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the pressure curve. It corresponds exactly to the steam-pressure curve marked out by the steam-engine indicator. The height of this curve above the horizontal line for any angle from 0° to 180° represents the electrical pressure, or voltage, when the coil is at that particular angle. This height, as we have seen, is the sine of the angle.

At 90° the curve has its greatest height, and the coil is perpendicular to the O line. The pressure is greatest at this point. The pressure for any other angle is, therefore, the maximum pressure; that is, the 90° pressure multiplied by the sine of the angle. For example, the sine of 30° is one-half, and the electrical pressure at 30° is one-half of the pressure at 90°.

From 180° to 360° the curve is below the horizontal line, which means that the pressure is minus, or in the reverse direction from the first. The pressure is, therefore, alternating in direction, and we have an alternating current in the armature. If armature is connected to line by collector rings instead of commutator, there will be an alternating current in the line. The distance below the line, that is, the sine of the angle, measures the amount of this minus pressure for any angle.

Fig. 20 is the pressure curve for two armature coils wound at an angle of 90° apart on the same armature. The heavy wave lines are the curves for the two coils separately. The dotted wave line shows the line pressure produced by the two coils acting together. For any angle the height of the dotted line above the horizontal is the sum of the heights of the two heavy lines. At 45° the dotted line crosses the horizontal. At this point one heavy line is as far above the horizontal as the other is below it; that is to say, the pressure in one coil is plus and the pressure in the other coil is equal and in the opposite direction to the first. The second pressure is, therefore, minus. These two pres

sures acting together actually produce zero pressure in the line. The last statement explains the fact that one pressure is called plus and the other minus. If we add a plus quantity to an equal minus quantity the sum is zero. Fig. 20 is the pressure curve for a

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190°

180

210

FIG. 20.

two-phase current. When one pressure is at its greatest value the other is at zero, because when one coil is at 90° the other is at 0°. Fig. 21 is the pressure curve for three coils wound on the same armature and 120° apart. This is the curve for a three-phase current.

Idle Current and Power Factor.

In an alternating-current circuit the actual power lags a certain angle behind the apparent power. The curves, Figs. 19 and 20, represent voltage. Voltage

multiplied by the whole current equals apparent power. The actual power is the apparent power multiplied by the cosine of the angle of lag. The cosine of the angle of lag is the power factor. Expressed in percentage,

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the power factor is the cosine of angle of lag multiplied by 100. To find actual power in watts, multiply apparent power in watts by power factor or cosine of angle of lag:

True power volts X amperes X power factor.

=

The wattless current, or idle current, is the actual current multiplied by the sine of the angle of lag. Table XIV gives sines, cosines and power factors for angles from 0° to 90°.

Examples:

1. What is the idle current if the angle of lag is 40° and the actual current 30 amperes?

19.2 amperes.

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Answer,

2. What is the true power if the apparent power

is 2,000,000 watts, that is, 2,000 kilowatts, and the angle of lag 25°?- Answer, 1,812.6 kilowatts.

3. If the voltage is 20,000, current 500 amperes, angle of lag 20°, what is the true power?- Answer, 9,397 kilowatts.

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There is the same difference between a kilowatt and a kilowatt hour that there is between a horse-power and a horse-power hour.

The output of a 1 horse-power engine running 1 hour is 1 horse-power hour.

Q. If a 1 horse-power engine runs 10 hours, how much greater is its output than if it runs 1 hour? Answer, the output is 10 times as great.

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Q. If a 1 horse-power engine runs 10 hours, how many horse-power hours does it give out? Answer, 10 horse-power hours.

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Q. Is it then a 10 horse-power engine? Answer, no; it is still a 1 horse-power engine.

Q. What is the difference, then, between horse

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