40 g 00 100 v 10 g 50g FIGURE 8-150. Using an ohmmeter to locate a shorted resistor.
resistor had a resistance of 15 ohms, the equivalent resistance of the parallel combination of Ri and R2.
Thus, it is necessary to open the circuit as shown in figure 8-153 in order to check the resistance of Rz- In this way the resistor is not shunted (paralleled) and the reading on the ohmmeter will indicate infinite resistance. On the other hand, if an open should occur in this circuit (figure 8-153) between the battery and point A, or between the battery and point B, current would not flow in the circuit.
As in a series circuit, a short in a parallel circuit will usually cause an open circuit by blowing the fuse. But, unlike a series circuit, one shorted component in a parallel circuit will stop current flow by causing the fuse to open. This can be seen by. referring to the circuit in figure 8-154.
If resistor R, is shorted, a path of almost zero resistance will be offered the current, and all the circuit current will flow through the branch containing the shorted resistor. Since this is practically the same as connecting a wire between the terminals of the battery, the current will rise Rz 302 300 308 3 Break FIGURE 8-152. A misleading ohmmeter indication.
to an excessive value, and the fuse will open. Since the fuse opens almost as soon as a resistor shorts out, there is no time to perform a current or voltage check. Thus, troubleshooting a parallel d.c.
circuit for a shorted component should be accomplished with an ohmmeter. But, as in the case of checking for an open resistor in a parallel circuit, a shorted resistor can be detected with an ohmmeter only if one end of the shorted resistor is disconnected.
Troubleshooting a series-parallel resistive circuit involves locating malfunctions similar to those found in a series or a parallel circuit.
In the circuit shown in figure 8-155, an open has occurred in the series portion of the circuit. When an open occurs anywhere in the series portion of a series-parallel circuit, current flow in the entire circuit will stop. In this case, the circuit will not function, and the lamp, Li, will not be lit.
If an open occurs in the parallel portion of a series-parallel circuit, as shown in figure 8-156, part of the circuit will continue to function. In this case, the lamp will continue to burn, but its brightness will diminish, since the total resistance Open 30 v Rz 300 Break 3025 300 3 2 a Break FIGuRE 8-153. Opening a branch circuit to FIGURE 8-151. Finding an open branch in a obtain an accurate ohmmeter parallel circuit. reading.
30 v 300 300 300 FIGURE 8-154. A shorted component causes the fuse to open.
of the circuit has increased and the total current has decreased.
If a break occurs in the branch containing the lamp, as shown in figure 8-157, the circuit will continue to function with increased resistance and decreased current, but the lamp will not burn.
To explain how the voltmeter and ohmmeter can be used to troubleshoot series-parallel circuits, the circuit shown in figure 8-158 has been labeled at various points. By connecting a voltmeter between points A and D, the battery and switch can be checked for opens. By connecting the voltmeter between points A and B, the voltage drop across Ri can be checked. This voltage drop is a portion of the applied voltage. Also, if R, is open, the reading between B and D will be zero. The conductor between the positive terminal of the battery and point E, as well as the fuse, can be checked for continuity by connecting the voltmeter between points A and E. If the conductor or fuse is open, the voltmeter will read zero.
If the lamp is burning, it is obvious that no open exists in the branch containing the lamp, and the voltmeter could be used to detect an open in the branch containing R2 by removing lamp, L1, from the circuit.
Troubleshooting the series portion of a seriesparallel circuit presents no difficulties, but in the Break Break FIGURE 8-156. An open in the parallel portion of a series-parallel circuit.
parallel portion of the circuit misleading readings can be obtained.
An ohmmeter can be used to troubleshoot this same circuit. With the switch open, the series portion of the circuit can be checked by placing the ohmmeter leads between points A and B. If R1 or the conductor is open, the ohmmeter will read infinity; if not, the value of the resistor will be indicated on the ohmmeter. Between points D and E the fuse and conductor can be checked for continuity, but in the parallel portion of the circuit, care must be exercised, since misleading ohmmeter indications can be obtained. To check between points B and E, the branch must be disconnected at one of these points, and while one of these points and the switch are open, the branch containing the lamp can be checked with the ohmmeter.
