all parts of the circuit.
This electron displacement is directed away from the negative terminal and
toward the positive terminal of the source (the battery). A brief surge of
current will flow as the capacitor charges.
If it were possible to analyze the motion of individual electrons in this
surge of charging current, the action described below would be observed (Figure
In the charging process of a capacitor, no current flows through the
capacitor. The material between the plates of the capacitor is an insulator.
Hwoever, to an observer stationed at the source or along one of the circuit
conductors, the action appears to be a true flow of current, even though the
insulating material between the plates of the capacitor prevents the current
from having a complete path. The current that appears to flow through a
capacitor is called displacement current.
When a capacitor is fully charged and the source voltage is equaled by the
counter EMF across the capacitor, the electrostatic field between the plates of
the capacitor is maximum (Figure 7-4). Since the
electrostatic field is maximum, the energy stored in the dielectric field is
If the switch is now opened (Figure 7-8 view A), the
electrons on the upper plate are isolated. The electrons on the top plate are
attracted to the charged bottom plate. Because the dielectric is an insulator,
the electrons cannot cross the dielectric to the bottom plate. The charges on
both plates will be effectively trapped by the electrostatic field, and the
capacitor will remain charged. However, the insulating dielectric material of a
practical capacitor is not perfect, so small leakage current will flow through
the dielectric. This current will eventually dissipate the charge. However, a
high quality capacitor may hold its charge for a month or more.
To discharge a capacitor, the charges on the two plates
must be neutralized. This is done by providing a conducting path between the two
plates (Figure 7-8 view B). With the switch in
position (4), the excess electrons on the negative plate
can flow to the positive plate and neutralize its charge. When the capacitor is
discharged, the distorted orbits of the electrons in the dielectric return to
their normal positions, and the stored energy is returned to the circuit. A
capacitor does not consume power. The energy the capacitor draws from the source
is recovered when the capacitor is discharged.
CHARGE AND DISCHARGE OF A CAPACITOR
Ohm's Law states that the voltage across a resistance is equal to the
current through the resistance times the value of the resistance. This means
that a voltage is developed across a resistance only when current flows through
A capacitor can store or hold a charge of electrons. When uncharged, both
plates of the capacitor contain essentially the same number of free electrons.
When charged, one plate contains more free electrons than the other plate. The
difference in the number of electrons is a measure of the charge on the
capacitor. The accumulation of this charge builds up a voltage across the
terminals of the capacitor, and the charge continues to increase until this
voltage equals the applied voltage. The charge in a capacitor is related to the
capacitance and voltage as follows:
Q = CE
Q = charge in coulombs
C = capacitance in farads
E = EMF across the capacitor in volts
CAPACITORS IN SERIES AND IN PARALLEL
Capacitors may be connected in series or in parallel to obtain a resultant
value that may be either the sum of the individual values (in parallel) or a
value less than that of the smallest capacitance (in series).
Capacitors in Series
The overall effect of connecting capacitors in series is to move the plates
of the capacitor farther apart. A capacitor is NOT a conductor. The dielectric
is influenced by a magnetic field, and the polarity that creates the
electrostatic field can only effectively exist at the outside plates of both
capacitors. The magnetic field's influence is reduced (Figure
7-9). The junction between C1 and C2
is essentially neutral. The total capacitance of the circuit is developed
between the leftmost plate of C1 and the rightmost plate
of C2. Because these outside plates are so far apart, the
total value of the capacitance in the circuit is decreased. Solving for the
total capacitance (Ct) of capacitors connected in series is similar to solving
for the total resistance (Rt) of resistors connected in parallel.
A paper capacitor is made of flat thin strips of metal foil conductors that
are separated by waxed paper (the dielectric material). Paper capacitors usually
range in value from about 300 picofarads to about 4 microfarads. The working
voltage of a paper capacitor rarely exceeds 600 volts. Paper capacitors are
sealed with wax to prevent corrosion, leakage, and the harmful effects of
Many different kinds of outer coverings are used on paper capacitors. The
simplest is a tubular cardboard covering. Some paper capacitors are encased in
very hard plastic. These types are very rugged and can be used over a much wider
temperature range than can the tubular cardboard type. Figure
7-12 shows the construction of a tubular paper capacitor.
With an AC voltage, in the first quarter-cycle (0 to 90 degrees), the
applied AC voltage is continually increasing. If there was no inductance in the
circuit, the current would also increase during the first quarter-cycle. This
circuit does have inductance. Since inductance opposes any change in current
flow, no current flows during the first quarter-cycle. In the next quarter-cycle
(90 to 180 degrees), the voltage decreases back to zero. Current begins to flow
in the circuit and reaches a maximum value at the same instant the voltage
reaches zero. The applied voltage now begins to buildup to a maximum in the
other direction, to be followed by the resulting current. When the voltage again
reaches its maximum at the end of the third quarter-cycle (270 degrees), all
values are exactly opposite to what they were during the first half-cycle. The
applied voltage leads the resulting current by one quarter-cycle or 90 degrees.
To complete the full 360-degree cycle of the voltage, the voltage again
decreases to zero, and current builds to a maximum value.
These values do not stop at a particular instant. Until the applied voltage
is removed, current and voltage are always changing in amplitude and direction.
