Alternating Current and Generator Principles

12-43 + − R1 R2ES R3 A B R4 + − R1 R23ES R4 resistors. 1k Ω 2k Ω 3k Ω + − R1 R2 ES=24 V R3 A B resistance RT of the entire circuit must be known. The total resistance of the circuit is given as: RT = R1 + R23 Where R23 = ( ) Parallel network R2 + R3 R2R3 Find REQ R23 = 2k Ω + 3k Ω 2k Ω 3k Ω Solve for REQ R23 = 5k Ω 6,000k Ω R23 = 1.2k Ω Solve for RT RT = 1k Ω + 1.2k Ω RT = 2.2k Ω With the total resistance RT now determined, the total IT can be determined. Using Ohm’s Law: IT = RT ES Substitute values IT = 2.2k Ω 24 V IT = 10.9 mA The current through the parallel branches of R 2 and R3 can be determined using the current divider rule discussed earlier in this handbook.

Recall Parallel Branch Resistance: R23 = 5,000 Ω 6,000 Ω R23 = 1.2k Ω Substitute values for I2: I2 = x (10.9 mA) 2,000 Ω 1,200 Ω I2 = 6.54 mA Now using Kirchhoff’s Current Law, the current in the branch with R3 can be determined. I 2 + I3 = IT Recall that IT = 10.9 mA I T – I2 = I3 Also recall that I2 = 6.54 mA Subtract I2 from IT to get I3 I 3 = 4.36 mA

Alternating Current (AC) & Voltage

Alternating current (AC) has largely replaced direct current (DC) in commercial power systems for a number of reasons. It can be transmitted over long distances more readily and more economically than DC, since AC voltages can be 12-44 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 AC. Space and weight can be saved since AC devices, especially motors, are smaller and simpler than DC devices. In most AC motors, no brushes are required, and commutation trouble at high altitude is eliminated. Circuit breakers operate satisfactorily under load at high altitudes in an AC system, whereas arcing is so excessive on DC systems that circuit breakers must be replaced frequently. Finally, most airplanes using a 24-volt DC system have special equipment that requires a certain amount of 400-cycle AC current.

AC and DC Compared Many of the principles, characteristics, and effects of AC are similar to those of DC. Similarly, there are a number of differences. DC 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 DC waveform in Figure 12-103. AC 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. DC and AC waveforms are compared in Figure 12-103.

Since AC constantly changes direction and intensity, the following two effects (to be discussed later) take place in AC circuits that do not occur in DC circuits: 1. Inductive reactance 2. Capacitive reactance

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, Faraday discovered that this could be accomplished. To show how an electric current can be created by a magnetic field, a demonstration similar to Figure 12-104 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. [Figure 12-104A] When the magnet is at rest inside the cylinder, the galvanometer shows a reading of zero, indicating that no current is flowing. [Figure 12-104B] In Figure 12-104C , 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, an emf is induced in the conductor. [Figure 12-105] The direction (polarity) of the induced emf 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 emf. [Figure 12-106] The left-hand rule is summed up as follows: 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 emf.

When a loop conductor is rotated in a magnetic field, a voltage is induced in each side of the loop. [Figure 12-107] 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 emf 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 emf depends on three factors: 1. Number of wires moving through the magnetic field 2. Strength of the magnetic field 3. Speed of rotation Generators of Alternating Current Generators used to produce an alternating current are called AC generators or alternators.

The simple generator constitutes one method of generating an alternating voltage. [Figure 12-108] It consists of 12-45 Closed switch Open switch Operation of circuit Waveform for DC Volts Time Waveform for AC Volts + Time − 0° 90° 180° 270° 360° N S N S N S Motion of magnet Galvanometer A B C Motion of magnet Coil Magnet at rest I 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 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.

loop conductor rotating in a magnetic field. As it is rotated in a counterclockwise direction, varying values of voltages are induced in it. Position 1 The 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. Position 2 The conductor is now moving perpendicular to the flux and cuts a maximum number of lines of force; therefore, a maximum voltage is induced. As the conductor moves beyond position 2, it cuts a decreasing amount of flux at each instant, and the induced voltage decreases.