A short in the series part of a series-parallel circuit will cause a decrease in total resistance, which will cause total current to increase. In the circuit shown in figure 8-159, the total resistance is 100 ohms and the total current is 2 amperes. If RI became shorted, total resistance would hecome 50 ohms, and the total current would double to 4 amperes. In the circuit shown, this would cause the 3-amp fuse to blow, but with a 5-amp fuse the circuit would continue to function. The result would be the same if Ra or R3 were to become shorted. The total resistance in either case would m Break FIGURE 8-155. An open in the series portion of a FIcURE 8-157. An open lamp in a series-parallel series-parallel circuit. circuit.
E F FIGURE 8-158. Using the voltmeter to troubleshoot a series-parallel circuit.
drop to 50 ohms. From this, it can be stated that when a short occurs in a series-parallel circuit, the total resistance will decrease and the total current will increase. A short will normally cause an open circuit by either blowing the fuse or burning out a circuit component. And, as in the case of an open, a short in a series-parallel circuit can be detected with either an ohmmeter or a voltmeter.
ALTERNATING CURRENT AND VOLTAGE Alternating current has largely replaced direct current in commercial power systems for a number of reasons. It can be transmitted over long distances more readily and more economically than direct current, since a.c. voltages can be increased or decreased by means of transformers.
Because more and more units are being operated electrically in airplanes, the power requirements are such that a number of advantages can be realized by using a.c. Space and weight can be saved, since a.c. devices, especially motors, are smaller and simpler than d.c. devices. In most a.c.
motors no brushes are required, and commutation trouble at high altitude is eliminated. Circuit breakers will operate satisfactorily under load at high altitudes in an a.c. system, whereas arcing is so excessive on d.c. systems that circuit breakers must be replaced frequently. Finally, most airplanes using a 24-volt d.c. system have special equipment which requires a certain amount of 400-cycle a.c. current.
A. C. and D. C. Compared Many of the principles, characteristics, and effects of alternating current are similar to those of direct current. Similarly, there are a number of differences which are explained later. Direct current flows constantly in only one direction with a constant polarity. It changes magnitude only when the circuit is opened or closed, as shown in the d.c. wave form in figure 8-160. Alternating current changes direction at regular intervals, increases in value at a definite rate from zero to a maximum positive strength, and decreases back to zero; then it flows in the opposite direction, similarly increasing to a maximum negative value, and again decreasing to zero. D.C. and a.c. wave forms are compared in figure 8-160.
Since alternating current constantly changes direction and intensity, two effects take place in
a.c. circuits that do not occur in d.c. circuits. They are inductive reactance and capacitive reactance.
Both are discussed later in this chapter.
Generator Principles After the discovery that an electric current flowing through a conductor creates a magnetic field around the conductor, there was considerable scientific speculation about whether a magnetic field could create a current flow in a conductor. In 1831, the English scientist, Michael Faraday, demonstrated this could be accomplished. This discovery is the basis for the operation of the generator, which signalled the beginning of the electrical age.
To show how an electric current can be created by a magnetic field, a demonstration similar to that illustrated in figure 8-161 can be used.
Several turns of a conductor are wrapped around a cylindrical form, and the ends of the conductor are connected together to form a complete circuit which includes a galvanometer. If a simple bar magnet is plunged into the cylinder, the galvanometer can be observed to deflect in one direction from its zero (center) position (4 of figure 8-161).
When the magnet is at rest inside the cylinder, the 500 Rz 200 v 10050 1, = 2 Amps FIGURE 8-159. Finding a short in a series-parallel circuit.
Wave form for DC Wave form for AC VOLTS VOLTS 180° 270° 360° 0° 90° Operation of circuit Closed ' Open Switch Switchi Time - Time FIGURE 8-160. D.C. and a.c. voltage curves.
galvanometer shows a reading of zero, indicating that no current is flowing (B of figure 8-161).
In C of figure 8-161, the galvanometer indicates a current flow in the opposite direction when the magnet is pulled from the cylinder.
The same results may be obtained by holding the magnet stationary and moving the cylinder over the magnet, indicating that a current flows when there is relative motion between the wire coil and the magnetic field. These results obey a law first stated by the German scientist, Heinrich Lenz. Lenz's law states that the induced current caused by the relative motion of a conductor and a magnetic field always flows in such a direction that its magnetic field opposes the motion.
