ELECTRIC CURRENTS AND CIRCUITS By: Richard D. Beard P.E.

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1 ELECTRICAL POWER There are two types of electric power in use, direct current (dc) and alternating current (ac). The most common use of direct current is automotive, including storage batteries, starter motors, and lighting circuits, as well as auxiliary equipment. Alternating current is more versatile, since its voltage can be easily stepped up and down, which permits it to be transmitted long distances with small losses. Most electrical power used today is alternating current. Direct current (dc) is supplied by a direct-current generator, a battery, or a rectifier. It flows continuously in the same direction. Battery or dc generator current flows smoothly, as shown in Figure 1. Rectified dc has pulses, as shown in Figures 2 and 3. The flow of dc current is resisted by the load and the wires in the circuit. Wire resistance depends on the material used, its diameter, and its length. Copper has a low resistance, steel has more, and nichrome wire has a great deal more. Battery-Generated Direct Current Half-Wave Rectified Direct Current 1

2 Full-Wave Rectified Direct Current Alternating current (ac) is supplied by an alternating current generator or alternator. Ac flows first in one direction, then reverses, and flows in the opposite direction. But when it changes direction, it does not jump from maximum value in one direction to maximum value in the other direction. Instead, it gradually increases in one direction to its maximum, then gradually falls back to zero. The current then builds up in the opposite direction to maximum value, after which it gradually returns to zero again, as shown in Figure 4. However, keep in mind that this is not a slow-motion event. The complete cycle usually takes place in just 1/60th of a second! Figure 4 One of the periods of increasing from zero to maximum and returning to zero, all in one direction, is called an alternation. Two alternations, one in one direction and one in the opposite direction, are called a cycle. If the current alternates or changes direction ten times, five cycles are completed. There are always twice as many alternations as cycles. The alternations are very rapid. The frequency of these alternations is measured in Hertz, which is the same as cycles per second. Most ac power in the United States is 60 Hz, while in other parts of the world, 50 Hz is common. In communications equipment, higher frequencies are used, such as kilohertz and megahertz, i.e., thousands and millions of cycles per second. 2

3 ELECTRICAL CHARACTERISTICS Electricity has two basic characteristics: voltage and current. 1. Voltage is also called potential, or electromotive force (abbreviated emf). It is considered the "pressure" of electricity. Voltage may be present, even though current may not be flowing. Voltage is measured with a voltmeter. If a voltmeter is connected across the terminals of a battery, the voltage or emf can be measured. Voltage is similar to pressure in a refrigeration system. 2. Current or amperage is the rate of flow of electrons and is similar to the flow of refrigerant in a refrigeration system, or the flow of water through a pipe. Current flow is measured with an ammeter. The ammeter must be connected in series with the wire in which the current flow is to be measured, unless it is a "hook-on" ammeter, in which case, the split core is clamped around the conductor. A wire or conductor offers resistance to the flow of current. The smaller the diameter of the wire, the larger the resistance. Similarly, the longer the wire, the greater the resistance. A wire's resistance to the flow of current also causes a drop in electrical pressure (voltage) along the length of the wire. Likewise, the greater the amount of current carried by the wire, the greater the voltage drop. This voltage drop is similar to the pressure drop in a refrigeration system. There is resistance to the flow of refrigerant, and a resulting drop in pressure from one end of the line to the other. The smaller the diameter of the line, and the greater its length, and the larger the amount of refrigerant flow, the greater the pressure drop. OHM'S LAW Many years ago, a man named George Ohm discovered the relationship between electrical pressure, current flow, and resistance. He found that the pressure drop, measured in volts, was equal to the current flow (in amperes) multiplied by the resistance (in units later named after him, "ohms"). The international electrical symbols are E for voltage, I for amperage, and R for resistance. Using these symbols, the relationship can be expressed as an equation: E = I R. This is known as Ohm's Law. It is a very important electrical fundamental. It means voltage is the product of current times resistance. Ohm's Law can be expressed two other ways. The current flow equals the electrical pressure divided by the resistance: I = E/R. Also, the resistance equals the electrical pressure divided by the current: R = E/I. As an example, if a current of 5 amperes flows in a length of wire, and the resistance of the wire is 10 ohms, then the voltage drop from one end of the wire to the other will be 5 10 = 50 volts (E = I R). If another wire has a resistance of 8 ohms and a voltage drop of 80 volts when a current flows through it, you calculate the current to be 80/8 =10 amperes (I = E/R). In still another wire, we know the voltage drop is 110 volts when 10 amperes of current flows. So the resistance is 110/10, or 11 ohms. (R = E/I). Figure 5 provides an easy reference to the different ways of expressing Ohm's law. If any one of the three letters is covered (representing the unknown quantity), then the two uncovered letters show how to obtain the answer. Thus, E (if covered) equals I x R, and I (if covered) equals E/R. When you cover R, the diagram shows E/I. 3