Position 3 At this point, the conductor has made one-half of a revolution 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 now reverses since the A conductor is moving downward, cutting flux 12-46 S N S N Inducted emf Flux forward Inductedemf Conductor moved up N S A B N S Motion of conductor emf in the opposite direction. As the A conductor moves across the South pole, the induced voltage gradually increases in a negative direction, until it reaches position 4. Position 4 Like position 2, the conductor is again moving 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.

Position 5 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 the loop. Cycle and Frequency Cycle Defined A cycle is a repetition of a pattern. 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 of a wavy line in a circle ~ . In the cycle of voltage shown in Figure 12-110, 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 alternations in a complete cycle: the positive alternation and the negative. Each is half a cycle.

Frequency Defined The frequency is the number of cycles of AC per second (1 12-47 N S N S Brushes C1 C2 A B + In currentOut current second). The standard unit of frequency measurement is the hertz (Hz). [Figure 12-111] 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 (rps).

Expressed in equation form: F = ×2 60 Number of poles rpm where P⁄2 is the number of pairs of poles, and rpm/60 the number of revolutions per second. If in a 2-pole generator, the conductor is turning at 3,600 rpm, the revolutions per second are: rps = = 60 revolutions per second60 3,600 Since there are 2 poles, P⁄2 is 1, and the frequency is 60 cycles per second (cps). In a 4-pole generator with an armature speed of 1,800 rpm, substitute in the equation: F = × as follows2 60 P rpm F = × 2 60 4 1,800 F = 2 × 30 F = 60 cps Period Defined The time required for a sine wave to complete one full cycle is called a period. [Figure 12-110] The period of a sine wave is inversely proportional to the frequency: the higher the frequency, the shorter the period. The mathematical relationship between frequency and period is given as: Period is t = f 1 Frequency is f = t 1 Wavelength Defined The distance that a waveform travels during a period is commonly referred to as a wavelength and is indicated by the Greek letter lambda (l). The measurement of wavelength is taken from one point on the waveform to a corresponding point on the next waveform. [Figure 12-110] Phase Relationships 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 12-48 S B Position 2 Quarter turn completed Conductors cutting directly across the magnetic field as conductor A passes across the North (N) magnetic pole and B passes across the South (S) magnetic pole.

Maximum positive voltage 0° 90° 180° 270° 360°C1 C2 N 0° 90° 180° 270° 360° S Position 4 Three quarters turn completed Conductors again moving directly across magnetic field A passes across South (S) magnetic pole and B across North (N) magnetic pole. C1 C2 Maximum negative voltage N 0° 90° 180° 270° 360° N S B Voltage drops to zero Position 3 One half turn completed Conductor again moving parallel to magnetic field, cutting minimum lines of force. C1 C2 N S A C1 C2 0° 90° 180° 270° 360° Zero voltage Position 1 Rotating conductors moving parallel to magnetic field, cutting minimum lines of force.

Magnetic field 0° 90° 180° 270° 360° N S A Position 5 Zero voltage Full turn completed Conductor A has made one complete cycle and is in same position as in position A. The generator has generated one complete cycle of alternating voltage or current. C1 C2 characteristics of one to the phase characteristics of the other. In Phase Condition superimposed on the same time axis. Notice that when the voltage increases in the positive alternation that the current also increases. When the voltage reaches its peak value, so does the current. Both waveforms then reverse and decrease back to a zero magnitude, then proceed in the same manner in the negative direction as they did in the positive direction.