When a conductor is moved through a magnetic field, as shown in figure 8-162, an electromotive force (e.m.f.) is induced in the conductor. The direction (polarity) of the induced e.m.f. is determined by the magnetic lines of force and the direction the conductor is moved through the magnetic field. The generator left-hand rule (not to be confused with the left-hand rules used with a coil) can be used to determine the direction of the induced e.m.f., as shown in figure 8-163. The first finger of the left hand is pointed in the direction of the magnetic lines of force (north to south), the thumb is pointed in the direction of movement of the conductor through the magnetic field, and the second finger points in the direction of the induced Motion of magnet Galvanometer
- Coil Motion of magnet Magnet at Rest B FIGURE 8-161. Inducing a current flow.
Motion of conductor FIGURE 8-162. Inducing an e.m.f. in a conductor.
e.m.f. When two of these three factors are known, the third may be determined by the use of this rule.
When a loop conductor is rotated in a magnetic field (see figure 8-164), a voltage is induced in each side of the loop. The two sides cut the magnetic field in opposite directions, and although the current flow is continuous, it moves in opposite directions with respect to the two sides of the loop.
If sides A and B and the loop are rotated half a turn and the sides of the conductor have exchanged positions, the induced e.m.f. in each wire reverses its direction, since the wire formerly cutting the lines of force in an upward direction is now moving downward.
The value of an induced e.m.f. depends on three factors:
(1) The number of wires moving through the magnetic field.
(2) The strength of the magnetic field.
(3) The speed of rotation.
Generators of Alternating Current Generators used to produce an alternating current are called a.c. generators or alternators.
Conductor Moved up Flux forward Inducted E.M.F.
Left hand Z Inducted E.M.F.
FIGURE 8-163. An application of the generator left-hand rule.
FIGURE 8-164. Voltage induced in a loop.
The simple generator shown in figure 8-165 constitutes one method of generating an alternating voltage. It consists of a rotating loop, marked A and B, placed between two magnetic poles, N and S. The ends of the loop are connected to two metal slip rings (collector rings), C1 and C2. Current is taken from the collector rings by brushes. If the loop is considered as separate wires A and B, and the left-hand rule for generators (not to be confused with the left-hand rule for coils) is applied, then it can be observed that as wire A moves up across the field, a voltage is induced which causes the current to flow inward. As wire B moves down across the field, a voltage is induced which causes the current to flow outward. When the wires are formed into a loop, the voltages induced in the two sides of the loop are combined. Therefore, for explanatory purposes, the action of either conductor, A or B, while rotating in the magnetic field is similar to the action of the loop.
Figure 8-166 illustrates the generation of alternating current with a simple loop conductor rotating in a magnetic field. As it is rotated in a counterclockwise direction, varying values of voltages are induced in it. At position 1, conductor A moves parallel to the lines of force. Since it cuts no lines of force, the induced voltage is zero. As the conductor advances from position 1 to position 2, the voltage induced gradually increases. At 2, the conductor moves perpendicular to the flux and cuts a maximum number of lines of force; therefore, a maximum voltage is induced. As the conductor moves beyond 2, it cuts a decreasing amount of flux at each instant, and the induced voltage decreases. At 3, the conductor has made one half of a revoltion and again moves parallel to the lines of force, and no voltage is induced in the conductor.
As the A conductor passes position 3, the direction of induced voltage reverses since the A conductor 340
Brushes In current Out current FIGURE 8-165. Simple generator.
now moves downward, cutting flux in the opposite direction. As the A conductor moves across the south pole, the induced voltage gradually increases in a negative direction, until at position 4 the conductor again moves perpendicular to the flux and generates a maximum negative voltage. From position 4 to 5, the induced voltage gradually decreases until the voltage is zero, and the conductor and wave are ready to start another cycle.
The curve shown at position 5 is called a sine wave. It represents the polarity and the magnitude of the instantaneous values of the voltages generated. The horizontal base line is divided into degrees, or time, and the vertical distance above or below the base line represents the value of voltage at each particular point in the rotation of Cycle and Frequency alternations in a complete cycle, the positive alternation and the negative. Each is half a cycle.
The number of times each cycle occurs in a period of time is called the frequency. The frequency of an electric current or voltage indicates the number of times a cycle recurs in 1 second.