4 Ohm's Law Diagram VOLTAGE DROP Many uses of electricity require two conductors, such as those used in ordinary household circuits. The two conductors in home wiring usually have 120 volts between them. This voltage is called line voltage, and for a complete circuit, line voltage equals the total voltage drop. For example, the line voltage at the terminals of a toaster is 120 volts, and the resistance of the nichromenickel wire in the toaster is 24 ohms. The current, therefore, is 120/24 = 5 amperes. If, however, a long extension cord (or one with a very small diameter) is used between the wall outlet and the toaster, additional resistance is inserted into the circuit. Suppose the cord's resistance is 10 ohms, as shown in Figure 6. This resistance is in series with the toaster's heating element, so it adds to the total resistance of the circuit. This total resistance is now = 34 ohms. The current flow (I) will be E/R, or 120/34 = 3.53 amperes. Thus, the toaster will not heat properly, since it requires five amperes, and only 3.53 amperes are flowing. The current has been reduced because of the voltage drop, caused by the resistance of the extension cord. 4

5 Long Extension Cord Connected to Toaster With five ohms of resistance in each line of the extension cord, the current flow of 3.53 amperes will cause a voltage drop in each line of 3.53 x 5 = volts. The total voltage drop of the extension cord, therefore, is = 35.3 volts. This voltage drop is subtracted from 120 volts, giving a voltage across the toaster terminals of = 84.7 volts (see Figure 6). This voltage can also be calculated by using the resistance of the toaster heating element, multiplied by the current flowing through it (E = I R). Thus, the calculated voltage is = 84.7 volts. Now if the toaster is connected directly to the wall outlet, the voltage drop will be very small or insignificant. So it is very important that line wires be sized large enough to carry the full load current. If a long line is used to feed power to the load, the wires must be large enough to avoid a large voltage drop. Voltage drop should be kept as low as possible; 2% or 3% is preferred. It should never exceed 10%. The National Electrical Manufacturers Association (NEMA) motor standards state that induction motors shall operate successfully under running conditions at rated load, with a voltage variation up to ± 10% with rated frequency. Electric motors, solenoids, and other electrical equipment operate best with full or rated voltage at the terminals. Rated voltage appears on the nameplate. Many single-phase permanent split-capacitor, shaded pole, split-phase, and capacitor-start motors are designed to the exact load requirements of the equipment they drive. When the applied voltage is below rated, electric current flows through the start windings for a longer time than is normally required to bring the motor up to rated speed. Continued start and stop operation will eventually cause motor burnout, unless the motor is properly protected. 5

6 On single-phase motors other than shaded pole and permanent split-capacitor types, the starting winding remains in the circuit longer than normal, in under-voltage situations, because it takes more time to accelerate the motor (and load) to the speed at which the start-winding disconnects. An under voltage of 10% reduces the starting torque and the maximum torque, each by 19%. Under-voltage also increases the full-load current and decreases the temperature rise. See Table 1 for dimensions and ampacities of insulated conductors. Wire Size AWG* Diameter in Inches, Bare Wire TABLE 1 Data For Copper Conductors Type TW Rated 60 C Resistance in Ohms per 100 ft. Ampacity (amps) Max. Motor Full Load (amps)** Max. Motor HP Rating Single- Phase 115 volt 230 volt 3 Phase 230 volt Min. Size Conduit, inch No. of Wires * AWG is the abbreviation for American Wire Gauge; sizes are solid round; sizes 4-8 are concentric stranded. ** The National Electrical Code requires that branch circuit conductors that supply motors must have a minimum current rating of 125% of the full-load current of the motor. The minimum allowable conduit size shown is the trade size of conduit or tubing. Voltage imbalance is a very serious problem for three-phase motors. When line voltages applied to a three-phase induction motor are not equal, unbalanced currents in the stator windings will occur. A small percentage voltage imbalance will result in a much larger percentage current imbalance. In fact, load currents will be six to ten times more out of balance than the voltages that produced them. Heat generated by unbalanced currents can cause winding failure. PARALLEL CIRCUITS The extension cord referred to previously has a resistance of 10 ohms, which is in series with the electric toaster element. This element has 24 ohms resistance; therefore, the total resistance of the circuit is 34 ohms. Suppose, however, that the extension cord is removed from the circuit, and another 10-ohm resistance, this time an electric iron, is connected in parallel with the toaster heating element. The new circuit would look like Figure 7. 6