When two waves, such as these in Figure 12-112A, are exactly in step with each other, they are said to be in phase. To be in phase, the two waveforms must go through their maximum and minimum points at the same time and in the same direction. Out of Phase Condition When two waveforms go through their maximum and minimum points at different times, a phase difference exists between the two. In this case, the two wave-forms are said to be out of phase with each other. The terms lead and lag are often used to describe the phase difference between waveforms. The waveform that reaches its maximum or minimum value first is said to lead the other waveform.

one starts to rise at the 0° position and voltage source two starts to rise at the 90° position. Because voltage source one begins its rise earlier in time (90°) in relation to the second voltage source, it is said to be leading the second source. On the other hand, the second source is said to be lagging the first source. When a waveform is said to be leading or lagging, the difference in degrees is usually stated. If the two waveforms differ by 360°, they are said to be in phase with each other. If there is a 180° difference between the two signals, then they are still out of phase even though they are both reaching their minimum and maximum values at the same time. [Figure 12-112C] A practical note of caution: When encountering an aircraft that has two or more AC busses in use, it is possible that they may be split and not synchronized to be in phase with each other.

When two signals that are not locked in phase are mixed, much damage can occur to aircraft systems or avionics. Values of Alternating Current There are three values of AC: instantaneous, peak, and effective root mean square (RMS). Instantaneous Value An instantaneous value of voltage or current is the induced voltage or current flowing at any instant during a cycle. The sine wave represents a series of these values. The instantaneous 12-49 One cycle One period (Time) One wavelength (Distance) Second cycle (Repeated) Vertical scale (voltage) Horizontal scale (Time) Positive alternation 1T 2T 3T 4T Negative alternation Cycle is defined as a repetitive pattern.

360° 1 second time Positive alternation 1T 0° 90° 180° 270° Frequency = 2 cycles per second 270° 180° 0° 90° Frequency = 2 cycles per second 1 second time Frequency = 8 cycles per second 360° Negative alternation 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. Peak Value The peak 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°. Maximum value is 1.41 times the effective value.

These are called peak values. Effective Value The effective value is also known as the RMS value or root mean square, which refers to the mathematical process by which the value is derived. Most AC voltmeters display the effective or RMS value when used. The effective value is less than the maximum value, being equal to .707 times the maximum value. The effective value of a sine wave is actually a measure of the heating effect of the sine wave. Figure 12-113 illustrates what happens when a resistor is connected across an AC voltage source. In Figure 12-113A, a certain amount of heat is generated by the power in the resistor. Figure 12-113B shows the same resistor now inserted into a DC voltage source.

The value of the DC voltage source can now be adjusted so that the resistor dissipates the same amount of heat as it did when it was in the AC circuit. The RMS or effective value of a sine wave is equal to the DC voltage that produces the same amount of heat as the sinusoidal voltage. The peak value of a sine wave can be converted to the corresponding RMS value using the following relationship. Vrms = ( 0.5 ) × Vp Vrms = 0.707 × Vp This can be applied to either voltage or current. Algebraically rearranging the formula and solving for Vp can also determine the peak voltage. The resulting formula is: Vp = 1.414 × Vrms Thus, the 110 volt value given for AC supplied to homes is only 0.707 of the maximum voltage of this supply. The maximum voltage is approximately 155 volts (110 × 1.41 = 155 volts maximum).

In the study of AC, any values given for current or voltage are assumed to be effective values unless otherwise specified. In practice, only the effective values of voltage and current are used. Similarly, AC voltmeters and ammeters measure the effective value. Opposition to Current Flow of AC There are three factors that can create an opposition to the flow of electrons (current) in an AC circuit. Resistance, similar to resistance of DC circuits, is measured in ohms and has a direct influence on AC regardless of frequency. Inductive reactance and capacitive reactance, on the other hand, oppose current flow only in AC circuits, not in DC circuits. Since AC constantly changes direction and intensity, inductors and capacitors may also create an opposition to current flow in AC circuits. It should also be noted that inductive reactance and capacitive reactance may create a phase shift between the voltage and current in an AC circuit. Whenever analyzing an AC circuit, it is very important to consider the resistance, inductive reactance, and the capacitive reactance. All three have an effect on the current of that circuit.