In a generator, the voltage and current pass through a complete cycle of values each time a coil or conductor passes under a north and south pole of the magnet. The number of cycles for each revolution of the coil or conductor is equal to the number of pairs of poles. The frequency, then, is equal to the number of cycles in one revolution multiplied by the number of revolutions per second. Expressed in equation form, F - Number of poles x t.p.m.
where 2 is the number of pairs of poles, and ".p.m. P Whenever a voltage or current passes through a series of changes, returns to the starting point, and then again starts the same series of changes, the series is called a cycle. The cycle is represented by the symbol. In the cycle of voltage shown in figure 8-167, the voltage increases from zero to a maximum positive value, decreases to zero; then increases to a maximum negative value, and again decreases to zero. At this point it is ready to go through the same series of changes. There are two the number of revolutions per second. If in a 2-pole generator, the conductor is turning at 3,600 r.p.m., the revolutions per second are
r.p.s. = 3600 = 60 revolutions per second.
Since there are 2 poles, = is 1, and the frequency is 60 c.p.s. In a 4-pole generator with an armature 341
Magnetic field 0° 90° 180°, 270°1 360° 0° 90°, 180° 270 360° Zero voltage Position 1 Rotating conductors moving parallel to magnetic field, cutting minimum lines of force.
Maximum positive voltage Position 2 Quarter turn completed Conductors cutting directly across the magnetic field as conductor A passes across the North magnetic pole and B passes across the S pole.
270° 360° 0° 90 180* 270 360° 10° 90 180 Voltage drops to zero Maximum negative voltage Position 3 Position 4 One-half turn completed Three quarter tum completed Conductors again moving parallel to magnetic Conductors again moving directly across magnetic field, cutting minimum lines of force. field 'At passes across South magnetic pole and "B" across N magnetic pole.
360° 0° 90 180° Conductor A has made one complete cycle and is in same position as in position A. The generator has generated one complete cycle of altemating voltage Zero voltage or current.
Position 5 Full turn completed FIGURE 8-166. Generation of a sine wave.
Negative amount that the two sine waves are out of phase is alternation indicated by the number of electrical degrees 0° 90° 180° 1 270° 360° between corresponding peaks on the sine waves. In Positive figure 8-169, the current and voltage are 30° out alternation of phase.
1 Second time - Frequency = 2 cycles per sec.
Values of Alternating Current Frequency = 2 cycles per sec.
90,180* 360 270°1 1 Second time
• Frequency = 8 cycles per sec.
FIGURE 8-167. Frequency in cycles per second.
speed of 1,800 r.p.m., substitute in the equation, F = 2 P r.p.m. , as follows:
60 F=½ 1800 60 F = 2 × 30 F = 60 c.p.s.
In addition to frequency and cycle characteristics, alternating voltage and current also have a relationship called "phase." In a circuit that is fed (supplied) by one alternator, there must be a certain phase relationship between voltage and current if the circuit is to function efficiently. In a system fed by two or more alternators, not only must there be a certain phase relationship between voltage and current of one alternator, but there must be a phase relationship between the individual voltages and the individual currents. Also, two separate circuits can be compared by comparing the phase characteristics of one to the phase characteristics of the other.
When two or more sine waves pass through 0° and 180° at the same time and reach their peaks at the same time, an in-phase condition exists, as shown in figure 8-168. The peak values (magnitudes) do not have to be the same for the in-phase condition to exist. When the sine waves pass through 0° and 180° at different times and reach their peaks at different times, an out-of-phase condition exists, as shown in figure 8-169. The There are three values of alternating current which should be considered. They are instantaneous, maximum, and effective.
An instantaneous value of voltage or current is the induced voltage or current flowing at any instant. The sine wave is a series of these values.
The instantaneous value of the voltage varies from zero at 0° to maximum at 90°, back to zero at 180°, to maximum in the opposite direction at 270°, and to zero again at 360°. Any point on the sine wave is considered the instantaneous value of voltage.
The maximum value is the largest instantaneous value. The largest single positive value occurs when the sine wave of voltage is at 90°, and the largest single negative value occurs when it is at 270°. These are called maximum values. Maximum value is 1.41 times the effective value. (See figure 8-170.)
The effective value of alternating current is the same as the value of a direct current which can produce an equal heating effect. The effective value is less than the maximum value, being equal to .707 times the maximum value. Thus, the 110-volt value given for alternating current supplied to homes is only .707 of the maximum voltage of this supply. The maximum voltage is approximately 155 volts (110 X 1.41 = 155 volts maximum).