7 Toaster And Iron Connected In Parallel Since the two appliances are in parallel, 120 volts is impressed across both heating elements. The full line voltage is impressed, because the conductors are of sufficient size that their resistance is low and the voltage drop is negligible. Current flowing through the toaster heating element is: I = E/ R, or 120/24 = 5 amperes. Current flowing through the electric iron heating element is: I = E/R, or 120/10 = 12 amperes. The total current through the wall outlet is, therefore, = 17 amperes. Since the voltage across both heating elements is 120 volts, and the total current is 17 amperes, the total parallel resistance may be determined: R = E/I = 120/17 = 7.06 ohms. Note that this total resistance is less than either of the individual resistances. Another way to calculate the total resistance for two resistances in parallel is: R TOTAL = (R 1 R 2 )/(R 1 + R 2 ). Using this formula, (24 10)/( ) = 240/34 = 7.06 ohms. Thus, when two or more resistances are connected in parallel to the same power source, each has full voltage impressed across it. POWER Power is the rate of using energy or doing work. It is measured in watts and horsepower. In direct current, the formula for calculating power is W = E I. Thus, when one ampere of current flows under pressure of one volt, energy is being consumed at the rate of one watt. When a six-volt battery connected to a small lamp causes 5 amperes of current to flow, it produces power at the rate of 6 5, or 30 watts. The electric power formula, mentioned above, also applies to single-phase ac circuits in which the load is pure resistance. For example, the toaster connected to 120 volts ac draws 5 amps of current. Therefore, its power is 5 120, or 600 watts. The iron connected to 120 volts draws 12 amps, so its power is = 1440 watts. Since 1000 watts equals a kilowatt (kw), the power of the electric iron can also be expressed as 1.44 kw. TOTAL ENERGY (KILOWATT-HOURS) Since power is the result of dividing the energy consumed (or produced) by the time it took to consume (produce) it, we have another electrical equation to work with. It is: electrical power = electrical energy/time This is another of those three-part mathematical equations that fit into a circle diagram (Figure 8). Notice that when you cover "electrical power," the uncovered segments show you "electrical energy/time." Now, cover up "electrical energy." The circle shows that if the power is measured in kilowatts, and the time is 7

8 measured in hours, electrical energy used would be the product of kilowatts times hours, or kilowatthours. One kilowatt used for one hour means one kilowatt-hour of energy is consumed. Electrical Energy Diagram Any time you have a product used or produced at a certain rate, and you want to find the total amount used or produced, you multiply the rate by the time. So it is reasonable that the total electrical energy used would be the rate (wattage) times the time. An electric meter keeps track of the rate of energy consumption. It records, by means of spinning dials, how long energy was used and at what power level. The total electrical energy consumed is then read directly off the meter, and the electric bill is calculated from this. INSULATORS AND CONDUCTORS Materials that conduct electric current always have some measure of resistance to current flow. The amount of this resistance depends on the material of which the conductor is made, its cross-sectional area, and its length. Temperature also affects the resistance of conductors. Gold, silver, and copper are the best conductors. Copper is the most commonly used for wires, bus bars and other current-carrying applications. Aluminum is also used as a conductor, but it has a slightly higher resistance than copper. Some alloys of nickel and chromium have high resistances, so they become very hot when current passes through them, making them ideally suited for heating elements in appliances, such as irons and toasters. Another class of materials, which offers great resistance to the flow of current, actually impedes current completely, so they are not considered conductors at all. We call them insulators. They are used to separate conductors from one another as, for example, insulation on wires. Insulation is also used to separate conductors from metal parts of a machine and protect people from contact with bare currentcarrying conductors. Example of insulators are glass, rubber, Bakelite, porcelain, wood, nylon, Teflon, and air. Since water with impurities in it is a good conductor, insulating materials must be kept dry if they are to retain their insulating qualities. In general, materials that are good conductors of heat are also good conductors of electricity. Similarly, good heat insulators are usually good electrical insulators, as well. 8

