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Power Is What You Buy

Volts, watts, amps and ohms are Man's method of measuring quantities of electrical power; to work with wiring, you should have a good understanding of these terms.   In this chapter we've printed all you'll need to know—
 
Volts, amperes, ohms and watts are technical terms that add up to one important thing: your monthly electric bill from the local utility company. This is reason enough why you should know what they mean! Their relationship is very simple, and if you know any two of the values in a circuit you can easily figure the others Volts, or "voltage," is a measure ot the push or pressure of electrical energy. Ohms, or "ohmage," is a measure of the resistance of the wires, wiring and other electrical conductors through which electricity flows. Amperes, or "amperage," is a measure of the electricity that flows as a result of the push of the voltage against the resistance of the conductors. As appears logical, the higher the voltage and the lower the resistance, the higher the current. These three factors are expressed in "Ohm's Law," the simplest and most useful formula in all of the   complicated   science   of   electronics. amperes equal volts divided by ohms.

Suppose an electric iron designed for service on 120 volts has a resistance of 10 ohms. How many amperes will it draw? That's easy: 120 divided by 10, or 12 amperes.

By simple transposition:

Volts equal amperes times ohms. Ohms equal volts divided by amperes.

Like all standards, these electrical units are purely arbitrary. By international agreement, a conductor has a resistance of one ohm if it lets one volt push a current of one ampere through it in one second.

"Power" is the rate of doing work. The electrical unit is the "watt," and is merely volts times amperes. Strictly speaking, this should be expressed as the "watt-second," because by its own definition an ampere doesn't become an ampere until the current has circulated for a short period of time.

Consolidated Edison
Company of New York

The amount of electrical energy used in your home registers on a watt-hour-meter, which is usually located at the power-wire entrance to the building. The difference in readings from month to month, recorded by the utility company's meter reader, is multiplied by the rate per kilowatt-hour to give your bill  in  dollars  and  cents.

(All four basic terms are named for pioneer physicists of the previous century. Ohm was a German, Volta an Italian, Ampere a Frenchman, and Watt a Scot.)

Since watts equal volts times amperes a simple transposition gives us amperes equal watts divided by volts. This is a very useful formula in practical work, because with it you can calculate the line currents of many appliances from the wattage figures on the name plates. Another useful one is obtained with a little mathematical juggling. You remember that volts equal amperes times ohms. Substituting amperes times ohms for volts in the power formula, we get watts equal amperes times ohms times amperes or watts equal amperes squared times ohms.

Impedance Versus Resistance

The foregoing formulas apply to all DC appliances and circuits, and to "heat" appliances used on AC circuits. In the latter category are ordinary screw-in and tubular incandescent lamps (but not fluores-cents), laundry irons, toasters, broilers, room heaters, curling irons, immersion and bottle warmers, electric blankets, etc.

In all motor-operated appliances, television and radio sets and other devices using transformers or coils of wire on iron cores of one shape or another, the opposition to the flow of current through the wire is increased and complicated by certain magnetic effects. In addition to the straight resistance of the wire, the latter effects introduce a second factor called "reactance," and the total effect of the two is called "impedance." This is also expressed in ohms. "Resist" and "impede" have the same general meaning, but "impedance" signifies AC operation. Ohm's Law works just as well with impedance figures substituted for resistance. However, impedance values are of limited significance to practical workers; watts and amperes are more important and are readily calculated from simple formulas.

Although the impedance of a "reactive" AC appliance determines the current in amperes pushed through it by the line voltage, amperes times volts does NOT give its true power rating; the product is called the "apparent power." This is where people with a rudimentary knowledge of electricity often go haywire on their calculations. In many AC devices, the current and the voltage do not always act together, odd as this may sound. Sometimes the current doesn't flow until after the voltage has passed; sometimes it flows before. The true power is indicated by a wattmeter, which is constructed to take these complex actions into account. The wattage figures on appliance nameplates are the true power.

The ratio of the true power to the apparent power is called the "power factor" of the device, and is expressed as a percentage. In pure heating appliances it is 100%, but in some broilers, hair dryers, etc., it may be less because of the motors in them. Motors for household machines and power tools run to as low as 40% and up to 75%; television and radio sets are somewhat higher.

