Electrical Capacitance

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CAPACITANCE

INTRODUCTION

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.

ELECTROSTATIC FIELD

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:

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.

SIMPLE CAPACITOR

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 A).

The orbits of the electrons are distorted in the electrostatic field. This distortion occurs because the electrons in the dielectric are attracted to the top plate while being repelled from the bottom plate. When switch S1 is opened, the battery is removed from the circuit, and the charge is retained by the capacitor. This occurs because the dielectric material is an insulator, and electrons in the bottom plate (negative charge) have no path to reach the top plate (positive charge). The distorted orbits of the atoms of the dielectric plus the electrostatic force of attraction between the two plates hold the positive and negative charges in their original position. Thus, the energy that came from the battery is now stored in the electrostatic field of the capacitor. Figure 7-5 shows the symbol for capacitor. The symbol is composed of two plates separated by a space that represents the dielectric. The curved plate of the symbol represents the plate that should be connected to a negative polarity.

The Farad

Capacitance is measured in units called farads. A 1-farad capacitor stores 1 coulomb (a unit of charge [Q] equal to 6.242 times 10 to the 18th electrons) of charge when a potential of 1 volt is applied across the terminals of a capacitor. This can be expressed by the formula:

C (farads) = Q (coulombs)
                        E (volts)

The farad is a very large unit of measurement of capacitance. For convenience, the microfarad or the picofarad is used. Capacitance is a physical property of the capacitor. It does not depend on circuit characteristics of voltage, current, and resistance. A given capacitor always has the same value of capacitance (farads) in one circuit as in any other circuit in which it is installed.

FACTORS AFFECTING THE VALUE OF CAPACITANCE

The value of capacitance of a capacitor depends upon three factors:

Plate area affects the value of capacitance in the same way that size of a container affects the amount of liquid that can be held by the container. A capacitor with a large plate area can store more charges than a capacitor with a small plate area. Simply stated, the larger the plate area, the larger the capacitance.

The second factor affecting capacitance is the distance between the plates. Electrostatic lines of force are strongest when the charged particles that create them are close together. When the charged particles are moved further apart, the lines of force are weakened, and the ability to store a charge decreases.

The third factor affecting capacitance is the dielectric constant of the insulating material between the plates of a capacitor. The various insulating materials used as the dielectric in a capacitor differ in their ability to respond to (or pass) electrostatic lines of force. A dielectric material, or insulator, is rated as to its ability to respond to electrostatic lines of force in terms of a figure called the dielectric constant. A dielectric material with a high dielectric constant is a better insulator than a dielectric material with a low dielectric constant. Dielectric constants for some common materials are listed in Table 7-1.

Since a vacuum is the standard reference, it is assigned a dielectric constant of one. The dielectric constants for all other materials are compared to that of a vacuum. Since the dielectric constant for air has been determined to be about the same as for a vacuum, the dielectric constant of air is also considered to be equal to one.

CAPACITOR RATING

In selecting or substituting a capacitor for use, consideration must be given to the value of capacitance desired and the amount of voltage to be applied across the capacitor. If the voltage applied across the capacitor is too great, the dielectric will break down, and arcing will occur between the capacitor plates. When this happens, the capacitor becomes a short circuit, and the flow of current through it causes damage to other electrical components. A capacitor is not a conductor. It is used as a power source that delivers current to the circuit at a different time than it would have originally received it. Each capacitor has a voltage rating (a working voltage) that should never be exceeded.

The working voltage of a capacitor is the maximum voltage that can be steadily applied without danger of breaking down the dielectric. The working voltage depends on the type of material used as the dielectric and on the thickness of the dielectric. (A high-voltage capacitor that has a thick dielectric must have a relatively large plate area to have the same capacitance as a similar low-voltage capacitor having a thin dielectric.) The working voltage also depends on the applied frequency because losses and the resultant heating effect increase as the frequency increases.

EXPEDIENT REPLACEMENT

In the event of an electrical casualty on a single-phase motor, certain expedient capacitor replacements can be made. The following is a guide for capacitor replacement when the exact replacement part is unavailable:

Remember, as with all expedient repairs, Army marine equipment must be returned to its original, like new, condition upon arrival at port.

A capacitor that may be safely charged to 500 volts DC cannot be safely subjected to an alternating voltage or a pulsating direct voltage having the same effective value of 500 volts. In practice, select a capacitor so that its working voltage is at least 50 percent greater than the highest effective voltage applied to it.

CAPACITOR LOSSES

Power loss in a capacitor may be attributed to dielectric hysteresis and electric leakage. Dielectric hysteresis is an effect in a dielectric material similar to the hysteresis found in a magnetic material. It is the result of changes in orientation of electron orbits in the dielectric because of the rapid reversals of the polarity of the line voltage. The amount of power loss due to dielectric hysteresis depends on the type of dielectric used. A vacuum dielectric has the smallest power loss.