9 REACTANCE Another electrical phenomenon that impedes the flow of current is reactance. There are two types of reactance, inductive and capacitive. Inductive reactance comes from electromagnetic fields generated by any coils that happen to be in the circuit. The other type of reactance, capacitive reactance, results from a capacitor being in the circuit. These two reactances are sometimes called inductance and capacitance, respectively. To understand how they work, we must go back to the graph of alternating current, because reactance affects only the flow of alternating current. Reactance has no effect as long as current is flowing in one direction and is not increasing or decreasing in value. Therefore, it does not affect dc current except when the current is turned on or off, or the dc current momentarily becomes weaker or stronger (pulsating dc). Reactance resists change in the value of the current, regardless of whether the change is increasing or decreasing. CONDITION OF ZERO REACTANCE Suppose you had current flowing in a wire in which there were no reactance. Figure 9 shows the voltage and amperage traces in a circuit having only resistance, not reactance. The solid line represents the changing values of voltage in this 60-Hz ac circuit, while the dotted line shows the current (in amperes). FIGURE 9 One Cycle of Alternating Current, With Only Resistance In The Circuit 9

10 At point A there is no voltage and no current is flowing. From point A to point B, both the voltage and the current increases,with it. At point B, both the voltage and the current have reached their maximum positive values. From B to C, both the voltage and the current decrease, until at C there is no voltage or current, the same as at A. From C to point D, the voltage and current again increase together, but this time in the opposite direction, until at D, they reach their maximum negative values. From D to E, the voltage and current gain diminish, until at E, they are both back to zero, and the cycle starts over again. This is what happens if there is no reactance in the circuit, only resistance. The voltage and current stay "in step." Because they rise and fall together, we say that the voltage and current are "in phase." EFFECT OF INDUCTIVE REACTANCE Now let us look at another circuit, this one represented by the graphs in Figure 10. This 60-Hz circuit includes only a coil, such as a solenoid coil, a transformer winding, or a motor winding. A change of direction or rate of flow of the current causes a changing magnetic field around the coil. The change in magnetic field is what causes the inductive reactance. FIGURE 10 Current lagging voltage by 90 The wire in the coil has resistance, but we will disregard it for the moment. With only a coil in the circuit, and ignoring the resistance of the wire, the only factor that reacts against the flow of electrons is the inductive reactance of the coil. 10

11 As in Figure 9, the solid line in Figure 10 represents voltage and the dotted line is the current. Again, let us remember that the voltage is the "pressure" of the electricity and the amperage is the rate of current flow. Now let's see what the graph shows us. Inductive reactance holds back the current but does not affect the voltage. At point A, the voltage is zero. Then 1/4 cycle later, at point B, voltage increases to maximum, but the current only reaches zero (point L). Inductive reactance has held back the current 90 behind the voltage. Note that current is increasing from L to M at the same time voltage is decreasing from B to C. By the time voltage has returned to zero at C, the current has increased to maximum at M. Then voltage starts to increase in the opposite direction, but current is decreasing in the original direction, and does not get back to zero until point N. At that time, voltage reaches its maximum in the negative direction (point D). This goes on throughout the rest of the cycle, and all the cycles following, as long as there is only inductive reactance in the circuit. This is often referred to as a "lagging" current, because the current lags behind the voltage. If, as in this example, there is nothing but inductive reactance in the circuit, the lag equals 1/4 of a cycle. We call this a 90 lag, since a full cycle is 360 and 1/4 of 360 is 90. Current can never lag behind voltage by more than 90. EFFECT OF CAPACITIVE REACTANCE Now we will look at how capacitive reactance affects a circuit. Figure 11 shows a simple ac circuit with a capacitor in it and nothing else. We will assume, as we did in the previous example, that the resistance is negligible. So the only impedance in this circuit is capacitive reactance. By tracing the graphs in Figure 11, you will see how current actually leads voltage. FIGURE 11 Current leading voltage by 90 11