The sine wave can be compared to a circle (Figure 7-14).
Just as a circle can be marked off into 360 degrees, the time of one cycle of a
sine wave can be marked off into 360 degrees. Figure 7-14
shows how the current lags the voltage, in a purely inductive circuit, by 90
degrees. Figures 7-13 view A and 7-14
also show how the current and voltage are in phase in a purely resistive
circuit. In a circuit having resistance and inductance, the current lags voltage
by an amount somewhere between 0 and 90 degrees.
The four parts of Figure 7-15
show the variation of the alternating voltage and current in a capacitive
circuit for each quarter of one cycle. The solid line represents the voltage
across the capacitor, and the dotted line represents the current. The line
running through the center is the zero, or reference point, for voltage and
current. The bottom line marks off the time of the cycle in terms of electrical
degrees. Assume that the AC voltage has been acting on the capacitor for some
time before the time represented by the starting point of the sine wave in the
As the voltage proceeds toward maximum at 90 degrees, its rate of change
becomes less and less. Hence, the current must decrease toward zero. At 90
degrees, the voltage across the capacitor is maximum, and the capacitor is fully
charged. There is no further movement of electrons from plate to plate. That is
why the current at 90 degrees is zero.
At the end of the first quarter-cycle, the alternating voltage stops
increasing in the positive direction and starts to decrease. It is still a
positive voltage, but to the capacitor, the decrease in voltage means that the
plate that has just accumulated an excess of electrons must lose some electrons.
The current flow must reverse its direct ion. Figure 7-15
view B shows the current to be below the zero line (negative current
direction) during the second quarter-cycle (90 to 180 degrees).
At 180 degrees, the voltage has dropped to zero. This means that for a brief
instant the electrons are equally distributed between the two plates. The
current is maximum because the rate of change of voltage is maximum. Just after
180 degrees, the voltage has reversed polarity and starts building up its
maximum negative peak, which is reached at the end of the third quarter-cycle
(180 to 270 degrees). During this third quarter-cycle, the rate of voltage
change gradually decreases as the charge builds to a maximum at 270 degrees. At
this point, the capacitor is fully charged and carries the full impressed
voltage. Because the capacitor is fully charged, there is no further exchange of
electrons. Therefore, the current flow is zero at this point. The conditions are
exactly the same as at the end of the first quarter-cycle (90 degrees), but the
polarity is reversed.
Just after 270 degrees, the impressed voltage once again starts to decrease,
and the capacitor must lose electrons from the negative plate. It must
discharge, starting at a minimum rate of flow and rising to a maximum. This
discharging action continues through the last quarter-cycle (270 to 360 degrees)
until the impressed voltage has reached zero. At 360 degrees, it is back at the
beginning of the entire cycle, and everything starts over again.
Figure 7-15 view D shows that the current always
arrives at a certain point in the cycle 90 degrees ahead of the voltage because
of the charging and discharging action. This time and place relationship between
the current and voltage is called the phase relationship. The voltage-current
phase relationship in a capacitive circuit is exactly opposite to that of an
inductive circuit. The current through a capacitor leads voltage across the
capacitor by 90 degrees.
The current and voltage are going through their individual cycles at the
same time during the period the AC voltage is impressed. The current does not go
through part of its cycle (charging or discharging), stop, and wait for the
voltage to catch up. The amplitude and polarity of the voltage and the amplitude
and direction of the current are continually changing. Their posit ions with
respect to each other and to the zero line at any electrical instant (any degree
between 0 and 360) can be seen by reading vertically from the time-degree line.
The current swing from the positive peak at 0 degrees to the negative peak at
180 degrees is not a measure of the number of electrons or the charge on the
plates. It is a picture of the direction and strength of the current
relationship to the polarity and strength of the voltage appearing across the
Since the plates of the capacitor are changing polarity at the same rate as
the AC voltage, the capacitor seems to pass an alternating current. Actually,
the electrons do not pass through the dielectric, but their rushing back and
forth from plate to plate causes a current flow in the circuit. It is convenient
to say that the alternating current flows through the capacitor. This is not
true, but the expression avoids a lot of trouble when speaking of current flow
in a circuit containing a capacitor.
Inductive reactance and capacitive reactance act to oppose the flow of
current in an AC circuit. However, another factor, the resistance, also opposes
the flow of current. Since in practice AC circuits containing reactance also
contain resistance, the two combine to oppose the flow of current. This combined
opposition by the resistance and the reactance is called the impedance and is
represented by the symbol Z.
Since the values of resistance and reactance are given in ohms, it might at
first seem possible to determine the value of the impedance by simply adding
them together. However, it cannot be done so easily. In an AC circuit that
contains only resistance, the current and voltage will be in step (in phase) and
will reach their maximum values at the same instant. Also, in an AC circuit
containing only reactance, the current will either lead or lag the voltage by 90
degrees. When reactance and resistance are combined, the value of the impedance
will be greater than either. It is also true that the current will not be in
phase with the voltage nor will it be exactly 90 degrees out of phase with the
voltage. It will be somewhere between the in-phase and the 90 degree
out-of-phase condition. The larger the reactance compared with the resistance,
the more nearly the phase angle will approach 90 degrees. The larger the
resistance compared to the reactance, the more nearly the phase difference will
approach 0 degrees.
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