Dielectric leakage occurs in a capacitor as the result of leakage of current through the dielectric. Normally, it is assumed that the dielectric will effectively prevent the flow of current through the capacitor. Although the resistance of the dielectric is extremely high, a minute amount of current does flow. Ordinarily this current is so small that for all practical purposes it is ignored. However, if the leakage through the dielectric is abnormally high, there will be a rapid loss of charge and an overheating of the capacitor.

The power loss of a capacitor is determined by loss in the dielectric. If the loss is negligible and the capacitor returns the total charge to the circuit, it is considered to be a perfect capacitor with a loss of zero.

CHARGING AND DISCHARGING A CAPACITOR

Charging

To better understand the action of a capacitor in conjunction with other components, the charge and discharge actions of a purely capacitive circuit are analyzed first. For ease of explanation, the capacitor and voltage source in Figure 7-6 are assumed to be perfect (no internal resistance), although this is impossible in practice.

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 7-7).

At the instant the switch is closed, the positive terminal of the battery extracts an electron from the bottom conductor. The negative terminal of the battery forces an electron into the top conductor. At this same instant, an electron is forced into the top plate of the capacitor, and another is pulled from the bottom plate. Thus, in every part of the circuit, a clockwise displacement of electrons occurs simultaneously.

As electrons accumulate on the top plate of the capacitor and others depart from the bottom plate, a difference of potential develops across the capacitor. Each electron forced onto the top plate makes that plate more negative, while each electron removed from the bottom causes the bottom plate to become more positive. The polarity of the voltage that builds up across the capacitor is such as to oppose the source voltage. The source voltage (EMF) forces current around the circuit of Figure 7-7 in a clockwise direction. The EMF developed across the capacitor, however, has a tendency to force the current in a counterclockwise direction, opposing the source EMF. As the capacitor continues to charge, the voltage across the capacitor rises until it is equal to the source voltage. Once the capacitor voltage equals the source voltage, the two voltages balance one another, and current ceases to flow in the circuit.

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 maximum.

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 review briefly, when a capacitor is connected across a voltage source, a surge of charging current flows. This charging current develops a CEMF across the capacitor which opposes the applied voltage. When the capacitor is fully charged, the CEMF equals the applied voltage, and charging current ceases. At full charge, the electrostatic field between the plates is at maximum intensity, and the energy stored in the dielectric is maximum. If the charged capacitor is disconnected from the source, the charge will be retained for some time. The length of time the charge is retained depends on the amount of leakage current present. Since electrical energy is stored in the capacitor, a charged capacitor can act as a source EMF.

Discharging

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 resistance.

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

Where:

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.

Note the similarity between the formulas for Rt and Ct:

If the circuit contains more than two capacitors, use the above formula. If the circuit contains only two capacitors, use the following formula:

NOTE: All values for Ct, C1, C2, C3, . . . Cn should be in farads. It should be evident from the above formulas that the total capacitance of capacitors in series is less than the capacitance of any of the individual capacitors.

Capacitors in Parallel

When capacitors are connected in parallel, one plate of each capacitor is connected directly to one terminal of the source, while the other plate of each capacitor is connected to the other terminal of the power source. Figure 7-10 shows all the negative plates of the capacitors connected together and all the positive plates connected together. Ct, therefore, appears as a capacitor with a plate area equal to the sum of all the individual plate areas. Capacitance is a direct function of plate area. Connecting capacitors in parallel effectively increases plater area and thereby increases total capacitance.

For capacitors connected in parallel, the total capacitance is the sum of all the individual capacitors. The total capacitance of the circuit may be calculated using this formula:

Ct = C1 + C2 + C3 + . . . Cn

Where: All capacitances are in the same units.

FIXED CAPACITOR

A freed capacitor is constructed so that it possesses a freed value of capacitance and cannot be adjusted. A fixed capacitor is classified according to the type of the material used as its dielectric, such as paper, oil, mica, or electrolyte. Two capacitors commonly found in the marine field are the electrolytic capacitor and the paper capacitor.

Electrolytic Capacitor

The electrolytic capacitor is used where a large amount of capacitance is required. As the name implies, an electrolytic capacitor contains electrolyte. This electrolyte can be in the form of a liquid (wet electrolytic capacitor). The wet electrolytic capacitor is no longer in popular use because of the care needed to prevent spilling of the electrolyte.

A dry electrolytic capacitor consists essentially of two metal plat es separated by the electrolyte. The capacitance values and the voltage ratings of the capacitor are generally printed on the side of the case.

Internally, the electrolytic capacitor is constructed similarly to the paper capacitor. The positive plate consists of aluminum foil covered with an extremely thin film of oxide. This thin oxide film, which is formed by an electrochemical process, acts as the dielectric of the capacitor. Next to and in contact with the oxide strip is paper or gauze that has been impregnated with a paste-like electrolyte. The electrolyte acts as the negative plate of the capacitor. A second strip of aluminum foil is then placed against the electrolyte to provide electrical contact to the negative electrode. When the three layers are in place, they are rolled up into a cylinder (Figure 7-11).