12 Starting at A on the voltage line and at L on the current line, follow the voltage and current curves for the first 90. As the voltage increases from zero, the current is dropping from its maximum positive value. At point M, the current has decreased to zero, while at the same time, voltage has reached its maximum. From point B to C, the voltage decreases, until (at C) it is zero. During the same time, the current increases from zero, at M, to maximum at N. but in the negative direction. Now let us go back to point L. The current is at maximum and begins to decrease while the voltage is increasing from A to B. So, current is a quarter-cycle or 1/240th of a second ahead of the voltage. This is called a "leading current." In a circuit having no resistance nor inductive reactance (only capacitive reactance) the current always leads the voltage by 90 (1/4 cycle). Ninety degrees is the maximum lead; current cannot lead voltage by more than 90. SOURCES OF CAPACITIVE REACTANCE Capacitive reactance may be produced, as in Figure 11, by an electrical condenser or capacitor, consisting of two sheets of conductor foil separated by a thin sheet of insulation. In an electrolytic capacitor, an oxide film acts as insulation. Capacitive reactance also occurs in long, parallel electric lines. The lines act like capacitor plates, and the air between the lines is the insulator. On transmission lines many miles long, high capacitive reactances are produced. Synchronous motors, with the field over-excited, also act as capacitors and add capacitive reactance to circuits. Thus, these motors are often called "synchronous condensers." POWER IN AC CIRCUITS The power in an electric circuit does not depend on the current alone. Power is the product of both current and voltage. In direct-current circuits, power is simple to measure, since both voltage and current are constant and in the same direction. But in an ac circuit, voltage and current are continually varying, from zero up to their maximums, then back to zero again. Therefore, the effective voltage and current will be less than their maximum values. Figure 12 shows the voltage and current graphs for a 120 volt, 60-Hz ac supply, drawing a current of 10 amps. These values 120 volts and 10 amps are the Effective Values (also called Root-Mean-Square, or RMS values), which are equal to.707 times the maximum values. The maximum values for this circuit are nearly 170 volts and 14 amperes. 12

13 Maximum vs. Effective Current and Voltage The instantaneous power at these maximum values would be 170 volts x 14 amps, or 2380 watts. However, the effective power would be 120 x 10 = 1200 watts. (Effective power = effective volts x effective amperes.) The circuit represented by Figure 12 has no net reactance, since the voltage and current are in phase with each other. But what about the other examples we've seen? What if the current leads or lags the voltage? What will the effective power be? When voltage and current are out of phase, the maximum current and voltage could still be 14 amps and 170 volts. But if the current is zero when the voltage is maximum, and vice versa, then effective power should be less than for an in-phase circuit (all other factors being equal). When out-of-phase circuits contain motors and capacitors, they have significant levels of inductive reactance, or capacitive reactance, or both. The total opposition to current flow in these circuits is the result of all three effects: resistance, inductive reactance, and capacitive reactance. The question is: how do you calculate their overall impact? We begin by showing how to figure the combined effect of just the inductive and capacitive reactance. FINDING TOTAL REACTANCE Inductive reactance causes current to lag behind the voltage, and capacitive reactance causes current to lead the voltage. Therefore, if we have both kinds of reactance in a circuit, they would tend to oppose each other, and cancel each other out. If a circuit has more inductive reactance than capacitive reactance, the current will still lag the voltage, but not by the full 1/4 cycle (that is, something less than 90 ). 13

14 So, total reactance is not found by adding the two specific reactances. Instead, you must subtract the smaller reactance from the larger. Whichever is larger determines whether it is a lagging current or a leading current. Thus, if a circuit has 10 ohms of inductive reactance and 6 ohms of capacitive reactance, the total reactance is 10-6 = 4 ohms of inductive reactance. The greater the difference between the two reactances, the more the current lags or leads. If one reactance is much larger than the other, the lag or lead could be nearly 90. But if they are nearly equal, the lag or lead will be quite small, say 10 or 20. If the two reactances are exactly equal, they offset each other, and current and voltage are in phase. There is no lag or lead in such cases. DETERMINING IMPEDANCE The total effect "holding back" current flow comes from both resistance and reactance, each measured in ohms. This total "holding back" effect is called impedance, because it impedes the flow of current. Although impedance is due to both resistance and reactance, it is not found by merely adding the two together. Instead, each factor must be squared, then the squares are added, and the square root of the sum is taken. This equation lets you calculate the length of the hypotenuse (c) in a right triangle, if you know the lengths of the other two sides (a and b). Since the impedance formula is really a right-triangle formula, you can find the total impedance by using a triangle, as in Figure 13. You draw the legs of the triangle to scale, with the X side proportional to the impedance and the R side proportional to the resistance. Then you can find the total impedance by measuring the length of the hypotenuse (Z). 14