In the study of alternating current, any values given for current or voltage are assumed to be effective values unless otherwise specified, and in Voltage Current 90° 180° 270° 360° FIGURE 8-168. In-phase condition of current and voltage.
VOLTAGE 180° 270° 360° 90° 150°
CURRENT FICURE 8-169. Out-of-phase condition of current and voltage.
practice, only the effective values of voltage and current are used. Similarly, alternating current voltmeters and ammeters measure the effective value.
cross-sectional area of the coil, and the material in the center of the coil or core. A core of magnetic material greatly increases the inductance of the coil.
INDUCTANCE When an alternating current flows through a coil of wire, the rise and fall of the current flow, first in one direction, and then in another, sets up an expanding and collapsing magnetic field about the coil. A voltage is induced in the coil which is opposite in direction to the applied voltage and which opposes any change in the alternating current (see figure 8-171). The induced voltage is called the counter-electromotive force(abbreviated It must be remembered, however, that even a straight wire has inductance, small though it may be when compared to that of a coil. A.C. motors, relays, and transformers contribute inductance to a circuit, Practically all a.c. circuits contain inductive elements.
The symbol for inductance in formulas is the capital letter "L. Inductance is measured in henrys (abbreviated h). An inductor (coil) has an inductance of 1 henry if an e.m.f. of 1 volt is induced in the inductor when the current through
c.e.m.t.), since it opposes the applied voltage. This property of a coil to oppose any change in the current flowing through it is called inductance.
The inductance of a coil is measured in henrys.
the inductor is changing at the rate of 1 ampere per second. However, the henry is a large unit of inductance and is used with relatively large inductors having iron cores. The unit used for In any coil, the inductance depends on several small air-core inductors is the millihenry (mh).
factors, principally the number of turns, the For still smaller air-core inductors the unit of Maximum value = 1.41 effective value 1 Effective value = .707 maximum value G H FIGURE 8-170. Effective and maximum values of voltage.
iron core • Mounted air core- ragon Inductance FIGURE 8-171. A.C. circuit containing inductance.
inductance is the microhenry (uk). Figure 8-172 shows a few of the various types of inductors, together with their symbols.
Inductors may be connected in a circuit in the same manner as resistors. When connected in series, the total inductance is the sum of the inductances of the inductors, or Lp = L1 + La + La, etc.
When two or more inductors are connected in parallel, the total inductance is, like resistances in parallel, less than that of the smallest inductor, or LI = I + Is The total inductance of inductors connected in series-parallel can be computed by combining the parallel inductances and then adding the series values. In all cases, these formulas are valid, providing the magnetic fields of the inductors do not interact.
Inductive Reactance The opposition to the flow of current which inductances put in a circuit is called inductive reactance. The symbol for inductive reactance is Xz, and is measured in ohms, just as resistance is.
In any circuit in which there is only resistance, the expression for the relationship of voltage and current is Ohm's law: I = R• Similarly, when there is inductance in an a.c. circuit, the relationship between voltage and current can be expressed as:
Voltage Reactance or 1 - $ Current = Where:
XL = inductive reactance of the circuit in ohms.
Radio frequency → Radio frequency choke Iron core - ell- Radio frequency 002500 FIGURE 8-172. Various types of inductors.
If all other circuit values remain constant, the greater the inductance in a coil, the greater the effect of self-induction, or opposition to the change in the value of current. As the frequency increases, the inductive reactance increases, since the greater the rate of current change the more the opposition to change by the coil increases. Therefore, inductive reactance is proportional to inductance and frequency or, XI = 2 TfL.
Where:
Xz - inductive reactance in ohms.
= frequency in cycles per second.
* = 3.1416.
In figure 8-173, an a.c. series circuit is assumed in which the inductance is 0.146 henry and the voltage is 110 volts at a frequency of 60 cycles per second. What is the inductive reactance and the current flow? (The symbol) represents an a.c.
generator.)
110V AC B0 cycles FIGURE 8-175. Inductances in parallel.
FIGURE 8-173. A.C. circuit containing inductance.
Solution: CAPACITANCE To find the inductive reactance: Another important property in a.c. circuits, XI = 2= X fX L besides resistance and inductance, is capacitance.