Incandescent lights have 100% power factor so a little straight arithmetic gives their current load. Add up the wattages of the individual bulbs on a circuit, divide by the assumed line voltage of 115 or 117, and the result in amperes is accurate enough for all practical purposes.

Many fluorescent lamps, on the other hand, particularly in older models and in sizes under double-48 inches, have very poor power factor, between about 45% and 60%. This is due to the presence in the circuit of lamp "ballasts," which consist of multiple turns of wire on iron cores. If only one or two such lamps are used in a house or apartment (usually in the kitchen), the extra line current is negligible.

In most newer types of fluorescents, the power factor is brought up to 90% and even 95% by the use of small capacitors (or "condensers"), whose purpose is to cancel or counterbalance the effect of the ballast winding. The extra cost is slight, and the reduction in line current becomes appreciable if, for example, several large lights are used in a workshop.

Regardless of the power factor, you pay only for the true watts. Your bills depend on the power of your appliances, the time they are kept on, and the utility's charge per kilowatt-hour of service. A kilowatt-hour means 1000 watts for a whole hour. Thus, a 500-watt laundry iron used for half an hour registers one-quarter kilowatt-hour on your electric meter. Read that again, and don't be confused by the fractions. If your power rate is say 3 cents per kilowatt-hour, the half hour's ironing cost only ¾ of a cent.

Figuring a Bill

Many people hesitate about buying air conditioners because they think they are "expensive" to run. The starting current of many conditioners is high for about three seconds, but after that they take less energy than many table-top broilers. For example,  a  typical room conditioner  of standard make is rated at 1005 watts. Suppose you leave it running steadily during a very hot spell. For one full day the consumption is then 1005 times 24 hours, or 24,120 watt-hours or 24.12 kilowatt-hours. If the rate is 4 cents per K.W.H., the cost of running the machine is 96.48 cents, less than one dollar!

The wattage ratings found on appliances are figured on a basis of an "average" line voltage of 115 or 117.

Motor name plates bear the nominal horsepower rating and the line voltage and line current. The conversion factor is 746; that is, horsepower equals watts divided by 746 or watts equals horsepower times 746.

On a typical ½ hp motor in my shop, the name plate reads "115 volts, 6 amperes." Volts times amperes gives the apparent power of 690 watts, but 1/3 of 746 makes the true power closer to 250 watts. Dividing 250 by 690 gives a power factor of about 40%.

Since the customer pays only for the true power he uses, why should he concern himself about power factor at all? If the wiring in his house is new and very heavy, he needn't. If it isn't, he finds that power factor rises to haunt him as he adds new machines such as clothes washers and dishwashers, garbage disposals, freezers, air conditioners, attic fans, etc., all of which have relatively low power factor. Low P.F. means high line current for the work done. The heating effect on the power wires of let us say 10 amperes is the same whether this current goes to a 1150-watt bowl heater of 100% P.F. or a 575-watt ventilator of 50% P.F.

I used the setup shown in the photo and diagram on page 21 to obtain a quick idea of the current drains of typical appliances:

Coffeepot, rated at 400 watts: 3½ amperes, 100% power factor.

Hot plate, rated at 700 watts: 6 amperes, 100% power factor.

Vacuum cleaner, rated at 550 watts: 6 amperes, 76% power factor.

High-fidelity amplifier, rated at 140 watts: 1.4 amperes, 83% power factor.

The higher the line current under any circumstances, the greater the power loss in the wires. The latter have appreciable resistance, and some work is done in overcoming it. The big joker here is that the heat loss does not go up gently with increased line current, but with the square of the current, as given in the formula watts equals amperes squared times ohms.
With current values on the order of 10, 15 and 20 amperes squared, or 100, 225 and 400, you can see that it doesn't take much resistance in the lines or in connecting devices to cause trouble. A slightly dirty contact in a plug, having a resistance let us say of one tenth of an ohm, wastes 22.5 watts when the current is 15 amperes. This is juice you pay for but does nothing for you. Poor quality attachment plugs found with some table-top broilers and room heaters, which usually draw the 15-ampere legal maximum from one branch circuit, often becomes so hot that you can blister your fingers if you touch them.