15 Impedance Formula Shown Graphically OHM'S LAW FOR AC For direct current, Ohm's Law states that current is equal to voltage divided by the resistance. The same law applies to alternating current, but instead of resistance, we must use the impedance. Ohm's Law for ac becomes: Figure 14 shows voltage and current in an ac circuit that has resistance and a net reactance. In this case, the reactance is mostly inductive, because the current is lagging the voltage by 36 or 1/10 of a cycle (1/600 of a second). 15

16 FIGURE 14 Current lagging voltage by 36 Since the current is lagging the voltage, we know that there is more inductive reactance in the circuit than capacitive reactance. That is, there is more reactance from motors, and other equipment with coils, than there is from capacitors, line capacitance, etc. Figure 15 represents another ac circuit in which the current is ahead of the voltage, this time by 26. We know that in this circuit there is more capacitive reactance than inductive reactance. The effect of capacitors in the circuit is greater than the effect of motors, etc. But in this case, the net reactance is less, and the voltage and current are closer to being in phase than they were in Figure 14. Remember: current can be out of step or out of phase either way, lagging or leading, and how much they are out of phase depends upon the net reactance. FIGURE 15 Current leading voltage by 26 16

17 POWER FACTOR In dc circuits, power (in watts) equals the voltage times the current. In ac circuits, power is calculated the same way, provided that voltage and current are in phase. But when current and voltage move out of phase, things are not so simple. The farther they are out of phase, the smaller the wattage, even though voltage and current stay at the same values. If there is no lead or lag, the wattage equals 100% of the volts times amps. But if the lead or lag is 10, then watts will equal only 98% of volts times amps. At a 20 lag or lead, wattage will be 94% of the product of amps and volts, and so on. The more the degrees of lag or lead, the smaller the percentage of volts and amps available as usable wattage. Expressed in trigonometric terms, this percentage equals the cosine of the number of degrees of lag or lead. This value is called the power factor. The power factor depends on the phase difference between voltage and current. It can be calculated using the following formula: P. F. = True Power/Volt-Amperes True power is the product of multiplying the current by the actual voltage drop across the impedances in the circuit. It can also be measured with a wattmeter. Volt-amperes is referred to as apparent power, and is found by multiplying the line voltage by the current in the circuit. Therefore, if you know the line voltage, the current flowing in the circuit, and the power factor, you can calculate the true power by multiplying: True Power = Line voltage amperes P.F. If you do not know the power factor, you can use a wattmeter to find the true power, or you can multiply the actual voltage drop by the current. But to find the voltage drop, you must first determine the total impedance, using the formula shown in Figure 13. Now if you measure line voltage with a voltmeter, current with an ammeter, and actual power with a wattmeter, you can determine the power factor by dividing actual wattage by the product of line volts and amperes. For example: an ac circuit carries a current of 15 amperes and is connected to a line voltage of 120 volts. When a wattmeter is attached to this circuit, it registers 1440 watts. Therefore, the power factor is: An 80% power factor corresponds to a current lag or lead (with respect to the voltage) of If there is more inductive reactance than capacitive reactance, the current lags the voltage by 36.9 or about 1/10 of a cycle. If there is more capacitive reactance than inductive reactance in the circuit, the current leads the voltage by Figure 16 shows a power triangle, drawn according to the values just discussed. The base represents the true power, as measured with a wattmeter (1440 watts), and the apparent power (1800 volt-amperes) is shown as the hypotenuse. We see that the altitude of this triangle represents yet another kind of power, the reactive power, sometimes called "wattless power," because each half-cycle of current produces a positive and a negative power burst, which, when combined, cancel each other out. In this case, the wattless power vector measures 1080 volt-amperes reactive, or 1080 vars, for short. This power is totally non-usable, as the current and voltage are not in phase. 17