While inductance is represented in a circuit by a X= = 6.28 × 60 × 0.146. coil, capacitance is represented by a capacitor.
To find current:
1 = Xi E 1 = 1º 55 I = 2 amperes.
In a.c. series circuits (figure 8-174), inductive reactances are added like resistances in series in a
d.c. circuit. Thus, the total reactance in the circuit illustrated in figure 8-174 equals the sum of the individual reactances.
The total reactance of inductors connected in parallel (figure 8-175) is found the same way as the total resistance in a parallel circuit. Thus, the total reactance of inductances connected in parallel, as shown, is expressed as, (Xx)r = (Xz)ı Any two conductors separated by a nonconductor, called a dielectric, constitute a capacitor.
In an electrical circuit, a capacitor serves as a reservoir or storehouse for electricity.
When a capacitor is connected across a source of direct current, such as a storage battery in the circuit shown in figure 8-176, and the switch is then closed, the plate marked B becomes positively charged, and the A plate negatively charged.
Current flows in the external circuit during the time the electrons are moving from B to A. The current flow in the circuit is maximum the instant the switch is closed, but continually decreases thereafter until it reaches zero. The current becomes zero as soon as the difference in voltage of A and B becomes the same as the voltage of the battery. If the switch is opened, the plates remain charged. However, the capacitor quickly discharges when it is short circuited.
The amount of electricity a capacitor can store depends on several factors, including the type of material of the dielectric. It is directly proportional to the plate area and inversely proportional to the distance between the plates.
B ++++++ FIGURE 8-174. Inductances in series. FIGURE 8-176. Capacitor in a d.c. circuit.
Battery SW position Capacitor position Meter FIGURE 8-177. A basic capacitor (condenser) circuit.
In figure 8-177, two flat metal plates are placed close to each other (but not touching). Usually the plates are electrically neutral; that is, no electrical charge will be evident on either plate. At the instant the switch is closed to the battery position, the meter will show a definite current surge in one direction, but almost instantly will return to zero.
If the battery is then taken out of the circuit and the switch closed in the capacitor position, the meter again shows a momentary current surge, but this time in an opposite direction. From this experiment it is apparent that the two plates store • energy when connected to a voltage source, and release the energy when short-circuited. The two plates make up a simple electrical capacitor, or condenser, and possess the property of storing electricity. The energy is actually stored in the electric, or dielectric, field between the plates.
Also, it should be clear that during the time the capacitor is being charged or discharged there is current in the circuit, even though the circuit is broken by the gap between the capacitor plates.
However, there is current only during the time of charge and discharge, and this period of time is very short. There can be no continuous movement of direct current through a capacitor. A good capacitor will block direct current (not pulsating
d.c.) and will pass the effects of alternating current.
The charge of electricity that can be placed on a capacitor is proportional to the applied voltage and to the capacitance of the capacitor (condenser).
Capacitance depends upon the total area of the plates, the thickness of the dielectric and the composition of the dielectric.
If a thin sheet of bakelite (mica-filled) is substituted for air between the plates of a capacitor, for example, the capacitance will be increased about five times.
Any electric charge produced by applied voltage and kept in bounds by an insulator (dielectric) creates a dielectric field. Once the field is created, it tends to oppose any voltage change which would affect its original position. All circuits contain some capacitance, but unless they contain a unit called a capacitor, the capacitance, for all practical purposes, is disregarded. Two conductors, called electrodes or plates, separated by a nonconductor (dielectric) make up a simple capacitor. The plates may be made of copper, tin, or aluminum.
Frequently, they are made of foil (metals compressed into thin sheets and capable of being rolled). The dielectric may be air, glass, mica, or an electrolyte made by an oxide film, but the type used will determine the amount of voltage that may be applied and the quantity of energy that will be stored, The dielectric materials have different atomic structures and present different quantities of atoms to the electrostatic field. All dielectric materials are compared to a vacuum and are given a numerical value according to the capacity ratio between them. The number given to a material is based on the same area and thickness as used in the vacuum. The numbers used to express this ratio are called dielectric constants and are expressed as the letter "K." The chart in figure 8-178 gives the K-value of some materials used.
If a source of alternating current is substituted for the battery, the capacitor acts quite differently than it does with direct current. When an 347