High line current, regardless of whether the amperes are honest ones from high P.F. appliances or sneaky ones from low P.F.-ers, introduces a second joker: reduced line voltage at the appliances themselves. This angle is discussed in detail in the section entitled "Is Your Wiring Adequate?" which follows this chapter on pages 22-31.

Knowing the power rating of an appliance and the approximate line voltage, you can work backward and make a pretty fair guess at the line current. It is important to know this so that you can add up the total current in any branch circuit and determine if the wire itself and the fuse or circuit breaker are of suitable size.

The formula was given previously as amperes equal· watts divided by volts but this does not, of course, take power factor into consideration. Add about 50% more in the case of "reactive" AC appliances and you have a workable result. For example, take an air conditioner marked 900 watts, 115 volts. Dividing the first figure by the second, we get 7.8; call it 8, add 50% for power factor and the result is 12 amperes.

With a device like a coffee pot or an iron, having virtually 100% P.F., the simple division gives an accurate figure. For example, an iron marked 660 watts takes 5.7 amperes at 115 volts.

Low Versus High Voltage

From the formula watts equal· volts times amperes you might get the glittering of an idea. Ignoring power factor for the moment, consider an appliance that takes 10 amperes at 120 volts, or 1200 watts. Would it do exactly the same job if it were designed to work on 60 volts and 20 amperes, again 1200 watts, or on 240 volts and 5 amperes, still 1200 watts? The answer is a strong, "Yes!" And since the power is the same in all three cases, so is your electric bill.

There is no advantage in going to lower voltage, but there is a tremendous advantage in going to the higher voltage: the line current is reduced by half, and with this lowered current heat losses and voltage drops in connecting wires come down, too. Remember that square-law business. With a plug resistance of .1 ohm, just for an example, the heat loss at 10 amperes is 10 times 10 times .1, or 10 watts, but at 5 amperes it is 5 times 5 times .1, or only 2½ watts! Some difference!

The starting current as well as the running current of motors is naturally lower on the higher voltage.

Cutting the current in half by going to 240 volts is the big reason why appliance dealers and utility companies urge customers to buy 240-volt air conditioners and to have an electrician run a separate line from the meter if the house already has three-wire, 1201240 volt service. A 240-volt motor doesn't cost any more than a 120-volt one; in fact, many of fractional horsepower motors used in home machines are readily convertible to either voltage through a quick switching of leads.

Practically all electric ranges are 240-volt operated. The wire required for 120-volt operation is prohibitively heavy and expensive to install.

Insulation No Problem

"What about the problem of insulation at the higher voltage?" No problem at all. If you'll examine sockets, outlets and other connectors closely, you'll see that they bear two current ratings, one in the 110-120 volt range and the other for 220-240. In other words, they're specifically designed for both voltages. Any standard power wires are more than adequately protected for 240 as well as 120 volts. Copper wire is expensive, but insulation is cheap.
 
In England, which must import every inch of copper it uses, the standard power line voltage for all house purposes has been 240 volts for as long as anyone can remember. Power cords there really look and feel like "cords," they are that thin.

So greatly does higher voltage alleviate the line overloading problem, and also make initial installation costs lower, that the power companies are going up the scale further than the 220-230-240 volt limit that has been standard in the United States for many years. In New York, for example, where huge new buildings with central air conditioning and whole ceilings of fluorescent lights are going up by the score, the Consolidated Edison Company is making 265/460 volt service available. This is a combination of single-phase power at 265 volts and three-phase power at 460 volts, exactly like the 120/208 volt service described in the section entitled "The Power System in Your Home."

Automobile manufacturers have shifted from six volts to twelve volts for precisely the same reasons of copper saving. The current needed at six volts to operate ignition, lights, radio, heater, cigarette lighter, convertible top, power doors and seats, etc., requires wire so heavy that installation is almost a plumbing job. With the current cut exactly in half at twelve volts, the wiring harness lends itself better to mass production methods.

Ignore any claims that the higher battery voltage is needed to give "increased power" for starting and other purposes in big present-day cars. This is pure advertising hog wash. Power in DC circuits, and there is no purer DC than comes from a storage battery, is just volts times amperes. ·

Left. apparatus setup used to measure line current of appliances: AC ammeter is on left. plug-in box is at center and iron under test is at right. Below, right, here  is  the setup in diagram form. See text.

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