18 Relationship Among True Power, Apparent Power, and Reactive Power Earlier you learned that voltage drop can be very significant when power lines are long and the current load is large. You saw that the voltage drop or line loss is equal to the current, in amperes, multiplied by the resistance of the line, in ohms. The voltage drop of a long, 10-ohm extension cord was 35.3 volts, when it carried 3.53 amperes of current. Connected to a 120-volt circuit, this would mean a voltage drop of more than 29%, and any voltage drop over 10% is not recommended. In a 120-volt circuit, even just a 10% voltage drop would mean a loss of 12 volts, leaving only 108 volts to operate 120-volt appliances. If a small motor is connected to a 120-volt circuit, and if the motor draws 3.53 amperes, the wattage of the motor would be , or watts (assuming a 100% power factor for simplicity's sake). But suppose, instead of the 120-volt circuit, you connected the motor to 240 volts. The motor's wattage would stay the same, and the motor would have the same power. But the current needed would be 423.6/240, or 1.77 amperes, just half of what was needed in the 120-volt circuit. Even if the motor is connected to the 240 volts through the same 10-ohm extension cord cited previously, the voltage drop turns out to be a smaller percentage of line voltage in the 240-volt circuit. Its new voltage drop falls to 17.7 volts (10 ohms 1.77 amps), which is only 7.4% of 240 volts. Percentage-wise, this is only one-fourth of the original voltage drop of 29.4%. Motors must be connected to their power supply so that voltage at their terminals is ±10% of rated voltage. So the 240-volt motor would operate fairly satisfactorily with a 7.4% voltage drop, whereas the 120-volt motor would not operate satisfactorily with a voltage drop of 29.4%. Many service engineers have cured voltage drop troubles by running a 240-volt line instead of the 120 line, and reconnecting terminals in the original motor for 240 volts, as is possible with motors built to operate on either 120 or 240 volts. 18

19 TRANSFORMERS Transformers operate on the principle of magnetic induction. In their simplest form, they consist of two or more coils of insulated wire, wound on a laminated steel core. The current supplied to one coil, called the primary or input coil, magnetizes the steel core, which then induces a voltage in the secondary or output coil. The ratio of voltages in the primary and secondary coils is the same as the ratio of turns of wire in the two coils. In Figure 17, the input or primary coil has twice as many turns as the secondary coil. Therefore, this is a two-to-one transformer, which means that any voltage fed into the primary will be reduced in half. If 480 volts is applied to the primary, 240 volts will be supplied at the secondary. This is an example of a stepdown transformer. If the voltage is to be increased or stepped up, this same transformer could be turned around and connected so that the input with n turns has 240 volts applied, and the output with 2n turns will supply 480 volts. FIGURE 17 Transformer, with twice as many turns in the primary as in the secondary Transformers rated 3 KVA or larger can be used for either step-down or step-up applications. Transformers rated 2 KVA or smaller usually have compensated windings and should be used for stepdown applications only. Where a 240-volt power source is not available, a step-up transformer could be used to boost a 120-volt power supply to 240 volts. A 1:2 ratio in the coils would provide the desired 240-volt output. Transmitting 120-volt or 240-volt electrical power over long transmission lines would require very large, heavy cables, so the voltage is usually stepped up to 2,400 volts or higher for normal distribution within a city. For long-distance lines, as between cities, for example, much higher voltages are utilized. Levels as high as 33,000, 66,000, and up to 500,000 volts are commonly used. By producing these high voltages, power losses are kept to a minimum, even with comparatively small wires. When voltage is increased, the wire diameter can be decreased, and yet the same power level (KVA) can be maintained. Most alternating current is generated at 13,800 volts, but stepped down to 2400 volts for city distribution. Then it is further reduced to 600, 480, 240, 208, or 120 volts for neighborhood distribution. Figure 18 shows another example of a transformer application. This is the type of transformer found in many 6-volt devices, such as a doorbell, that need to be connected to 120-volt power. 19

20 FIGURE 18 A Bell-Transformer, Supplying 6-Volt AC Suppose that, instead of a doorbell, the six-volt side of this transformer were connected to a heater coil that drew 60 amperes. Then the wattage used on the 6-volt side would be 6 60, or 360 watts. This would mean that the 120-volt primary would have to supply 360 watts of power, also. But the current in the primary would only be 3 amperes ( ). From this example, you see that the current goes up in the same proportion as voltage goes down, and vice versa. One of the basic laws of engineering is that we can never get something for nothing. No matter what the device, it cannot deliver a greater output than input. In fact, we must always put a little more in than we take out, for some energy is always lost as heat. The efficiency of a machine is found by dividing the work taken out by the work or energy put in. Large motors have efficiencies of 80% to 95%, while small motors usually run 55% to 80% efficient. But transformers are much, much more efficient than that. Efficiencies as high as 98 to 99% are not uncommon in transformers. If you've ever felt the outside of a motor or transformer, you know where the lost energy goes. Figure 19 shows a step-down transformer with a 2400-volt primary and volt secondary. The primary coil has 10 times as many turns as the secondary, so across the entire secondary coil, we get , or 240 volts. 20