The DC electrolytic capacitor has two disadvantages compared to a paper capacitor. The electrolyte type is polarized and has a low-leakage resistance. This means that should the positive plate be accidentally connected to the negative terminal of the source, the thin oxide film dielectric will dissolve, and the capacitor will become a conductor. That is, it will short. These electrolytic capacitors are very comon in DC systems. DC electrolytic capacitors have the polarity indicated on the casing or capacitor terminals. They should never be connected into an AC circuit. The polarity must be observed. The electrolytic capacitor could explode if these precautions are not observed.

The AC electrolytic capacitor has been specially developed for single-phase AC motors. These capacitors, which are generally encased in plastic, are called start capacitors. They have 20 times the capacitance of motor-run capacitors. The start capacitors are small in size and high in capacitance. Not intended for constant use, the start capacitor can be readily removed from the motor's starting circuit after a short time.

These AC capacitors effectively provide a two-phase current to the single-phase motor. This is done by allowing the initial source current to arrive in one winding before it arrives in the other single-phase motor windings. Chapter 17 discusses the operation of this capacitor at length.

Paper Capacitor

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 moisture.

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.

Paper capacitors are generally used for run capacitors in single-phase motors. These capacitors are metal-cased and have a low capacitance for constant operation in the AC circuit. The larger size and lower capacitance is necessary for effective heat transfer.

Oil capacitors are often used in high-power electrical equipment. An oil-filled capacitor is nothing more than a paper capacitor immersed in oil. Since oil-impregnated paper has a high dielectric constant, it can be used to produce capacitors with a high capacitance value. Many capacitors will use oil with another dielectric material to prevent arcing between plates. If arcing should occur between the plates of an oil-filled capacitor, the oil will tend to reseal the hole caused by the arcing. Such a capacitor is called a self-healing capacitor.

Polychlorinated biphenyl or PCBs were commonly used to impregnate capacitors. This oil is used as a lubricant, for heat transfer, and as a fluid for a tire-resistant application. PCBs are toxic. If a capacitor is leaking, remove it from the circuit immediately. Personnel should not come in contact with the liquid. Treat it as if it is a very hazardous material, and dispose of it according to local regulations.

CAPACITIVE AND INDUCTIVE REACTANCE

When the voltage and current values are changing through a cycle together so that the values begin, peak, and change direction together, they are in phase. When these same values fail to stay in phase because one value leads or lags the other value, the circuit is said to be out of phase. The deviation from the simultaneous starting, peaking, and directional change of in-phase values is a direct result of the effects capacitance and inductance have on the circuit.

A circuit having pure resistance (if such a circuit could exist) would have the alternating current and voltage rising, falling, and changing direction together. Figure 7-13 view A shows the sine waves for current and voltage in a purely resistive AC circuit. The voltage and current do not have the same amplitude, but they are in phase.

In the case of a circuit having inductance, the opposing force of the counter EMF would be enough to prevent the current from remaining in phase with the applied voltage. In a DC circuit containing pure inductance, the current took time to rise to a maximum even though the full applied voltage was immediately at maximum. View B shows the waveforms for a purely inductive AC circuit in steps of quarter-cycles.

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.

INDUCTIVE REACTANCE

When the current flowing through an inductor continuously reverses itself, as in the case of an AC system, the inertia of the CEMF is greater than with DC. The greater the amount of inductance, the greater the opposition from this inertia effect. Also, the faster the reversal of current, the greater this inertia opposition. This opposing force that an inductor presents to the flow of alternating current cannot be called resistance, since it is not the result of friction within a conductor. The name given to it is inductive reactance because it is the reaction of the inductor to alternating current. Inductive reactance is measured in ohms, and its symbol is XL.

The induced voltage in a conductor is proportional to the rate at which magnetic lines of force cut the conductor. The greater the rate (the higher the frequency), the greater the CEMF. Also, the induced voltage increases with an increase in inductance; the more ampere-turns, the greater the CEMF. Reactance then increases with an increase of inductance.

CAPACITORS AND ALTERNATING CURRENT

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 figure.

At the beginning of the first quarter-cycle (0 to 90 degrees), the voltage has just passed through zero and is increasing in the opposite direction. Since the zero point is the steepest part of the sine wave, the voltage is changing at its greatest rate. The charge on a capacitor varies directly with the voltage. Therefore, the charge on the capacitor is also changing at its greatest rate at the beginning of the first quarter-cycle. In other words, the greatest number of electrons are moving off one plate and onto the other plate. Thus, the capacitor current is at its maximum value (Figure 7-15 view A).

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 plates.

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.

IMPEDANCE

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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