21 FIGURE 19 Center-Tapped Transformer A center tap is taken off the secondary winding. This line is called the "neutral" wire, and it is connected to ground. Between the neutral and either of the two outside secondary lines, we have 120 volts. These three lines, the two outside lines and the neutral, may be connected to an entrance switch and fuse box in a home, as shown in Figure 20. Note that the neutral is not opened by a switch, nor is it ever fused. Fuses and switches are installed in hot lines only. 21

22 Single-Phase, 120/240V Entrance, With House Circuits Three-wire, single-phase 120/240 volt systems are commonly used in domestic service. The 120-volt lines connect to lighting and small appliances. The 240-volt service supplies the electric ranges and larger motors, such as in air conditioning condensing units, for example. THREE-PHASE CIRCUITS So far, we have been discussing single-phase alternating current, in which there is only one voltage and one current, although they may not be in phase with each other. In power generating stations, alternating current is produced by generators, sometimes called alternators. The alternators are wound with three sets of coils, so that they actually generate three circuits or phases of electricity. The rpm and the number of poles are selected to produce the required frequency, as determined by the formula: rpm = 120 f/n where: rpm = speed of rotor in revolutions per min. f = frequency of generated power in hertz n = number of electrical poles in alternator. The smallest possible number of poles in an alternator is two (one pair). You can calculate the required rpm of such an alternator in 60-Hertz service by using the formula: 22

23 rpm = (120 60)/2 = 3600 rpm The coils in a three-phase alternator are spaced so that the phases follow one another at equal intervals. Three separate currents flow from the alternator, and each current has the same characteristics as a single-phase current. Figure 21 illustrates the voltages of three-phase, 60-Hertz power. FIGURE 21 Phase Voltages In a Three-Phase Circuit The curve marked "A" is the voltage of one phase; "B" is the second phase, 1/180 of a second later; "C" is the third phase, 1/180 of a second after phase 2. So each phase is 1/3 of a cycle, or 120 apart. Three separate power lines are used to carry the three separate and distinct phases or currents. As shown in Figure 22, lines 1 and 2 carry phase A; lines 2 and 3 carry phase B; and lines 1 and 3 carry phase 3. Thus, the three lines can handle three-phase ac power. 23

24 Three-Phase, Three-Wire, 240 Volt Power Keep in mind that in three-phase ac, the current may lag or lead the voltage in each phase, depending on relative values of inductive and capacitive reactance. Therefore, three phase ac also has a power factor. In Figure 23, the solid curves indicate the voltages and the dotted curves indicate currents, which, in this example, lag the voltages by 28. So the power factor is 88% (The cosine of 28 =.88.) FIGURE 23 Current Lagging Voltage In a Three-Phase Circuit; 88% Power Factor In most cities, three-phase power distribution lines fan out from a network of sub-stations. These transformer facilities step down voltages to 2400 volts of potential across any pair of the three-wire local distribution lines. Then, for residential and small-business service requiring 120 volts and 240 volts, a single-phase step-down transformer is connected to one of the three phases, as was shown in Figure

25 THREE-PHASE TRANSFORMERS For factories and large buildings, three-phase power is required to run large motors. Therefore, all three lines are strung into these facilities, usually to another step-down transformer that will deliver 208, 240, 480, or 600 volts, three-phase. These are the common voltages for 3-phase motors. However, some motors are designed for even higher voltages. When the lower-voltage 3-phase motors are used, either a 3-phase transformer or three single-phase transformers are connected between the lines. One method of wiring the coils in a three-phase transformer is known as a "delta" connection, the other is called a "wye" or "star" connection. These are shown in Figure 24. Normally, the primary windings of a three phase transformer are connected in delta, while the secondary may be either wye (star) or delta-connected. Three-Phase Transformer, With a Delta-Connected Primary And Two Secondary Alternatives 25

26 Nowadays, it is common practice to use 208-volt systems, because we can take 3-phase 208-volt power and single-phase 208/120-volt power, all from the same transformer. As you can see in Figure 25, the setup uses only four wires: three power lines and a neutral. Between any two power lines, you have 208- volt single-phase power. Between the neutral and any power line, you have 120 volts. Transformer Wired To Provide Both 208-Volt 3-Phase And 120-Volt Single Phase From The Same Source Copyright 1993, 2001, By Refrigeration Service Engineers Society. 26